MANUAL FOR CIVIL AND ENVIRONMENTAL
ENGINEERING LABORATORY REPORTS
James N. Jensen
Christine Human
Todd Snyder
Department of Civil, Structural and Environmental Engineering
University at Buffalo
Buffalo, New York
© August, 2006
Preface
T
he purpose of this manual is to serve as a
technical writing reference for you in your
civil engineering lab courses (CIE 360, 361,
and 362). In addition, we believe that the material
presented here will be helpful throughout your
time at UB and in your professional career. Refer
to it often as questions arise about technical writing.
HOW TO USE THIS MANUAL
It is recommended that you read Chapters 1, 2, and
3 before you start writing your first lab report.
Use the table of contents to find additional help on
specific writing areas (e.g., tables and figures or
citation styles).
You will find several features of this manual
especially helpful:

Mental Notes
Important ideas are highlighted in the text
in boxes called “Mental Notes.”

Real World Alerts
Important applications of the material in
this manual to your professional career are
highlighted in grayed paragraphs called
“Real World Alerts.”

Chapter Summaries
Each chapter ends with a chapter summary.

Glossary Items
Words and phrases in boldface italic are
defined in the Glossary.

Example Lab Report
Two example lab reports are provided in
Appendix A. One of these reports is discussed in detail in Chapter 2.

Lab Report Format
The required format for the lab reports is
listed in Section 1.3.5. Refer to it often.
We begin with a note about the format of this
manual. This manual contains a great deal of useful information about writing lab reports. However, your lab reports do not need to be formatted the
same way that the manual is formatted (i.e., two
columns, large drop capital letter at the beginning
of the chapter, etc.) As you will learn in Chapter
1, writers choose formats and styles that best
communicate their ideas. We developed this format to help communicate with you, just as you
will make stylistic decisions about how to get
ideas across to the readers of your lab reports.
ACKNOWLEDGEMENTS
Some of the material in this text was based on a
textbook written by one of us (Jensen, 2006). We
would like to thank the staff at the Center for
Technical Communications for reviewing an early
draft of some of the material in Chapters 2 and 3.
ii
Table of Contents
Chapter 1: Introduction
1.1 What is Technical Writing?
1.2 Lab Notebooks
1.3 Identifying the Goals, Target Audience, and Constraints
1.3.1 Goals
1.3.2 Target audience
1.3.3 Constraints
1.3.4 Formatting issues
1.3.5 Imposed constraints for civil engineering lab reports
1.4 Writing as a Group
1.5 Proofreading and Spell Checking
1.5.1 Proofreading
1.5.2 Spell checking
1.6 Summary
Chapter 2: Overall Organization of Lab Reports
2.1 General Organization Schemes
2.1.1 Outlines
2.1.2 Signposting
2.1.3 Typical lab report sections
2.2 Title Page
2.3 The Abstract
2.4 The Introduction (Background/Theory) Section
2.5 Methods Section
2.6 Results Section
2.7 Discussion Section
2.8 Conclusions (and Recommendations)
2.9 Reference List
2.10 Appendices
2.11 Summary
Chapter 3: Organizing Sections of Lab Reports
3.1 Paragraph Structure
3.2 Sentence Requirements
3.3 Word Choice
3.4 Grammar
3.4.1 Introduction
3.4.2 Subject-verb match
3.4.3 Voice
3.4.4 Tense
iii
3.4.5 Pronouns
3.4.6 Adjectives and adverbs
3.4.7 Capitalization and punctuation
3.5 Citation
3.6 Proofreading Example
3.7 Summary
Chapter 4: Manipulating and Communicating Data
4.1 Importance of Units
4.1.1 Introduction
4.1.2 Dimensional units
4.1.3 Units and functions
4.2 Accuracy, Precision, Significant Digits, and Rounding
4.2.1 Introduction to accuracy and precision
4.2.2 Accuracy
4.2.3 Precision
4.2.4 Reporting data
4.2.5 Significant digits
4.2.6 Exceptions to the rule: numbers with no decimal point and exact numbers
4.2.7 Rounding and calculations
4.3 Engineering Models
4.4 Error Analysis
4.4.1 Introduction to error analysis
4.4.2 Propagation of uncertainty
4.5 Uses of Figures and Tables
4.5.1 Introduction
4.5.2 Common characteristics of tables and figures
4.5.3 Figure structure
4.5.4 Table structure
4.6 Summary
Chapter 5: Tools
5.1 Using Microsoft Word
5.1.1 Introduction
5.1.2 Spell checking and grammar checking
5.1.3 Equation editor
5.1.4 Group tools
5.2 Using Microsoft Excel
5.3 Linear Regression
5.3.1 Introduction
5.3.2 Linear regression analysis
5.3.3 Calculating linear regression coefficients
5.4 Fitting Models to Data Using Solver
5.4.1 Background
5.4.2 Using Solver for model fitting
5.4.3 Using Solver with constraints
5.5 Summary
iv
Chapter 6: Other Engineering Documents
6.1 Reports
6.2 Letters
6.3 Memorandums
6.4 Email
6.5 Summary
Glossary
References and Bibliography
Appendix A: Example Lab Reports
Appendix B: Rules for Civil and Environmental Engineering Lab Reports
Appendix C: Checklist for Civil and Environmental Engineering Lab Reports
Appendix D: Common Problem Areas in Technical Writing
Appendix E: SI Units
Appendix F: Engineering Models
v
Chapter 1
Introduction
E
ngineers solve problems. Much of your engineering education has been spent learning
analysis techniques. In effect, you have
been learning to communicate using mathematics.
However, your job is not finished once you have
arrived at a solution. You must be able to communicate your solution using graphics, in writing,
and orally. You may be required to send a memo
to your superior at work, submit a report to a local
agency, or give a presentation at a public hearing.
Remember, your hard work will count for little if
you cannot communicate the solution effectively
to others. In the civil engineering laboratory
courses (CIE 360/361 and 362), you will get the
opportunity to practice and improve your technical
communication skills.
Real World Alert
Employers today recognize the importance of
good communication skills and increasingly cite
technical communication as a major factor in selecting new hires.
the audience has the technical background to recognize it. As you go up the abstraction ladder, the
terms become less precise, allowing a greater freedom of interpretation. At the top of the ladder is
an electrical device. The resistor certainly is an
electrical device, but so is a light bulb, a stereo
system, or a computer. Good technical writing
should restrict the reader’s ability to find various
meanings. You should therefore use the lowest
level of abstraction possible. In your laboratory
reports, you will find the use of photographs very
helpful, particularly to help you describe the experimental setup.
electrical device
circuit component
resistor
33-kilohm, 1 watt resistor
Technical writing is not easy. Many students
will struggle initially to communicate effectively,
but it will get easier with practice. The main focus
of this manual is to help you write a better laboratory report. As a guide, two complete example
reports are included in Appendix A. It is also
hoped that this manual will provide the background you need for writing better reports, term
papers, and journal articles in the future.
1.1 WHAT IS TECHNICAL WRITING?
How does technical writing differ from other
forms of writing? To help explain the goal of
technical writing, consider the idea of an abstraction ladder (Finkelstein, 2005). Figure 1.1 shows
the picture of a 33-kilohm, 1-watt resistor at the
bottom of the abstraction ladder. The photograph
is the most precise way of describing the resistor if
Figure 1.1: Abstraction Ladder
(after Finkelstein, 2005)
As a civil engineering example, assume you
tested the tensile strength of two materials and
found the tensile strength of material A to be 90
ksi and the tensile strength of material B to be 100
ksi. A common mistake would be to report: “Materials A and B differ in strength.” Why is this a
mistake? The reader is not told which material is
stronger, by how much, or what the writer means
by “strength.” A more precise statement would
be: “The tensile strength of material B is 11%
greater that the tensile strength of material A.”
An abstraction ladder for the tensile strength example is shown in Figure 1.2.
CHAPTER 1: INTRODUCTION
“Materials A and B differ in strength.”
“Material B is stronger than material A.”
“Material B has a higher tensile strength
than material A.”
“The tensile strength of material B is 11%
greater that the tensile strength of material
A.”
“The tensile strength of materials A and B were
90 and 100 ksi, respectively.”
2
1.3 IDENTIFYING THE GOALS,
TARGET AUDIENCE, AND
CONSTRAINTS
Before you write a single word of a lab report, you
must identify clearly three elements: the goals of
the report, the target audience, and the constraints
on producing the report. Each of these elements
will be discussed in more detail in this section.
Mental Note
Before preparing a lab report, write down the
goals of the report, the target audience, and the
constraints on the production of the report
Figure 1.2: An Abstraction Ladder for the Tensile Strength Example
1.3.1 Goals
As the examples above illustrate, precision
sets technical writing apart from other forms of
writing. As Finkelstein (2005) writes, “The goal
of technical writing, then, is not to be creative or
interesting; it is not to employ rich imagery or metaphors. The goal of technical writing, first and
foremost, is to communicate complex information
clearly and precisely for the audience and purpose
at hand.” To achieve this goal, technical writing:




Relies heavily on visual display of data
Uses numerical data to precisely describe
quantity and direction
Is accurate and well documented
Is grammatically and stylistically correct.
1.2 LAB NOTEBOOKS
To write a good lab report, it is necessary to
have all the pertinent information recorded in
your lab notebook. What should you record?
First, write enough detail about the procedures
so that the experiment could be repeated by
another person with the same results. Second,
make sure that the results are recorded unambiguously. Additional information on creating a
proper laboratory notebook is given in Appendix B.
One of the most important activities in the design
of any report is to identify the report goals. What
are you trying to accomplish with the report? Unless your goals are identified clearly, the report
will fail. Why? First, you cannot decide what
information should be presented (or how to
present it) unless you have defined the goals
thoughtfully. Second, you need to know the goals
to evaluate whether or not you have communicated the ideas successfully.
The general goal of all lab reports is to inform
the reader: to detail the experimental methods employed, to document your findings, and to communicate their significance so that others may replicate your results. However, the focus of your
report will depend upon your specific objectives.
Are you trying to demonstrate your understanding
of a specific concept? Are you required to compare your results to published values? Are you
trying to validate a theoretical or numerical model?
For the example lab report in Appendix A, you
might write:
The goals of the lab write-up are to
demonstrate our understanding of the
mechanical properties of fiber reinforced polymer composites tested in
tension, to detail the experimental methods employed, to present the results
obtained, to compare the mechanical
properties of the composite to its
3
MANUAL FOR CIVIL AND ENVIRONMENTAL ENGINEERING LABORATORY REPORTS
component polymer, and to discuss
the variation of mechanical properties
in the fill and warp directions.
Knowing your goals allows you to decide what
should go in the write-up and how the material
should be prioritized. Once your report is complete, you should compare the report with your
goals to ensure the goals have been met.
1.3.2 Target audience
In addition to the goal of the report, you also
should identify the target audience. The target
audience consists of the intended recipients of the
information you are presenting. As with report
goals, identification of the target audience is critical to the success of your report. You must keep
the background and technical sophistication of the
target audience in mind when writing the report.
The intended audience for your lab report is
obviously your professor. You therefore may argue that since your professor already knows the
experimental theory, there is no need to report it.
For your lab reports, consider the target audience
to be an interested party (perhaps another engineering student) who may wish to understand your
work and/or repeat your experiment in the future.
Real World Alert
In your career, you will give oral and written presentations to many audiences, including colleagues
(i.e., fellow engineers), managers, elected officials, students, and the general public. The interests and backgrounds of the audience are as important as their technical sophistication. Each audience member will interpret the presentation
through his or her own point-of-view. To engage
the audience fully, you must know the backgrounds of its members. As an example, consider
the choices available to an engineer presenting an
idea for a new bridge design. For an audience of
managers and corporate executives, the engineer
may wish to emphasize the low operation and
maintenance costs of the new design. For fellow
engineers, the engineer would likely focus on the
technical specifications and structural response
data. Subtle changes often can make the presenta-
tion match the interests and background of the audience more closely.
1.3.3 Constraints
Identification of constraints on the report is also
important. Common constraints are: document
length, resource limitations, and format.
It is very important to heed the document
length constraint. Many engineering reports, proposals, and lab reports have gone unread because
they exceeded the imposed page limit.
The resources limitations also cannot be ignored. As a student you must learn to allocate
your time so that the report (or term paper) can be
submitted on time. Again, lab reports have gone
unread because they were submitted after the imposed deadline.
Real World Alert
Practicing engineers also must budget time for
report/presentation preparation. Other resources
required to produce a high-quality technical document (or oral presentation) include money for
personnel, graphics creation, printing, reproduction, and distribution.
1.3.4 Formatting issues
The format of the report is the way the type is arranged on the page. It is important that your work
is formatted so that the important details stand out.
Format can be broadly divided into typography
and layout.
Typography is the part of format that deals
with your choice and size of font. The text of this
document is written in 11-point Times Roman.
Times Roman belongs to a class of fonts called
serif fonts. The letters have little lines on the bottom that help to create a baseline and make it easier for the eye to jump from one line to the next.
Many newspapers use a variation of Times Roman. The indented examples in this document are
written using Arial, a sans serif font. Sans serif
CHAPTER 1: INTRODUCTION
fonts do not have the little lines on the bottom and
hence provide a good contrast (for example, in
headings).
The general guidelines for typography given
below are from Alley (1996). It is important to
use boldface and italics sparingly to avoid distracting and confusing the reader. Boldface should
generally be restricted to headings, subheadings,
and figure or table titles. Italics should be restricted to subheadings and glossary terms or to
emphasize a word or sentence. Always ask yourself if the use of boldface or italics helps to clarify
the point being discussed. If the answer is yes,
then their use is justified. The use of underlining
should be avoided whenever possible, as it is generally considered to be a poor substitute for italics.
Also avoid strings of ALL CAPITAL letters in the
text, as these are hard to read. Bottom line: select
a formatting scheme for to ensure clear communication and use it consistently.
Mental Note
Use boldface or italics only if they help to clarify the point being discussed and use them
consistently
Layout is the arrangement of words on the
page. Layout includes the spacing between lines,
margins, indentation, spacing between paragraphs
etc. A well-laid-out document is pleasing to look
at, easy to read, and will help to emphasize the
important information. In general, be generous
with “white space” when laying out your document (Alley, 1996). You also will need to choose
a hierarchy for the headings and subheadings.
Section hierarchy can be shown by using white
space, by varying the size of the font, or by indenting the section (see also Section 2.1.2). Again, use
a consistent layout scheme throughout the report.
1.3.5 Imposed constraints for civil
engineering lab reports
The following constraints are imposed for your lab
reports. All other constraints must be chosen by
your lab group.







4
Document length: maximum of six pages,
excluding the title page and appendices
Submission date: final report due one
week after the laboratory period
Single sided
Single spaced
Use Times Roman (12 pt) for text
Use Arial (18 pt, 14 pt, or 12 pt) for headings and subheadings
Page numbers “bottom of page – center.”
Number all pages except the title page.
1.4 WRITING AS A GROUP
In your lab classes, you will have the opportunity
to practice writing as a group.
Real World Alert
In practice, engineers frequently write reports in
collaboration with others.
Technical writing in itself is not easy. Writing
a document as a group poses its own additional
problems. How will you divide up the work?
How will you communicate with each other? Who
will pull the whole report together? What to do if
a group member fails to adhere to the agreed schedule? This section will help to address some of
these concerns.
The steps involved in producing a good lab
report are summarized below:







Identify your report goals, audience, and
constraints
Produce a detailed outline of the report
Divide the work
Write individual sections
Produce a draft report
Review of the draft report as a group
Produce a final report
It is strongly recommended that you take time at
the end of each lab session to complete the first
two or three bulleted items. A good outline will
5
MANUAL FOR CIVIL AND ENVIRONMENTAL ENGINEERING LABORATORY REPORTS
save you a great deal of time in preparing your lab
report.
The purpose of the outline is to organize the
information you developed during the experiment.
The outline should include section headings and a
list of the major points under the prescribed headings. For general guidelines on organizing the report, see Chapter 2. The outline also will help to
ensure you have all the information you will need
before leaving the lab.
Mental Note
A good outline will save you a great deal of
time in preparing your lab report
Once the outline is complete, you will be able
to divide up the work and set the work schedule.
Tasks should be rotated weekly. Each report will
require a team leader. The team leader is ultimately responsible for producing the report.
Completed sections should be sent to the team
leader for incorporation into the draft report. Each
group member should adhere to the report constraints to make the job of team leader easier. The
easiest way to communicate and share files is by
email.
The draft report should be distributed to all
group members for review at least two days before
the final report is due. Check the logic and flow of
the report to ensure the report moves smoothly
from section to section. Ultimately, check the report against the report goals to ensure the goals
have been met. It is often advantageous to meet
in person to discuss comments on the draft report
so that any disagreements can be resolved quickly.
All too often, group members fail to meet the
agreed deadlines and the final report is thrown
together hours (sometimes minutes) before it is
due, leaving the team leader little time to pull the
report together. The result is a disjointed, inconsistent, poorly written, poorly presented report.
Mental Note
If the lab report is thrown together at the last
minute, then it will be disjointed, inconsistent,
poorly written, and poorly presented
After the final report has been produced by the
team leader, all members of the group must sign
the report before it is submitted. If a group member fails to sign the report, then it will be assumed
that the member did not contribute to the report
and he or she will receive a zero.
Whenever you work as a group, conflicts may
arise.
To minimize the potential for conflict,
please try to abide by the following Code of Cooperation suggested by McNeill et al. (1995):
1. Every member is responsible for the
team’s progress and success.
2. Attend all team meetings and be on time.
3. Come prepared.
4. Carry out assignments on schedule.
5. Listen to and show respect for the contributions of other members; be an active listener.
6. Constructively criticize ideas, not persons.
7. Resolve conflicts constructively.
8. Pay attention; avoid disruptive behavior.
9. Avoid disruptive side conversations.
10. Only one person speaks at a time.
11. Everyone participates; no one dominates.
12. Be succinct; avoid long anecdotes and examples.
13. No rank in the room.
14. Respect those not present.
15. Ask questions when you do not understand.
16. Attend to your personal comfort needs at
any time, but minimize team disruption.
17. Have fun.
It is important to remember that “every member is responsible for the team’s progress and success” (McNeill et al., 1995).
1.5 PROOFREADING AND
SPELL CHECKING
Draw a line in the sand: from this point forward,
every document with your name on it reflects on
you personally. Never allow your name on a document unless you are satisfied with it. In the lab
courses, each group member is responsible for
proofreading and checking their own work, although the final responsibility lies with the team
CHAPTER 1: INTRODUCTION
leader who must check the entire document before
submission.
1.5.1 Proofreading
The secret to good proofreading is practice. You
can check your proofreading skills by asking others to read your work and give you feedback.
Proofreading is needed to catch errors. The
authors of this manual have seen numerous embarrassing errors that could have been caught by
sharp proofreading, including:
“erogenous data” instead of “erroneous data”
“for all intensive purposes” instead of
“for all intents and purposes”
What should you look for when you proofread
a report? A proofreading checklist is provided in
Appendix C to assist you. An example of proofreading is given in Section 3.6.
1.5.2 Spell checking
There is no room for spelling errors in technical
documents. One misspelled word could destroy an
otherwise strong document.
The fundamental rule of spelling is: never,
never, never trust your spell checker. Spellchecking software is a good first start, but you
must learn to proofread your writing very carefully. Spell checkers will miss misspellings that result in another word (e.g., house/horse, dear/deer
etc.). As an example, the paragraph below passes
Microsoft Word’s spell checker. Can you find the
typographical errors?
Their are many explanations for the
pore data. One ideas is that the
equipment had to many power failures. A uninterruptible power supply
and better trained personal might
help.
1.6 SUMMARY
Before preparing your lab report, write down the
goals of the report, the target audience, and the
6
constraints on the production of the report. Constraints include report length, time constraints, and
the required formatting listed in Section 1.3.5.
In formatting your report, use boldface and
italic font weights consistently to emphasize important points. Use white space to make your report pleasing to look at and easy to read.
Use an outline, division of labor, communication between group members, and your best cooperation skills to write a group report. Recall that
all members of the group must sign the report before it is submitted. If a group member fails to
sign the report, then it will be assumed that the
member did not contribute to the report and he or
she will receive a zero. Be sure to use good proofreading to eliminate factual, grammatical, spelling, and formatting errors in the report.
Chapter 2
Overall Organization of Lab Reports
W
hether your experiment went smoothly
or not, it is still possible to write a good
report. The key to a good laboratory
report is organization. In this chapter, general organization will be discussed. Organization at the
paragraph, sentence, and word level is the subject
of Chapter 3.
2.1 GENERAL ORGANIZATION
SCHEMES
2.1.2 Signposting
Organizing a lab report is only half the battle. You
also must let the reader know that you are well
organized. Showing the audience your organization is called signposting.
Mental Note
To organize a presentation, structure the material using an outline and show the structure to
your audience with signposting
2.1.1 Outlines
The primary tool used to structure a presentation is
the outline. An outline is a structured (or hierarchical) list showing the skeleton of the technical
document or technical presentation.
The purpose of the outline is to divide the report into manageable pieces. An outline shows
three elements of the presentation:



The main ideas (listed in the outline as
major headings)
The order of the main ideas
The secondary topics (subheadings) that
support and flesh out the main ideas
The main ideas, of course, depend on the goal of
the report and the target audience (see Section
1.1). Typical major headings for lab reports will
be presented in Section 2.1.3.
The outline is a wonderful tool for organizing
a presentation. It shows at a glance the relationships between parts of the report. The outline
helps you to see if the report is balanced: that is,
whether the level of detail in a certain part of the
report corresponds to the importance of that part in
achieving your goals. The outline also helps determine the needs for more data or more tables and
figures. An outline can be changed easily as the
report evolves. In fact, as the outline is annotated
(that is, as more levels of subheadings are added),
the report will nearly write itself.
An example of signposting is the headings
used in this manual. The consistency of the headings tells you where you are in the document:
1. Chapter titles: Bold 20- and 24-point
Times New Roman font, initial letters
capitalized
Example:
Chapter 2
2. Section titles: Bold 13-point Times
New Roman font, all caps
Example: 2.1 GENERAL …
3. Subsection titles: Bold 12-point Times
New Roman font, only first word capitalized
Example: 2.1.1 Outlines
The remainder of this chapter will discuss the content of each section of a lab report. The section
content will be illustrated with an example lab report. The entire example lab report may be found
in Appendix A. (The report in Appendix A was
written under an eight-page limit.) You may want
to take a moment to determine the signposting
scheme in both examples in Appendix A.
CHAPTER 2: OVERALL ORGANIZATION OF LAB REPORTS
8
2.1.3 Typical lab report sections
2.3 THE ABSTRACT
In Section 2.1.1, it was emphasized that outlines
should be used to develop organized presentations.
What headings and subheadings should be employed? Clearly, the details of the outline will
depend on the type of experiment and its objective. Although every lab report is slightly different, several elements are common to most reports.
The common elements are:
Lab reports, as with most technical documents
typically begin with an abstract. The purpose of
the abstract is to provide a brief summary of the
remainder of the document. The abstract should
include the important points from each element in
the document. An extended abstract (often written
for non-technical audiences) sometimes is called
an executive summary.
A properly written abstract should be a miniature version of the entire technical document. The
word abstract comes from the Latin abstractus,
meaning drawn off. In a true sense, think of the
abstract as being drawn off of the whole document.
Thus, an abstract should include:









Title page
Abstract
Introduction/Background/Theory
Methods
Results
Discussion
Conclusions (and recommendations)
References
Appendices
The content of each of these report sections will be
discussed in Sections 2.2 through 2.9.




2.2 TITLE PAGE
All reports must have a title page. The title page
should include the:





Experiment title
Class name and number
Author’s names
Name of person to whom the report is
submitted, and
Date
The experiment title should be straightforward, informative, and less than ten words. For
example, the title of the sample report in Appendix
A is:
An introduction (with enough background material to show the importance of the work),
A statement on the methods or models
employed,
A short summary of the results and
their meaning, and
Conclusions and recommendations.
The abstract is typically a single paragraph of
between 100 and 200 words. The abstract is a
summary of the document and thus it cannot be
written until the report is complete. It should be
intelligible and complete in itself. In particular, it
should not cite figures, tables, or sections of the
report. When writing the abstract, it is often helpful to summarize each section of the report and
then try to arrange these sentences into a single
paragraph.
Mental Note
The abstract is a summary of the document and
contains an introduction, methods statement,
short summary of the results and their meaning, and conclusions and recommendations
Tension Testing of Glass Fiber Reinforced
Polymer
To simply write “Lab #6” does not tell the reader
anything about the content of the report. Readers
would be forced to turn to the next page to see
whether this is the report they were expecting.
The abstract from the example lab report in
Appendix A reads:
9
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL REPORT MANUAL
Abstract
An experiment was conducted to test
whether a glass fiber reinforced polymer
(GFRP) had better mechanical properties
than its component polymer. In addition,
the mechanical properties of the GFRP in
the fill and warp directions were compared. Tensile tests were performed according to ASTM methods by displacement control using an MTS universal testing machine and a data acquisition sampling rate of 1.0 Hz. Test coupons were
cut from a ten–layer laminate of a polymer
(vinyl ester resin DERAKANE 411) and a
woven glass fiber fabric. Results showed
that embedding the woven glass fiber fabric within the polymer increased both the
stiffness and strength of the material
(modulus of elasticity increased from 3.38
GPa to about 17 GPa and the tensile
strength increased from 80 MPa to about
300 MPa). However, the composite was
more brittle than the polymer (as indicated
by a lower percent elongation). There was
a slight variation in mechanical properties
in the warp and fill directions, presumably
due to the different number of fibers in the
two directions.
Note that the abstract contains all the elements of
the full report: introduction and goals (1st and 2nd
sentences), methods (3rd and 4th sentences), and
results/conclusions (5th through 7th sentence).
2.4 THE INTRODUCTION (BACKGROUND/THEORY) SECTION
The next element is the introduction. In writing
the introduction section, assume that the reader
knows only the title of the report. After reading
the introduction, the reader should have a good
idea of the motivation for the report (i.e., why the
report was written). The introduction therefore
will orient the reader by giving a problem description and definition, stating the purpose or objectives of the particular experiment, and providing
important background and/or theory. In some cases, a brief summary of earlier research may be relevant. If the introductory section seems long,
then it is often better to add subheadings (such as
Objectives, Theory, Background, or Previous Research).
The introduction section is the appropriate
location for a statement of the objectives of the
work. A clear statement of objectives is of the
utmost importance because the objectives of the
experiment usually are analyzed in the conclusion
section to determine whether the experiment was
successful.
Mental Note
The introduction section takes the reader from
the title to an appreciation of why the document was written
In the reinforced polymer lab report (Appendix A), the introduction and background are separate sections. The section called “Introduction”
orients the reader to the problem (1st paragraph)
and presents the lab goals (2nd paragraph):
Introduction
Fiber-reinforced composite materials
are formed by embedding fibers of a
strong, stiff material into a weaker, softer
material, known as the matrix. The resulting composite material has superior mechanical properties to the two individual
materials. The mechanical properties of
the composite are dependent on the number and orientation of the fibers.
In this experiment, a glass fiber reinforced polymer (GFRP) was tested. The
GFRP was made from layers of woven
glass fiber fabric embedded within a vinyl
ester resin matrix. The fabric used had
slightly more fibers in the warp direction
than in the fill direction. The testing had
two objectives. The first objective was to
compare the mechanical properties of the
GFRP composite to the properties of its
component polymer. The second objective was to compare the mechanical properties of the GFRP in the fill and warp directions.
The section called “Background” gives the theory.
In the example in Appendix A, an outline of the
background section is as follows:
CHAPTER 2: OVERALL ORGANIZATION OF LAB REPORTS
1. Definition of stress and strain
2. Mechanical properties of materials
3. Published mechanical properties of the individual material
a. Polymer Matrix
b. Woven Glass Fiber Fabric
2.5 METHODS SECTION
A section on the methods employed usually follows the introduction. The methods section describes your overall approach. For experimental
work, the methods section also describes what was
measured, how it was measured, what data were
collected, and how the data were analyzed.
How much detail should you include? If the
method section is written correctly, then another
person should be able to duplicate your experiment exactly. If you simply followed a standard
procedure, such as an American Society of Testing
and Materials (ASTM) protocol, then it is sufficient to refer to the actual standard:
Testing was performed in accordance with
ASTM D3039–76, Standard Test Method
for Tensile Properties of Fiber-resin Composites.
While there is no need to restate a standard protocol, it is very important to provide detail where
your procedure differed from the standard. Similarly, if you are simply following a set of instructions from your lab handout, then there is no need
to regurgitate the handout. Place it in an appendix.
However, if the procedure is not standard, then
you will need to give a detailed account of the
measurement methods including a justification of
your approach.
Mental Note
The methods section should provide enough
detail so that another person can duplicate your
work exactly
The methods section should be a narrative, not
a set of instructions (i.e., not: “First, weigh the
sample. Then put the sample in …”). The steps
10
can be presented in list form if this improves clarity. Often, the information about the experimental
set-up can be communicated most effectively by
drawings or photographs. Remember to state what
you really did, not what you were supposed to do.
If, for example, you had equipment problems that
prevented you from completing the test, then say
so even if you eventually analyzed data collected
by another group.
The methods section from the example lab report in Appendix A reads (figures omitted to save
space – see Appendix A for the complete section):
Methods
To quantify the effects of glass fiber
reinforcement, standard mechanical properties (modulus of elasticity, tensile
strength, percent elongation, and Poisson’s ratio) were measured on coupon
samples of a GFRP. Since the glass fiber
fabric used in this study has slightly more
fibers in the warp direction than in the fill
direction, it was expected that two directions would have slightly different mechanical properties.
Tensile tests were performed according to ASTM D3039–76, Standard Test
Method for Tensile Properties of Fiberresin Composites, using an MTS universal
testing machine. All the tests were performed by displacement control. The rate
of loading was 0.0847 mm/sec. Data were
collected using a data acquisition system
with a sampling rate of 1.0 Hz. The test
setup is illustrated in Figure 1.
[Figures 1 and 2 omitted]
Test coupons were cut from a ten–
layer laminate. The laminates were made
by a hand lay–up process. Dimensions of
the test coupons are shown in Figure 2.
Three coupons were prepared and
tested in both the fill and warp directions.
Note in this example that the study approach is
presented and justified in the first paragraph. The
second and third paragraphs give the overall experimental procedure, with some measurement details.
11
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL REPORT MANUAL
2.6 RESULTS SECTION
The results section comes next. In this section, the
actual results are presented, but not interpreted.
For many labs, the results can be summarized in a
graph or table. For your results to be effective,
you must focus the reader’s attention with a sentence or two to introduce each graph or table. The
raw data can be put in the appendix.
Graphics should be clear, easy to read, and
well labeled. In general, use a table when the actual values are important and a graph to show
trends in data. See Section 5.4 for ways to improve your tables and figures.
In most cases, it is sufficient to provide a sample calculation in the report. Place the remaining
calculations in an appendix. As with the methods
section, remember to state what really happened,
not what was supposed to happen.
The results section from the example lab report in Appendix A is shown below. (Figures 3-5
and Table 2 are omitted to save space.)
Results
Figures 3 and 4 show the stress-strain
plots for the specimens tested in the fill
and warp directions, respectively. Note
that the stress-strain plots are nearly linear, indicating a constant modulus of
elasticity (eq. 3).
Table 2 gives a summary of the mechanical properties of the GFRP in both
the fill and warp direction. The modulus of
elasticity was determined in the strain
range of 0.001 to 0.003 as specified in
ASTM standards. Note that the variability
between replicates was low.
Photographs of the specimens after
failure are shown in Figure 5. Note the
brittle nature of the material at the point of
failure.
Note that the results section is short and direct.
The reader first is directed to the appropriate data
(in this example, in figures or tables). A very
short (typically one- or two-sentence) description
of the trends in the data also is presented.
Mental Note
The results section is short: direct the reader to
the data and describe the trends in the data
briefly
2.7 DISCUSSION SECTION
The discussion section follows the results and is
perhaps the most important section of the report.
This is where you show that you understood the
experiment and its objective.
You may want to ask yourself:




What do the results indicate?
What is the relevance of the results?
How do the results compare to theory or
published data?
What ambiguities exist?
Since the discussion section is where you explain, analyze and interpret the results, the results
section must be complete before you write the discussion. With a group report, the person responsible for the discussion is usually not the person
producing the results section. Timely completion
of the results section therefore becomes critical to
the success of the report. All too often, the discussion section is written without reference to the results. The discussion section then becomes a
laundry list of potential problems with the experimental set-up, with little reference to the actual
work performed or the results obtained.
Mental Note
The discussion section includes the interpretation and relevance of the results, and comparison to theory or other data
If the results are not what you expected, then
you need to find logical explanations: assigning
all inconsistencies to human error or faulty
equipment is insufficient. The explanations should
match the direction and magnitude of the errors.
CHAPTER 2: OVERALL ORGANIZATION OF LAB REPORTS
You must be specific about the possible sources of
error. Were the instruments malfunctioning or not
precise enough for the measurements being made?
As an example of the latter problem, consider the
following common laboratory situation. In the undergraduate soils laboratory, the most accurate
scale measures to an accuracy of 0.1 g. To determine the amount of water in a particular soil sample, you must weigh the soil sample wet, then dry
it in an oven and weigh again. The amount of water is therefore the wet weight minus the dry
weight. Assume we have a 10 g soil sample,
which is 10% water. We therefore would expect
the wet weight minus the dry weight to be 1 g.
However, due to the accuracy of the scale, the error in the amount of water could be as high as ±0.2
g, or 20%. To reduce the relative error, a larger
soil sample must be used to determine the water
content.
Consider also whether the error was avoidable.
If the error was the result of the experimental design, then discuss how the design could be improved. In some cases, it is legitimate to compare
outcomes with classmates – not to change your
result, but to look for and discuss anomalies between the groups.
The discussion section for the example in Appendix A is shown below.
Discussion
The test results show that the material behavior was very consistent. All three
samples tested yielded very similar values
of modulus of elasticity and tensile
strength (see Figures 3 and 4). The consistent nature of the material behavior is
also apparent from the summary of mechanical properties shown in Table 2. For
example, the modulus of elasticity in the
fill direction varied from 16.27 to 16.83
GPa across the three samples, a variation
of less than 5%.
Comparison of the measured mechanical properties of the GFRP (Table 2)
with the published mechanical properties
of the polymer matrix (Table 1) shows the
large increase in both stiffness and
strength of the GFRP due to the embedment of the woven glass fiber fabric, which
act to reinforce the softer polymer matrix.
The modulus of elasticity increased from
12
3.38 GPa to about 17 GPa and the tensile
strength increased from 80 MPa to about
300 MPa. However, the strain to failure
(%EL) decreased from 5-8% for the polymer alone to around 2% for the composite
material. This decrease is significant and
indicates brittle failure. The brittle nature of
the composite material is illustrated in Figure 5.
There are about 5% more threads in
the warp direction than the fill direction.
The test results show a 7.7% increase in
elastic modulus and 17.9% increase in
tensile strength in the warp direction compared to the fill direction. These results
imply that the increase in stiffness and
strength is not linearly proportional to the
number of fibers.
Note that the discussion section contains quantitative conclusions about the data (“…the modulus of
elasticity in the fill direction varied from 16.27 to
16.83 GPa across the three samples, a variation of
less than 5%.”), while the results section contained
only qualitative statements about the data (“Note
that the variability between replicates was low.”).
The division between the results and discussion sections is not always clear-cut. In fact, the
results and discussion sections often are combined
in short reports. To illustrate the difference between results and discussion, consider a report on
the effects of coagulant dose on the removal of
turbidity. In the results section, the turbidity data
might be reported. General trends (for example,
that turbidity generally decreased as the coagulant
dose increased) may be noted. More detailed interpretation of the data would be placed in the discussion section, where, for example, model predictions might be compared quantitatively to the data
collected in the study.
2.8 CONCLUSIONS (AND RECOMMENDATIONS)
The last main section of a typical lab report is the
conclusions and recommendations. The conclusions and recommendations must be among the
most carefully worded sections of the report, since
many readers may turn here first. In this section,
13
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL REPORT MANUAL
you relate your results to the lab’s problem statement and objectives.
Conclusions and recommendations are generally quite concise and often appear in a list format.
The conclusions should stem directly from the discussion and answer the question: to what extent
did you attain the lab’s objective? Conclusions
should not list anything new. Conclusions should
be a summary of the main points from the discussion. In the recommendations, you address any
steps you should take to improve the results in the
future. Note that not all reports will have recommendations.
Real World Alert
The recommendations section is a critical part of
an engineering report. Why? Remember that engineers often select intelligently from among alternatives. The preferred alternative often is highlighted in the recommendations section.
Note that the conclusions section simply summarizes and prioritizes the findings discussed earlier
in the report. No new ideas are introduced.
2.9 REFERENCE LIST
To refer to other people’s work, two pieces of information are required. First, the work must be
cited in your report. The proper methods of citing
material are discussed in Section 3.5. Second, bibliographic information on the referenced work
must be provided in a reference list. There are
many acceptable formats for listing references in
technical material. The guiding rules are that the
references should be complete (so that the reader
can find the referenced material easily) and consistent (i.e., use the same format for all books or
journals cited). Examples of reference formats are
shown below:
For books:
An example conclusions section from the lab
report in Appendix A is given below:
Conclusions
Tensile tests were performed on
GFRP and its mechanical properties were
determined. The findings are summarized
below.

GFRP has superior properties to the
individual materials.

Embedment of a woven glass fiber fabric within a polymer matrix increased
both the stiffness and strength of the
material when compared to the mechanical properties of the polymer
alone.

Inclusion of the glass fibers produced
a more brittle material

There is a slight variation in mechanical properties in the warp and fill directions, presumably due to the different number of fibers in the two directions.
Author’s last name, author’s initials (for
second authors, initials followed by name),
book title in boldface, publisher’s name, publisher’s location, publication date.
Example: Keller, H. The Story of My Life.
Doubleday, Page & Co., New York,
NY, 1903.
For journal articles:
Author’s last name, author’s initials (for
second authors, initials followed by name), article title, journal name in boldface italic, volume number in boldface, issue number in parentheses, page range, date.
Example: Dallard, P., A.J. Fitzpatrick, and
A. Flint. The London Millennium Footbridge. Structural Engineer, 79(22),
17-35, 2001.
For web pages:
Author’s last name, author’s initial, document
title, date of Internet publication, date of
access <URL>.
CHAPTER 2: OVERALL ORGANIZATION OF LAB REPORTS
Example: Anonymous. Gustave Eiffel. August 20, 2006. Accessed August 25,
2006.
<http://en.wikipedia.org/wiki/Gustave_Eiffel>
Be careful about the differences between a list
of references and a bibliography. A reference list
consists only of the material cited in the text. A
bibliography lists all useful sources of information, even if they were not cited specifically in the
text.
2.10 APPENDICES
Appendices may include raw data, calculations,
graphs, material data sheets, and other quantitative
materials that were part of the experiment. What
should be included in the main body of the report
and what should be included as an appendix? As a
guide, ask yourself the following question: is presentation of this material central to the reader’s understanding of the experiment? If your answer to
this question is yes, then the material should be
placed in the main body of the report. If the answer is no and the material is supplemental and
included in the report only for completeness, then
it should be placed in an appendix.
Mental Note
Put material in an appendix if it is not central
to the reader’s understanding of the experiment
All appendices should be referred to in the
main body of the report. Use a separate appendix
for each kind of item (raw data, calculations, etc.).
2.11 SUMMARY
Lab report preparation should begin with an outline. Make sure that the outline is clear to the
14
reader through the use of signposting. Typical
sections in a lab report include a title page, abstract, introduction/background/theory, methods,
results, discussion, conclusions (and recommendations), references, and appendices. The purpose
and structure of each section was discussed in detail in this chapter. All references cited in the report should be listed in a reference list. Make sure
that the information in the reference list is complete and consistent.
Chapter 3
Organizing Sections of Lab Reports
Y
ou learned about the typical organization
of a lab report in Chapter 2. The content
of each section of the report also were discussed in Chapter 2. In this chapter, organization
at the paragraph, sentence, and word level will be
elucidated.
At the conclusion of this chapter, an example
is given where you can test your proofreading
skills. Common words and phrases that are misused in technical writing are given in Appendix
D.
3.1 PARAGRAPH STRUCTURE
Beyond organizing the overall lab report, each
paragraph also should be structured. Each paragraph should tell a complete story and be structured by sentence. The paragraph should begin
with a topic sentence. The topic sentence states
the purpose of the paragraph. Each following sentence should support the topic sentence. Paragraphs should end with a concluding sentence,
which summarizes the main points of the paragraph. Thus, each sentence in the paragraph has a
specific purpose.
Mental Note
Paragraphs should consist of a topic sentence,
supporting sentences, and a concluding sentence
As an example, analyze the paragraph under the
heading “3.1 Paragraph Structure” and identify the
topic, supporting, and concluding sentences.
3.2 SENTENCE REQUIREMENTS
A sentence is a grammatical structure containing a
subject and a verb. Sentences should express a
single idea. There are two common problems with
sentences in technical documents: overly long sen-
tences (with more than one idea) and too short
sentences (lacking a subject or verb). Avoid
stringing several ideas together into a run-on sentence. Run-on sentences have one or more conjunctions (e.g., and, but, or, nor, for, so, or yet) to
combine disparate ideas. Consider the sentence:
Soil properties were measured by
standard procedures and all results
were rounded to three significant figures.
This is a run-on sentence. It contains two ideas
and should be split into two sentences at the word
“and”:
Soil properties were measured by
standard procedures. All results were
rounded to three significant figures.
Sentences can be too short if they do not include both a subject and a verb. Incomplete sentences are called sentence fragments. A common
sentence fragment in technical writing creeps in
when stating trends. For example:
The higher the water content, the
weaker the concrete.
Why is this a sentence fragment not a sentence?
This fragment has no verb and thus is not a sentence. Try to avoid such constructions in your
technical writing. The example above could be
rewritten as:
Higher water content results in weaker
concrete.
3.3 WORD CHOICE
The lowest level of organization is the choice of
words. In choosing words to form sentences, try
to be as concise, simple, and specific as possible.
Mental Note
Choose words that are concise, specific, and
simple
CHAPTER 3: ORGANIZING SECTIONS OF LAB REPORTS
Concise writing means that you should use the
minimum number of words to express the thought
clearly. To write concisely, avoid long prepositional phrases. Examples of common wordy
phrases and suggested substitutions are listed in
Table 3.1. An example of a sentence with a long
prepositional phrase is:
16
technical communication should be simple. In
other words, use simple words to express your
ideas as clearly as possible. Avoid sentences such
as:
Experiment failure mode was encountered on three sundry occasions.
Instead, write more clearly:
In order to find the optimum beam
width, experiments were conducted.
The experiment failed three times.
It is preferable to write:
To find the optimum beam width, experiments were conducted.
The heart of technical writing is its specificity.
Make your writing specific by avoiding general
adjectives such as: many, several, much, and a
few. Quantify your statements when you can:
Table 3.1: Examples of Long Prepositional
Phrases to be Avoided
The mixing temperature was 5oC
above that specified in the standard
method.
(adapted from Smith and Vesiland, 1996)
Wordy Prepositional
Phrase
Possible Substitute
due to the fact that...
because...
in order to...
to...
in terms of...
reword sentence and delete phrase1
in the event that...
if...
in the process of...
delete, or use “while” or
“during”
it just so happens
that...
because...
on the order of2...
about...
Notes:
1. For example: The sentence “In terms of energy,
Alternative 3 was lowest.” could be rewritten
as: “Alternative 3 had the lowest energy use.”
2. This phrase sometimes is used to indicate an order of magnitude (i.e., a power of ten), as in:
“On the order of 1,000 bolts were employed in
the construction project.”
Although the general public sometimes feels
that technical writing is impenetrable, written
Not: The mixing temperature was
several degrees above that specified
in the standard method.
3.4 GRAMMAR
3.4.1 Introduction
Important ideas about spelling and grammar will
be reviewed in this section. The purpose of this
discussion is not to provide you with a comprehensive list of the rules of grammar, but rather to
identify common trouble spots in technical writing.
There are no excuses for errors in grammar or
spelling in technical writing. The most important
rules are reviewed here. Problem words are discussed in Appendix D. For more details, please
examine any of the excellent books listed in the
bibliography.
You should be aware that there is some disagreement on several grammatical rules. It is important to differentiate firm rules from one writer’s
opinion. It is frustrating to learn and use one approach from a mentor, only to have it totally dismantled by another mentor. When in doubt about
17
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL REPORT MANUAL
the feedback you have received about your writing, always ask questions.
3.4.2 Subject-verb match
The subject and verb must match in number. In
other words, use plural forms of verbs with plural
nouns and singular forms of verbs with singular
nouns. For example, you should write:
The contacts of the pressure transducer were corroded.
Not: The contacts of the pressure
transducer was corroded.
The subject of the sentence is plural (“contacts”)
and thus a plural verb (“were”) is required.
“doer” is identified. The person performing the
action is not identified (either directly or by category) in the passive voice.
There is some difference of opinion about
which voice is best for technical writing. In general, the active voice is preferred. Why? In engineering, you usually want to know who did the
action. You should write:
We called the client last Thursday.
Not: The client was called last Thursday.
In lab reports, the “doer” often is obvious and
the passive voice may be acceptable, as in:
Data were tested against a linear model.
Mental Note
The subject and verb should match in number
In most cases, the “subject-verb match” rule is
simple. However, some sticky situations arise. For
example, is the noun “data” plural or singular? In
most of the technical literature, the word “data” is
considered to be a plural noun. (Formally, it is the
plural of the noun “datum.”) A growing number
of technical writers consider “data” to be singular
when referring to a specified set of data. The safe
bet is to treat “data” as a plural noun:
The data fall within two standard deviations of the mean.
Not: The data falls within two standard
deviations of the mean.
If you wish to use a singular noun, use “data set,”
as in:
The data set was larger last week.
3.4.3 Voice
In grammar, voice refers to the person (people) or
thing(s) doing the action. There are two general
voices: active and passive. In the active voice, the
As Finkelstein (2005) writes: “Right or wrong,
good or bad- technical and scientific audiences
(often) expect passive voice in technical writing.”
While laboratory reports are generally written in
the passive, make sure you know what is expected
when you write other documents, both here at the
University and in professional practice.
Regardless of whether the active or passive
voice is used, you should always avoid the use of
the first person in technical writing. For example,
write:
Team 5 developed an experimental
plan.
Or: We developed an experimental
plan.
Not: I developed an experimental
plan.
3.4.4 Tense
Tense refers to when the action occurred. Many
students struggle with the correct verb tense. In
technical writing, use the present tense unless describing work done in the past. Some of your lab
reports will be about action done in the past. For
example, by the time you write the report, the experiment itself is already complete. Therefore,
you would write:
CHAPTER 3: ORGANIZING SECTIONS OF LAB REPORTS
18
The objective of the experiment was…
However, the report, theory, permanent equipment, and results still exist when the reader reads
the report. In this case, use the present tense:
The purpose of this report is …
Hooke’s Law concerns …
The tensile testing machine is…
The results show…
3.4.5 Pronouns
Pronouns are substitutes for nouns. Examples of
pronouns include the words he, she, it, they, and
them. An all-too-common problem with pronouns
in technical (and non-technical) writing is gender
bias. In the older technical literature, scientists and
engineers were identified as males. It used to be
common to write:
An engineer must trust his abilities.
[incorrect]
This construction is not proper, as it implies that
all engineers are men.
One approach to remedying this situation is
the use of the pronouns “they” or “their” in place
of “he” and “his.” This leads to the statement:
An engineer must trust their abilities.
[incorrect]
Unfortunately, the solution is grammatically incorrect. Why is it incorrect? In this case, the subject (“an engineer”) is singular and the pronoun
(“their”) is plural. A much better solution to
gender-specific pronouns is to rework the sentence
completely so that the subject and pronouns match
in number, as in:
Engineers must trust their abilities.
Mental Note
Avoid gender-specific pronouns
Another common problem is the proper use of
the pronouns “who,” “that,” and “which.” When
in doubt, use “who” for human subjects and “that”
or “which” for nonhuman subjects. The pronoun
“that” is used in reference to a specific noun, while
“which” adds information about a noun and usually is used in clauses set off by commas. Thus:
The teaching assistant who was supervising the lab compiled the data.
The human subject takes the pronoun “who.” On
the other hand:
The equipment that malfunctioned
was installed improperly.
Here, use “that” in referring to a specific piece of
equipment. (Which equipment? The equipment
that malfunctioned.) Finally:
The submitted lab report, which was
missing page three, earned an F.
In this case, use “which” to add information in a
separate clause. Often, you can avoid “who, that,
which” problems by incorporating the information
as adjectives. For the examples presented above,
you could write:
The supervising teaching assistant
compiled the data.
The malfunctioning equipment was installed improperly.
The submitted lab report was missing
page three. It earned an F.
3.4.6 Adjectives and adverbs
Adjectives modify nouns and adverbs modify
verbs. Avoid the use of long lists of adjectives,
sometimes called adjective chains. In adjective
chains, it is often difficult to identify the noun.
Consider the sentence:
High grade precut stainless steel
beams were analyzed.
19
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL REPORT MANUAL
The beam characteristics are clearer if the sentence
is rewritten:
Precut beams made of high-grade
stainless steel were analyzed.
Adjective and adverb placement also can be
problematic. You should avoid placing an adverb
between the word “to” and the verb. This construction is called a split infinitive. For example,
you should write:
The gear ratio was designed to drive
the system efficiently.
3.4.7 Capitalization and punctuation
Many neophyte technical writers find it necessary
to use nonstandard capitalization and abbreviations. Please do not give in to this temptation. Few
words in technical writing are capitalized. As
suggested by Smith and Vesiland (1996), you
usually capitalize the names of organizations,
firms, cities, counties, districts, agencies, and
states. In general, do not capitalize general references to these entities. Thus:
Not: The gear ratio was designed to
efficiently drive the system.
We analyzed drinking water from the
City of Buffalo.
Having railed against them, it should be noted
that split infinitives are a tricky construction. The
rule against split infinitives appears to stem from
Latin, where splitting an infinitive is impossible.
Place an adverb between “to” and the verb only to
emphasize the adverb or to produce a sentence that
sounds better. For example, the phrase:
(capitalize “city” because it is specific to Buffalo),
but:
To boldly go where no one has gone
before…
has a split infinitive, but sounds better (at least to
many people) than:
To go boldly where no one has gone
before…
Adjectives should be located next to the nouns
they modify. Consider the two sentences:
We only tested three specimens.
We tested only three specimens.
In the first sentence, “only” modifies “tested”: we
only tested the specimens rather than, say, testing
and constructing the specimens. In the second
sentence, “only” modifies “three” (which, in turn,
modifies “specimens”): we tested only three specimens, rather than four specimens. Make sure
that the adverb (or adjective) modifies only the
verb (or noun) you intend to modify.
The city water met all applicable standards.
(Do not capitalize “city” because it is a general
adjective here.) In addition, the titles of engineering studies and official titles of people are capitalized.
Standard abbreviations for scientific and engineering units and parameters should be used (see
Appendix E). If in doubt, define an abbreviation
the first time it is used. There is no need to capitalize the words as an abbreviation is defined. Thus:
The standard operating procedure
(SOP) was followed.
Not: The Standard Operating Procedure (SOP) was followed.
And not: The SOP was followed.
The last construction is improper if using the abbreviation for the first time, but desirable if the
abbreviation “SOP” already has been defined in
the document.
Common non-technical abbreviations include:
e.g. (exempli gratia = for example)
i.e. (id est = that is)
etc. (et cetera = and so forth)
et al. (et alia = and others)
CHAPTER 3: ORGANIZING SECTIONS OF LAB REPORTS
20
(Note: not abbreviated “et. al.” or
“et. al”)
These common abbreviations sometimes are italicized (e.g., e.g.) to indicate their non-English origins.
Commas should be used to define clauses and
separate items in a list. Usually, a comma is used
even before the last item in a list. For example:
Materials included cement, water, and
aggregate.
If the items in a list are long (or the items include
commas or conjunctions), then use semicolons to
separate them:
Materials included wood, natural materials, and fiber; steel and concrete;
and thermoplastic resins.
3.5 CITATION
You are professionally and morally obligated to
give credit when you use ideas from other people.
Taking someone else’s words or ideas without
credit is call plagiarism. Plagiarism is defined in
the University at Buffalo’s University Standards
and Administrative Regulations as:
copying or receiving material from a
source or sources and submitting this
material as one’s own without acknowledging the particular debts to
the source (quotations, paraphrases,
basic
ideas),
or
otherwise
representing the work of another as
one’s own
(Source: University at Buffalo Student
Conduct Rules, Article 3 a: University
Standards, Definitions of Academic
Dishonesty, definition b.)
Students who plagiarize will receive a score of
zero on the report and will be subject to disciplinary action.
Mental Note
Give credit for words or ideas that you use
Real World Alert
Engineers who plagiarize can lose their professional licenses.
Plagiarism is not just copying words from
someone else. Plagiarism also means taking
another person’s ideas without giving them due
credit. Always read your work carefully to make
sure that you have not inadvertently included
someone else’s ideas “without acknowledging the
particular debts to the source.”
Credit is shown by citing the work from which
the material was taken. There are many citation
styles. One style (employed in this manual) is to
list the author’s name and publication data (in parentheses) following the material cited, as in:
The model was taken from the work of
Smith (2002).
Numbers, usually written as superscripts (e.g.,
Smith2), may be used with a numbered reference
list.
In nearly all cases, you paraphrase the material (i.e., rewrite it in your own words). On rare occasions (when the original words are required), it
may be necessary to quote the words exactly. Quotation should be done sparingly and the citation
always must be given. Indicate a direct quotation
by the use of quotation marks or by doubly indenting the material.
An example of paraphrasing and quotation is
as follows. Consider the following original material (from Paradis and Zimmerman, 1997):
“Long sentences, often amounting to
more than 30 words, are usually too
complicated. Determine the main actions of the sentence. Then sort these
into two or more shorter sentences.”
You could use this material in several ways:
1. Paraphrase with citation (preferred approach):
21
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL REPORT MANUAL
Long sentences should be broken up
into smaller sections according to their
main actions (Paradis and Zimmerman, 1997).
2. Quotation using quotation marks with citation:
Run-on sentences can be problematic. According to Paradis and Zimmerman (1997): “Long sentences, often amounting to more than 30 words,
are usually too complicated. Determine the main actions of the sentence. Then sort these into two or
more shorter sentences.”
3. Quotation using indentation with citation:
Run-on sentences are confusing to
the reader. Several approaches have
been developed to identify and eliminate run-on sentences. For example:
Long sentences, often
amounting to more than 30
words, are usually too complicated. Determine the main
actions of the sentence. Then
sort these into two or more
shorter sentences. (Paradis
and Zimmerman, 1997).
It is plagiarism to write the following (work paraphrased, but no citation given):
Long sentences – some can be up to
30 words long – should be subdivided.
To do this, find its main actions and
create a shorter sentence for each
main action.
3.6 PROOFREADING EXAMPLE
To test your knowledge of grammar and for practice in proofreading, read the paragraph below and
list the errors you encounter. Allow 60 seconds
for this exercise. You should review Appendix D
before proofreading the paragraph.
Warning: The following text may contain errors!
Abstract
Project personnel conducted a laboratory
study to definitively determine the engineeering feasability of polychlorinated biphenyl (PCB) removal by granular activated carbon.
The study used an expanded bed granular activated carbon reactor in the upflow mode. PCB concentrations in the column effluent was measured
by standard techniques. Study data is
consistent with surface diffusion as the
rate-limiting step, although much scatter in
the data is observed. Columns were sacrificed at the conclusion of the study and
carbon analysis revealed PCB saturation
is the first 50 percent of the bed. Future
studies will be conducted on the affect of
the recycle rate on column performance.
A list of errors (with the corresponding section
numbers in parentheses) is given below:
CHAPTER 3: ORGANIZING SECTIONS OF LAB REPORTS
First sentence: The phrase “to definitively determine” is a split infinitive (3.4.6). In addition, the
words “engineeering” (engineering) and “feasability” (feasibility) are misspelled (1.3.2).
Second sentence: The phrase “...expanded bed
granular activated carbon reactor…” contains an
adjective chain (3.4.6).
Third sentence: This sentence contains a subject/verb mismatch (“...concentrations … was...”)
(3.4.2). Use of the passive voice (3.4.3) is discouraged, unless it is clear who analyzed the samples
from other parts of the report.
Fourth sentence: This sentence contains a subject/verb mismatch (“...data is...” ) (3.4.2). The
phrase “...much scatter in the data is...” is fine,
since the subject (“scatter”) is singular.
Fifth sentence: This sentence is a run-on sentence
(3.2). Also, the sentence should read “...saturation
in the first...” (rather than “...saturation is the
first...”).
Sixth sentence: Use of the passive voice is inconsistent with the active voice used elsewhere in the
paragraph (3.4.3). Also, “affect” should be “effect” (Appendix D).
An improved version of the abstract is shown below:
Abstract
Project personnel conducted a laboratory
study to determine definitively the engineering feasibility of polychlorinated biphenyl (PCB) removal by granular activated carbon (GAC). The study used an
expanded bed GAC reactor in the upflow
mode. A contract laboratory measured
PCB concentrations in the column effluent
by standard techniques. Study data are
consistent with surface diffusion as the
rate-limiting step, although much scatter in
the data is observed. Columns were sacrificed at the conclusion of the study. Carbon analysis revealed PCB saturation in
the first 50 percent of the bed. We plan to
conduct future studies on the effect of the
recycle rate on column performance.
22
3.7 SUMMARY
Lab reports must be organized at the paragraph,
sentence, and word level. Choose words to make
your writing concise, simple, and specific. In your
technical writing, be aware of the rules of grammar and spelling. Strive to use the active voice
and avoid gender-specific language. Always proofread your work before allowing it to leave your
hand.
Chapter 4
Manipulating and Communicating Data
Y
ou will collect large amounts of data in the
labs this year. Your job as an engineer is
not completed until the data are manipulated properly and presented in a meaningful way
in your lab reports. In this chapter, the methods of
manipulating data, comparing data with models,
and presenting data will be presented.
4.1 IMPORTANCE OF UNITS
4.1.1 Introduction
Most of the numbers you will deal with as an engineer have units. For example, a voltmeter does
not measure 6.2; it measures 6.2 millivolts. A successful engineering calculation results in not only
the right value, but also the right units for that value.
The units for many physical properties have
been standardized. The standardized system of
units is called the Système Internationale d’Unitès
or SI units. A list of SI units appears in Appendix
D.
4.1.2 Dimensional analysis
One tool for checking the units of an expression is
dimensional analysis. Dimensional analysis refers to the manipulation of units without numbers.
This technique can be used to determine the units
of a result of an engineering calculation. Dimensional analysis also can be used to determine the
units of an unknown variable.
As an example, dimensional analysis can be
used to determine the units of viscosity. Viscosity
refers to the property of a fluid offering resistance
to flow. It is formally defined as the ratio of the
shearing stress to the shear. The shearing stress is
a force per unit area and the shear is the change in
the velocity with respect to distance. Thus:
{viscosity} 
{shearing stress}
{shear}
 {force} 


{area} 


 {velocity} 


 {distance} 
  kg  m  


2

 s
 m2






 m 
 
 s 
 m 




kg

m-s
The units of viscosity, denoted {viscosity}, are kg
per m per s. Common units of viscosity are centipoise = cp = 0.01 g/cm-s. The viscosity of water,
chocolate syrup, and peanut butter at room temperature are about 1 cp, 6104cp, and 2105 cp,
respectively.
4.1.3 Units and functions
Dimensional analysis leads to four rules when you
perform an operation on a number. First, you can
add or subtract numbers only when they have the
same units. You can use this fact to check equations and calculations in your lab reports: additive
terms must have the same units.
Second, when you multiply, divide, or exponentiate (i.e., the raise a number to an exponent),
you must perform the same operation of the units
of the number. An example was shown in Section
4.1.2 for determining the units of viscosity.
Third, some mathematical functions can operate only on dimensionless parameters. Examples
of such functions include the exponential, logarithmic, and trigonometric functions. For the
CHAPTER 4: MANIPULATING AND COMMUNICATING DATA
functions eax, log(y/b), and cos(2πω), you know
that the terms ax, y/b, and 2πω must be dimensionless.
Fourth (a corollary to the third rule), exponential, logarithmic, and trigonometric functions also
produce dimensionless results. In other words, the
values produced by the functions eax, log(y/b), and
cos(2πω) are dimensionless.
As before, dimensional analysis can be used to
check units or determine units, since the collection
of terms operated on and produced by exponential,
logarithmic, and trigonometric functions must be
dimensionless. For example, in first-order chemical reactions, concentrations decrease over time by
e  k1t ,where k1 is called the first-order rate constant
and t is time. The exponent, -k1t, must be dimensionless. If time has units of seconds, then the
first-order rate constant must have units of inverse
seconds (denoted 1/s or s-1). In other words, firstorder rate constants always have units of 1/time.
4.2 ACCURACY, PRECISION,
SIGNIFICANT DIGITS, AND
ROUNDING
4.2.1 Introduction to accuracy and
precision
Engineers measure characteristics of the real
world. If life were perfect, then you could collect
data and determine exactly the parameter of interest to you. This is almost never the case. As an
example, consider a lab in which you must measure the length of a beam. Common experience
tells you that if you performed the measurement
numerous times, you may get different results. If
each one of your lab-group partners made the
measurement, you would likely get even more variety in the responses. In spite of the variability,
there is one true distance (at least, one true distance when measuring at a fixed scale).
4.2.2 Accuracy
How can you describe how closely your measurements are to the true answer? The relationship
between measurements and the true value is called
accuracy. A measurement is said to be accurate if
it is near the true value. How near the true value?
24
Accuracy depends on tolerance (i.e., the allowable
error.) For example, 1% error in the measurement
of a birdhouse part may be acceptable (i.e., the
measurement considered accurate), while a measurement error of 1% in a telescope mirror may be
unacceptable (i.e., the measurement considered
inaccurate).
4.2.3 Precision
The relationship between repeated measurements
is called precision. A set of measurements is said
to be precise if the measurements are similar in
value. For example, suppose the measurements of
the beam’s length are 31.6, 31.5, 31.6, and 31.4
cm. This set may be said to be precise (although
inaccurate if the beam is machined to be 40.0 cm
long).
You may have seen the concepts of accuracy
and precision illustrated with a dartboard or archery target. If the goal is to hit the bull’s eye, then
accurate shots are near the bull’s eye and precise
shots are clustered together (but not necessarily
near the bull’s eye).
4.2.4 Reporting data
The concepts of precision and accuracy do not
help you to record data and calculations. A particularly troublesome area of data and calculations
reporting is the number of decimals places to report. In the beam-measuring problem, suppose
you and a friend measure the length of a beam to
be tested. You use a meter stick and find the distance to be 40.6 cm. Your friend uses a yardstick
and finds the distance to be 15 11/16 inches. Your
friend realizes that the answer is supposed to be
reported in centimeters and performs the following
conversion:
length
= (15 11/16 inches)×
(2.54 cm/inch)
= (15.6875 inches)×
(2.54 cm/inch)
= 39.84625 cm
Thus, your friend reports the distance as 39.84625
cm. Is it really true that your measurement is only
accurate to the nearest 0.1 cm, but your friend’s
measurement is accurate to 0.0001 cm? The answer is, emphatically: no! Just because your cal-
25
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL +REPORT MANUAL
culator reports five figures after the decimal point
does not mean that the measurement is accurate to
five figures after the decimal point.
Mental Note
Do not blindly report the number of decimal
places provided by your calculator or spreadsheet
How should you report measurements? Report
one more digit than the number of digits you are
certain about. In other words, the last digit is understood to be estimated and may include some
uncertainty.
An example will help here. Suppose you are
weighing concrete test specimens to test the
strength of a new concrete formulation. The scale
is marked in grams. You interpolate between
gram markings to estimate tenths of grams. It
would be proper to report a weight of 79.6 g.
When another engineer reads this number, he or
she will know that there is some uncertainty in the
tenths of grams, because it is the last digit reported.
to mentally separate each digit, ignoring the decimal place. One way to do this is to put each
number in a box:
0.
0
5
0
4
Counting the boxes from left to right, the first box
containing a non-zero digit is the third box from
the left. Number this box “1” and continue counting from left to right until you run out of digits:
0.
0
Box #
5
1
0
2
4
3
count in this direction
The last box is the third numbered box. Thus,
0.0504 has three significant digits. How many
significant digits are in the number 120.0? Repeating the procedure by separating each digit (ignoring the decimal place):
1
2
0.
0
4.2.5 Significant digits
The number of decimal places to report is not always as obvious as in the weighing example
above. To determine the number of decimal places, it is important to understand the idea of significant digits (or significant figures). Determine the
number of significant digits by the following procedure (for numbers containing a decimal place):
1. Starting on the left side of the number,
move right until you encounter the first
non-zero digit (ignoring the decimal
place). Count this first non-zero digit as
“one.”
2. Continue moving to the right, counting
each digit (still ignoring the decimal
place). When you reach the last digit of
the number on the right, you have counted
the number of significant digits.
As an example, count the number of significant digits in the number 0.0504. It is a good idea
Counting the boxes from left to right, the first box
containing a non-zero digit is the first box from
the left. Number this box “1” and continue counting from left to right until you run out of digits:
Box #
1
1
2
2
0.
3
0
4
count in this direction
The last box is the fourth numbered box. Thus,
120.0 has four significant digits
4.2.6 Exceptions to the rule: numbers with
no decimal point and exact numbers
The procedure in Section 4.2.5 for counting the
number of significant digits works for most numbers. The rule implies that leading zeros to the left
of the decimal point are ignored. What about
numbers with no decimal point? Does the number
CHAPTER 4: MANIPULATING AND COMMUNICATING DATA
8 have the same number of significant digits as 8.,
or 8.0, or 8.00? Numbers without decimal places
are tricky. It is clear from Section 4.2.5 that 8.,
8.0, and 8.00 have one, two, and three significant
digits, respectively. However, you do not know
how many significant digits there are in the number 8 when it is written without a decimal point.
To avoid this uncertainty, refrain from writing
numbers without decimal points. If you wish to
indicate three significant figures with the number
seven hundred, write it as “700.” not “700” (i.e.,
write it with a decimal point). (In addition, always
include a leading zero when reporting numbers
between 1 and –1. It is much clearer to the reader
if you write –0.14 or 0.56 than if you write the
numbers as –.14 or .56.)
You also can use scientific notation to show
the number of significant digits. Count the number of significant digits in a number in scientific
notation by applying the procedure of Section
4.2.5 to the mantissa. Thus, the numbers 7.102,
7.0102, and 7.00102 have one, two, and three
significant digits, respectively. (Again, mantissas
without decimal places are tricky: avoid writing
numbers such as 7102.)
What about exact numbers? You may wish to
do calculations that involve numbers that are exact. Exact numbers have no variability. For example, there are exactly 100 cm in a meter, exactly
three feet in a yard, and exactly eight sides in an
octagon. In engineering calculations, you may
wish to incorporate exact numbers into calculations.
How many significant digits are there in an
exact number? Exact numbers are treated as if
they have an infinite number of significant digits.
This may seem a little strange at first, but as you
will see in Section 4.2.8, the number of significant
digits in exact numbers is ignored in calculations.
4.2.7 Rounding and calculations
Always report your calculations with the number
of significant digits consistent with the data. Determining the number of significant digits involves
two steps: deciding which digits to drop and deciding what to do with the digits you report. The latter process is called rounding.
There are two simple rules for rounding:
26
1. If the digit to be dropped is less than five
(5), then write the last digit retained as is.
2. If the digit to be dropped is greater than or
equal to five, then increase the last digit
retained by one.
For example, if you determine that four significant
digits are appropriate, you would round 95.673 to
95.67 (since the digit dropped, 3, is less than 5).
Similarly, if you determine that five significant
digits are appropriate, you would round 0.0124457
to 0.012446 (since the digit dropped, 7, is greater
than 5).
How do you determine the appropriate number
of significant digits in a calculation? Two rules
will suffice here:
1. When multiplying or dividing numbers,
report the result to the number of significant digits of the value with the smallest
number of significant digits.
2. When adding or subtracting numbers, report the result to the number of decimals
places of the value with the smallest number of decimal places.
It is important to note the difference between how
numbers are reported in different calculations. In
multiplication and division, the reported value is
based on the smallest number of significant digits
in the calculation. This rule implies that the product or division of numbers cannot be more precise
than the least precise number.
For example your calculator may report:
56.122 ÷ 2.31 = 24.2952381
(Warning: too many digits reported)
How would you round the results of this calculation? You round the result to 24.3, because the
smallest number of significant digits in the numbers on the left side of the equation is three (the
number 2.31 has three significant digits).
In addition and subtraction, the second rule
says that the reported value is based on the smallest number of decimal places (numbers to the
right of the decimal place) in the calculation. As
an example, your calculator may report:
27
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL +REPORT MANUAL
23.52 + 4.215 + 6.1 = 33.835
(Warning: too many digits reported)
How would you round the results of the calculation of 23.52 + 4.215 + 6.1= 33.835? You round
the sum to 33.8, because the number 6.1 has only
one digit to the right of the decimal point. Note
that the sum is reported to three significant digits,
even though one of the numbers on the left side
(the number 6.1) has only two significant digits.
One last caveat concerning reporting the results of calculations. Exact numbers play no role
in determining the number of digits reported.
Why should exact numbers not affect the number
of reported digits in multiplication and division?
Recall from Section 4.2.6 that exact numbers are
treated as having an infinite number of significant
digits. Thus, exact numbers do not affect the
number of reported digits in multiplication and
division. Why? Exact numbers can never have
the smallest number of significant digits and can
never control the number of digits reported.
In addition and subtraction, it also makes
sense that exact numbers should not play a role in
determining the number of digits reported. For
example, suppose you are trying to convert a temperature reading from degrees Kelvin to degrees
Celsius. A temperature of zero degrees Kelvin
(0oK) is defined to be exactly –273.16oC. Thus,
298.103oK is equal to –273.16 + 298.103 =
24.943oK. You report this temperature to three
decimal places because the number “–273.16” is
exact and does not affect the number of decimal
places reported.
4.3 ENGINEERING MODELS
In your labs, you often will compare your measured values with preconceived notions of how nature works. The preconceived notions, based on
scientific principles, are called models. For example, you might wish to confirm that the acceleration of an isolated beam is consistent with the
model: F = ma.
You also will use empirical models. Empirical models are not based on scientific principles,
but used to describe the data in a convenient manner. An example is a sixth-order polynomial used
to draw a smooth curve through the data. Be care-
ful not to overinterpret empirical models. The
mechanics of fitting models to data is described in
Appendix E.
4.4 ERROR ANALYSIS
4.4.1 Introduction to error analysis
In your experiments, you will be making many
measurements (e.g., weight, length, diameter, voltage, and water pressure) and all these measurements will be subject to some uncertainty. Error
analysis is the study and evaluation of these uncertainties. As an engineer, you will need to estimate
how large the uncertainties are and to understand
how to make them smaller, when necessary. It
should be clear here that the word error does not
mean mistake or blunder, but rather the inevitable
uncertainty that occurs when measurements are
made. Different methods of measurements have
different levels of uncertainty. The measured value is reported as:
measured value = best estimate ± uncertainty
Assume that you want to know the diameter of a
steel reinforcing bar. The method you use to
measure the diameter will depend upon the accuracy you require. If you need only an approximate
answer, you may be satisfied with estimating the
diameter. Perhaps you can determine that the diameter of the bar is ½ in, with an uncertainty of ±
⅛ inch. If you require a more accurate measure of
the bar diameter, you may choose to use a ruler,
which may have an accuracy of ±1/16 inch, or you
may use vernier calipers. Good experimental design requires that you pick the technique with the
required level of accuracy.
4.4.2 Propagation of uncertainty
Once you have determined the uncertainty in each
measurement, you need to determine how the uncertainties will affect the quantity you want to calculate. Suppose you want to determine the density
of a concrete cylinder. Since density (γ) is weight
per unit volume, you need to determine the weight
(W), length (L), and diameter (D) of the concrete
specimen. Knowing the uncertainty in the mea-
CHAPTER 4: MANIPULATING AND COMMUNICATING DATA
surement of W, L, D, the next step is to determine
how these uncertainties propagate through to the
density. The rules for propagation of uncertainty
are different depending whether you are adding
and subtracting quantities, or multiplying and dividing them.
For addition and subtraction:
If several quantities x,….., w are
measured with small uncertainties
dx,……, dw, and the measured values
used to compute
q  x  ....  z  (u  .......  w)
then the uncertainly in the computed
value of q is the sum of the original
uncertainties
dq  dx  ....  dz  du  .....  dw
28
When quantities are multiplied or divided, the
fractional uncertainties add, therefore
d


dW
dD dL
2

W
D
L
In words, the fractional uncertainty in the density
is equal to the fractional uncertainty in the weight,
plus twice the fractional uncertainty in the diameter, plus the fractional uncertainty in the length.
If W = 28 lb, D = 6 in, and L = 12 in, our best
estimate of the density is γ = 0.083 pci (140 pcf).
Now if the uncertainties are dW = ±0.5 lb, dD =
±1/32 = 0.03 inch, and dL = ±1/32 = 0.03 inch,
then:
d
0.03 0.03
0.5

2

 0.03
6
12
0.08252 28
d  2.5 103 pci  4 pcf
For multiplication and division:
If several quantities x,……, w are
measured with small uncertainties
dx,……, dw, and the values are used
to compute
q
x  ........  z
u  ........  w
then the fractional uncertainty in the
compute value of q is the sum of the
fractional uncertainties in x,…., w
dq dx
dz du
dw

 ...... 

 ..... 
q
x
z
u
w
Returning to the example, the equation for density
is given by:

W
W

V D 2
L
4
The density should therefore be written: γ=140±4
pcf. The best estimate of the density is 140 pcf,
but the actual density may range from 136 pcf to
144 pcf.
In the above example, the final uncertainty
assumes the extreme values of all measurements
occur at the same time. This approach will certainly give an upper bound on the uncertainty, but
is it realistic? If the original uncertainties are
random and independent a more realistic (and
smaller) estimate of the final uncertainty is given
by similar rules in which the uncertainties (or fractional uncertainties) are added in quadrature. The
full rules can therefore be restated (Taylor, 1997).
For sums and differences:
Suppose x,….., w are measured with
uncertainties dx,……, dw, and the
measured values are used to compute
q  x  ....  z  (u  .......  w)
If the uncertainties in x,…., w are
known to be random and independent,
then the uncertainly in the computed
value of q is the quadratic sum of the
original uncertainties:
29
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL +REPORT MANUAL
dq 
dx 2  ....  dz 2  du 2  .....  dw2
In any case, dq is never larger than
their ordinary sum
dominate the final result. This fact can be used to
your advantage to simplify error calculations. If
one term has a fractional error of 5% and the other
terms have a fractional error of 1%, only the first
term need be considered.
dq  dx  ....  dz  du  .....  dw
4.5 USES OF FIGURES AND TABLES
For multiplication and division:
4.5.1 Introduction
Suppose that x,……, w are measured
with uncertainties dx,……, dw, and the
values are used to compute
q
x  ........  z
u  ........  w
If the uncertainties are independent
and random, then the fractional uncertainty in q is the sum in quadrature of
the original fractional uncertainties
2
2
2
 dx 
 dz   du 
 dw 
dq
    ......        .....   
q
 x 
 z   u 
 w
In any case, it is never larger than
their ordinary sum
dq dx
dz du
dw

 ......  
 ..... 
q
x
z
u
w
If we assume the measurement errors in
the concrete weight, length and diameter
are random and independent, the uncertainty in the density can be recalculated.
2
Nearly every technical presentation you develop
will contain data. The number of ways of presenting quantitative information is limited only by
your imagination. However, some data presentation tools are more appropriate in a given situation
than others.
The two main ways to present numbers are
tables and figures. Tables are used when the actual values are important. For example, a table
would be an excellent way to show the estimated
construction, operation, and maintenance costs for
three highway on-ramp designs. In this case, the
exact costs are important and the audience wants
to see the numbers.
On the other hand, figures are used to show
trends in the data: that is, to show the relationships
between variables. For example, suppose you collect data on the movement of an actuator in response to stimuli of varying voltage. A figure
would be an appropriate way to show the trend in
the dependent variable (here, the actuator movement) as a function of the independent variable
(here, the applied voltage).
4.5.2 Common characteristics of tables and
figures
While tables and figures are very different, they
share several features. First, every table and figure
must have a number. Many numbering schemes
are possible (e.g., “Table 1” or “Figure 4.2” or
d
2
2
2
 1.8%   20.5%   0.3%   3.8%  1.8% “Table II” or “Figure C”), but table and figure
0.08252
numbers are essential, especially in technical writing. Why number your tables and figures? A
d  3 pcf
number allows the figure or table to be referred to
So: γ=140±3 pcf
from the text. For example, you may write in the
text:
Use of the quadratic sum leads to a smaller
estimate of the error. In addition, the terms with
the largest fractional error (in this case the weight)
d
2
2
 dW 
 dD   dL 
 
  2
  

 D   L 
 W 
2
CHAPTER 4: MANIPULATING AND COMMUNICATING DATA
Remember: do not include a table or figure that is
not referred to by number in the text.
Mental Note
Do not include a table or figure that is not first
introduced in the text
Second, every table and figure must have a
title. Titles are needed to give the audience a short
description of the content of the table or figure.
Titles should be concise and descriptive. They
need not be complete sentences. Examples of table and figure titles are listed in Table 4.1. The
numbers and titles appear together either at the top
or bottom of the table or figure. Commonly (but
not universally), table titles are placed at the top of
tables and figure titles are placed at the bottom of
figures. (Note that Table 4.1 has a number and
title located together at the top of the table. Also,
Table 4.1 was referred to in the text, so you knew
when to look at it.)
Mental Note
Every table and figure must have a title and a
number
Third, tables and figures must be interpreted.
This means that you should summarize of the main
points in the table or figure when you refer to the
table or figure for the first time. To continue the
example above, you may write:
In Figure 2.3, the average concrete
density is plotted against the percentage aggregate content. Note that the
average concrete density appears to
increase linearly with the percentage
aggregate content.
Many inexperienced technical writers make the
mistake of simply throwing the data at the audience rather than presenting the data. They write:
The data from the first study are
shown in Figure 2.3. A second study
was conducted in May, 2005.
You included the table or figure for a reason. To
satisfy that reason (and help you achieve your
presentation goals), you need to guide the audience through the interpretation of the data in
your tables and figures.
Fourth, units must be listed for all data in
tables and figures. In tables, units usually accompany the column or row headings. In figures, the
axes must be labeled with units shown.
4.5.3 Figure structure
Recall that figures are used when the relationships
between variables are important. There are three
common types of figures used in technical presentations: scatter (or x-y) plots, bar charts, and pie
charts.
Scatter plots. The scatter plot (or x-y plot) is
the most common type of graph in technical work.
It is used when the independent variable is continuous: that is, when the independent variable
could take any value. Examples of continuous
variables are time, flow, and voltage. In the scatter plot, the independent variable is plotted on the
x-axis (also called the abscissa) and the dependent
variable (or variables) is plotted on the y-axis (also
called the ordinate). In general, symbols are used
for data and lines are used for calculated values
(i.e., for model fits or model predictions). An example of a scatter plot is shown in Figure 4.5.
Heat of Vaporization
(BTU/lb)
In Figure 2.3, the average concrete
density is plotted against the percentage aggregate content.
30
600
500
400
300
200
100
0
0
200
400
Vapor Pressure (psi)
Figure 4.5: Heat of Vaporization of Some
Common Refrigerants
(an example of a scatter plot)
600
CHAPTER 5: MANIPULATING AND COMMUNICATING DATA
31
Table 4.1: Examples of Poor and Improved Table and Figure Titles
Poor Title
Problems with Poor Title
Improved Title
Table 2: Experimental
Data
too vague: what data will the table
contain?
Table 2: Ergonomic Data for Three Automobile Seat Designs
Figure 4.2: Problems
with Acid Rain
insufficient detail: figure titles
usually list the dependent and independent variables
Figure 4.2: Effects of pH on the Survivorship of Brown Trout in Lakes Receiving
Acid Rain
Figure A.32: Current vs
Voltage
insufficient detail: lists only the dependent and independent variables
without putting the information in
context
Figure A.32: Current-Voltage Curves for
Four Electrode Configurations
Bar charts. Bar charts are used when the
independent variable is discrete (i.e., not continuous). Discontinuous independent variables are
common in engineering. For example, you may
wish to show how the properties of steel vary with
material type or how energy efficiency varies with
pump category. The type of material or category
of pump is a discrete variable and the use of a bar
chart is appropriate.
Heat of Vaporization
(BTU/lb)
In Figure 4.5, the independent variable (vapor
pressure) is continuous. Thus, a scatter plot is appropriate. Note the important elements: figure title
(here, at the bottom of the figure), axes titles with
units, tick marks (small lines) near axes labels, and
the use of symbols for data. If more than one dependent variable were plotted, a legend would be
necessary. Note that a legend is not necessary if
only one dependent variable is plotted. (Legends
are discussed with bar charts below.)
One final note on scatter plots. Most common
graphing programs (including Microsoft Word,
Microsoft Excel, Corel WordPerfect, and Corel
QuattroPro) have a figure type (also called a chart
type) called “line.” In the line chart type, the x
data points are spaced evenly, regardless of their
values. The data in Figure 4.5 are replotted as a
line chart in Figure 4.6. Notice that the relationship between heat of vaporization and vapor pressure appears to be distorted in the line chart. There
are very few cases where the line type is the best
way to present technical data. It is recommended
that you avoid the line chart type completely.
600
500
400
300
200
100
0
23
23
37
45
62 504
Vapor Pressure (psi)
Figure 4.6: Heat of Vaporization Data
Replotted as a Line Plot
(data identical to Figure 4.5)
Mental Note
Avoid using the line chart type
An example of a bar chart is given in Figure
4.7. Note the descriptive title, inclusion of units,
and tick marks on the y-axis. Tick marks general-
32
65000
3
55000
2.5
45000
35000
2
25000
1.5
Aluminum Copper
Resistivity
15000
Gold
Silver
Tensile strength
3
2.5
2
1.5
1
0.5
0
Aluminum Copper
Resistivity
80000
60000
40000
20000
0
Gold
Silver
Tensile strength (lb/in)
Resistivity ( cm)
Figure 4.8: Bar Chart with Skewed y-Axes
Tensile strength
Figure 4.7: Physical Properties of Conductors
(an example of a bar chart with a legend)
In both scatter and bar charts, you must select
the ranges of the axes carefully. Clearly, the
ranges must be selected to encompass all data. In
addition, it is a good idea to start the y-axis at zero
(unless you have negative y values). Why? Starting at zero gives the audience a better view of the
relative values of your data. In Figure 4.7, for example, it is obvious that the tensile strength of silver is about twice that of gold. If the data are replotted using smaller ranges for the y-axes, a
skewed view of the relative resistivities and tensile
strengths is created (see Figure 4.8). For example,
the tensile strength of silver appears to be about
five times that of gold in Figure 4.8.
This lesson can be extrapolated. In general,
do not let the software pick the look of your tables
and figures. Always look critically at the default
table or figure produced by the software package.
Use your judgment: edit tables and figures to best
meet your presentation goals.
(data identical to Figure 4.7)
Pie charts. Pie charts are used to show the
relative contributions of several factors to a whole.
In most cases, pie charts are used to show percentages. Thus, pie charts have no independent variable. Although pie charts are not used very frequently in engineering, they can show the relative
importance of discrete factors very effectively.
An example of a 3-D pie chart is shown in
Figure 4.9. The slices of the pie may be defined
with a legend or labels. Slice labels are used in
Figure 4.9.
Bathtub
or
show er
Toilet
Faucets
Washing
m achine
Figure 4.9: Water Use in the Home
(an example of a pie chart)
Mental Note
Do not let the software pick the look of your
tables and figures
Tensile strength (lb/in)
ly are not used on the x-axis in bar charts with vertical bars, since the tick marks would interfere
with the bars. Also note in Figure 4.7 that two yaxes are used. Multiple y-axes are useful when the
independent variables have different units or vastly different scales.
In the bar chart in Figure 4.7, two variables are
plotted and therefore a legend is required. A legend tells the audience the meaning of each symbol, bar, or line. In this case, the legend tells you
that the white bar represents the resistivity and the
black bar represents tensile strength.
Resistivity ( cm)
CHAPTER 4: MANIPULATING AND COMMUNICATING DATA
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL +REPORT MANUAL
33
Table 4.3: Characteristics of Standard Steel
Reinforcing Bars
4.5.4 Table structure
As stated previously, tables are used to present
data when the actual values are important. Tables
should be limited to the minimum number of columns needed to show the relevant data. In general, independent variables are listed in the first or
leftmost column(s), with dependent variables
listed in columns to the right.
With today’s software, it is easy to create wild
tables with myriad types of lines, shadings, colors,
and font styles. However, these devices should be
used sparingly and consistently. Each table has a
goal and the “bells and whistles” should be used
only to make your point clearer.
An example of a table is given in Table 4.2.
Table 4.2: Characteristics of Standard Steel
Reinforcing Bars
(example table with column order changed caution: table illustrates problems!)
Weight (lb/ft)
0.167
0.376
0.668
1.043
1.502
#2
#3
#4
#5
#6
Diameter (in)
Weight (lb/ft)
0.250
0.375
0.500
0.625
0.750
0.167
0.376
0.668
1.043
1.502
Table 4.2 is well constructed. Note that the table
is numbered and has a descriptive title. The independent variable (reinforcing bar type) is listed
first. Units are given for all data (i.e., for every
column). Lines are used minimally and mainly
serve to separate the table from the surrounding
text.
To demonstrate the importance of the order of
the columns, examine Table 4.3. Table 4.3 contains the same data as Table 4.2, but the column
order has been change. Note how difficult it is to
interpret Table 4.3. Even though the most important information probably is the weight, placing a
dependent variable first does not communicate the
information very effectively.
Table 4.4 demonstrates the potential distractions in table design. The use of many fonts, lines,
and types of shading adds little to the message and
can be distracting.
Diameter (in)
#2
#3
#4
#5
#6
0.250
0.375
0.500
0.625
0.750
Table 4.4: Characteristics of
Standard Steel Reinforcing Bars
(example table with distractions caution: table illustrates problems!)
(an example of a table)
Type
Type
Type
#2
#3
#4
#5
#6
Diameter
(in)
Weight
(lb/ft)
0.250
0.375
0.500
0.625
0.750
0.167
0.376
0.668
1.043
1.502
4.6 SUMMARY
Keep in mind that most numbers in engineering
have units. Use dimensional analysis (i.e., manipulating units without numbers) to check equations and determine the units of unknown quantities. Remember that many functions operate on
and produce only dimensionless values.
In your labs, you will generate and use data.
Data may have errors, described qualitatively by
the concepts of precision and accuracy. Calculated values should be presented with an appropriate number of significant digits (usually not the
number given by your calculator or spreadsheet).
CHAPTER 4: MANIPULATING AND COMMUNICATING DATA
Measurement errors can propagate through
calculations. A formal error analysis can help you
determine the impact of measurement errors on
calculated values.
Engineers often rely on models to analyze data. Models are preconceived notions based on
scientific principles. Empirical models are not
based on science. Be careful in overinterpreting
the fit of empirical models.
Use the proper technique to present data.
Tables are used when the actual values are important, while figures are used to show trends in the
data. Every table and figure must have a number
and a descriptive title. In addition, every table and
figure must be referred to from the text of a written document and its main points summarized.
Be sure to use the most appropriate type of
figure: scatter (x-y) plots when the independent
variable is continuous, bar charts when the independent variable is not continuous, pie charts to
show relative proportions, and line charts almost
never. Look critically at the default table or figure
produced by software and ask how it could be
modified to best meet your presentation goals.
34
Chapter 5
Tools
T
o produce excellent lab reports, you have
several tools at your disposal. This chapter
reviews the use of Microsoft Word and Microsoft Excel for the production of lab reports and
other technical documents. In addition, the use of
Microsoft Excel for linear regression and nonlinear optimization also is reviewed.
5.1 USING MICROSOFT WORD
5.1.1 Introduction
It is assumed that you have a firm grasp of the basics of creating a document in Word. The basic
unit in Microsoft Word is the paragraph. Once
you format a paragraph in Microsoft Word, the
formatting will remain until you change it. It is
expected that you can:
1. Create a basic document
2. Change font type and weight (italics, boldface, etc.)
(Main Menu: Format●Font… or buttons
on the Formatting Toolbar)
3. Add page numbers
(Main Menu: Insert●Page Numbers…)
to Main Menu: Options and click the Spelling &
Grammar tab. At a minimum, check the boxes
labeled:
Check spelling as you type
Always suggest corrections
Check grammar as you type
Potential grammar and spelling errors will be highlighted with a wavy underline, as in “frnctional.”
Using the grammar checker is an excellent way to
learn more about grammar and improve your technical writing.
When spell checking, be extremely careful
about accepting Microsoft Word’s suggestion for a
replacement. For example, if you misspell the
word functional as “frnctional,” Microsoft Word
will suggest the replacements frictional, fractional, and functional. Blindly accepting the first suggestion will lead to an unreadable document.
5.1.3 Equation editor
As an engineer, you frequently will need to insert
equations into lab reports or other technical documents. Microsoft Word has an embedded equation
editor. The equation editor allows you to present
equations in a more readable form. For example,
an equation can be written like this:
 e a x
y  sin 
 2
1
4. Get help
(Main Menu: Help●Microsoft Word Help
or F1).
The remainder of this section is devoted to more
advanced topics in Microsoft Word.
5.1.2 Spell checking and grammar checking
You can access the spell- and grammar-checking
functions through the Main Menu (Tools●Spelling
and Grammar…) or by pressing F7.
It is recommended that you allow Word to
highlight potential errors in spelling and grammar
as you type. To show possible errors real-time, go




rather than like this:
y = sin(exp(–a1x)/2π)
The equation editor is accessed by Main
Menu: Insert●Object…, then select Microsoft Equation X.X from the Create New tab. (A common
version of the equation editor is Microsoft Equation 3.0.) Once loaded, the equation editor will
open a special equation box and a window containing symbols in a palette, as shown in Figure
5.1. You may wish to play with using the palette
to obtain the equation you desire.
CHAPTER 5: TOOLS
36
5.1.4 Group tools
Figure 5.1: Microsoft Word’s Equation Editor
The equation editor is an excellent tool for
learning about modern typography in technical
documents. For example, it is common practice
to:




Write variable names in italics
Write mathematical function names in
plain text
Use – rather than a hyphen (-) for a minus
sign
Write numbers (including numbers in superscripts and subscripts) in plain text
Examples include:
F = ma
y = cos(αt)
C = C0e–at
(note plain text for the numeral 0)
If you have questions about the proper formatting,
then type the equation into the equation editor to
see an example.
One final caveat on using the equation editor
should be noted. The equation editor often will
interpret words it does not recognize as variable
names and italicize them. For example, the equation editor will produce:
stress  E (strain)
You can eliminate the incorrect italicizing by selecting the offending text in the equation editor
and selecting from the Equation Editor Menu:
Style●Text to obtain, for example:
stress = E(strain)
Microsoft Word allows you to track any changes
made in a document. This allows a group of
people to edit a document and see the changes
made by other members of the group.
To turn on the tracking feature, go to Main
Menu:
Tools●Track
Changes●Highlight
Changes…, then check the box called “Track
changes while editing.” For more information, see
the Microsoft Word Help feature.
5.2 USING MICROSOFT EXCEL
It is assumed that you know the basics of Microsoft Excel (how to enter data, how to enter formulas using relative and absolute referencing, and
how to create a simple figure). Microsoft Excel
can be used to help produce sophisticated technical documents. A few examples of the use of Microsoft Excel in producing lab reports will be given.
Using the text and column/row formatting features, Microsoft Excel can produce publicationquality tables. In addition, calculations can be
performed in Microsoft Excel and tabular data imported into Microsoft Word by simply copying
and pasting. Watch out for too many “bells and
whistles” in formatting (see Section 5.4.4). Also,
make sure that the numbers are displayed with the
proper number of significant figures (see Section
5.2).
Microsoft Excel also can be used to produce
excellent figures. Note that the text in the figures
(e.g., axes titles) can be formatted with text as superscripts or subscripts or in italics. For example,
to change the x-axis title from Acceleration
(m/s2) to Acceleration (m/s2), select the character 2 and click Main Menu: Format●Selected Axis
Title…, then check Superscript. Also remember to
delete the legend when you have only one series of
data.
5.3 LINEAR REGRESSION
5.3.1 Introduction
A very common model used in engineering is the
linear model. In the linear model, the dependent
37
CIVIL ENGINEERING LAB REPORT MANUAL
variable is related to the independent variable
raised to the first (or zero) power. Thus, linear
models include: y = 2x + 5 and y = xe3.2 – π. Model such as y = 4x2 or y = sin(x) are not linear, because the dependent variable (y) is not related to
the independent variable (x) raised to the first (or
zero) power.
Linear models are common for two reasons.
First, many natural phenomena are linear. For
example, force is linearly related to acceleration in
a system of constant mass through F = ma.
Second, many non-linear systems can be linearized through a transformation of variables. For
example, a common kinematic equation is:
data) is equal to (y – ŷi)2. Thus, the sum of the
squares of the errors, SSE, is:
n
  y  yˆ i 
i 1
Combining:
y = mx + b
n
i 1
i 1
Expanding:
n
 
n
n
SSE   y i2  2m  xi y i   2b   y i 
i 1
i 1
n
n
i 1
i 1
The goal of linear regression is to find the values of m and b that minimize SSE (in other words,
to find the values of m and b so that the derivative
of SSE with respect to m and the derivative of SSE
with respect to b are both zero). You can verify
the derivatives below:
 
n
n
n
SSE
 2  xi y i   2m  xi2  2b  xi 
m
i 1
i 1
i 1
n
n
SSE
 2   y i   2m  xi   2nb
b
i 1
i 1
Setting the derivatives equal to zero creates two
equations in the two unknowns m and b:
In Section 5.3.1, the equation for a straight line
was written as:
n
 
n
n
i 1
i 1
2m  xi2  2b  x i   2  xi y i 
y = mx + b
i 1
n
Suppose this equation is your model for a physical
phenomenon. Using the nomenclature of Section
E.1, you can write the linear equation as:
ŷi = mxi + b
where ŷi is the model-predicted value of y when x
= xi. The subscript i goes from 1 to n (n data
pairs). Also recall from Section E.1 that the
square of the error (i.e., the square of the difference between the model prediction and measured
 
i 1
2mb  x i   m  x i2  nb 2
Note that in a linear model, a plot of the dependent
variable (on the y-axis) against the independent
variable (on the x-axis) is a straight line. The line
has a slope of m and an intercept of b. The parameter m has units of (units of y)/(units of x). The
parameter b has the same units as y.
5.3.2 Linear regression analysis
n
2
2
SSE    y i  yˆ i     y i  mxi  b 
y = ½at2
This equation is not linear: y depends on t2, not on
t raised to the first or zero power. It can be made
linear by defining a new independent variable, x,
equal to t2. Thus, a linearized model is: y = ½ax.
The general form of the linear model is:
2
n
2m  x i   2nb
 2   yi 
i 1
i 1
Solving this system of two equations in two unknowns:
m
n
1  n  n 
 xi y i    xi   y i 
n  i 1
i 1
 i 1
1 n 
2
 xi    xi 
n  i 1 
i 1
n
2

n
 xi  x  y i  y 
i 1
n
2
 xi  x 
i 1
eq. 5.1
CHAPTER 5: TOOLS
b
where: x 
and y 
n
1 n

  y i  m  xi   y  mx
n  i 1
i 1

eq. 5.2
1 n
 xi = arithmetic mean of x values
n i 1
1
 y i = arithmetic mean of y values.
n i 1
n
5.3.3 Calculating linear regression
coefficients
You can calculate m and b in three ways. First,
you could use a spreadsheet. Enter the xi and yi
data in columns. Calculate the arithmetic mean
(average) of x and y. Enter xi – x , yi – y , and (xi –
x )2 in columns. Then calculate m and b from eqs.
5.1 and 5.2. Your spreadsheet can be reused for
other linear regression problems.
Second, use Microsoft Excel’s built-in regression functions.
For example, the functions
SLOPE and INTERCEPT can be used to find the
slope and intercept, respectively. These formulas
should be typed in as: =SLOPE(range containing
y values, range containing x values) and
=INTERCEPT(range containing y values, range
containing x values). For example, if the x data
are in cells B2 through B5 and the y values are in
cells C2 through C5, then the slope and intercept
can be found by typing into any two cells the formulas:
38
5.4 FITTING MODELS TO DATA
USING SOLVER
5.4.1 Background
Most spreadsheet packages have a built-in nonlinear solver to analyze constrained optimization
problems. In Microsoft Excel, the built-in subprogram is called Solver.
Before using Solver, it is necessary to set up
your spreadsheet properly. Your spreadsheet must
have guesses in separate cells for each parameter
to be estimated. In addition, your spreadsheet
must have the objective function formula in another cell. In other words, your spreadsheet must
have a cell (called the target cell) that evaluates to
the objective function. The objective function
might be, for example, the SSE that Solver will
attempt to minimize.
Solver can be accessed by selecting the Solver
option under Tools on the main menu. Use Help
for more information. The Solver window, shown
in Figure 5.2, will appear.
=SLOPE(C2:C5, B2:B5) and
=INTERCEPT(C2:C5, B2:B5)
Figure 5.2: Solver Window
Microsoft Excel combines a number of useful linear regression functions in the Data Analysis tool
called “Regression.” To access these tools, select
Regression option under ToolsData Analysis on
the main menu. Use Help for more information.
Third, regression coefficients can be calculated in Microsoft Excel by plotting the data and
using the ChartAdd Trendline option. Check
Help for more details.
Solver requires four pieces of information from
you. First, Solver needs to know the location of
the target cell (i.e., the cell evaluating to the objective function). Enter the target cell in the text box
labeled: Set Target Cell:.
Second, Solver needs to know if you wish to
maximize the objective function, minimize the
objective function, or set the objective function
equal to a fixed value. Make your selection by
39
CIVIL ENGINEERING LAB REPORT MANUAL
clicking on the appropriate radio button after:
Equal To:. If you are setting the objective function equal to a value, then enter the value in the
text box after: Value of:.
Third, Solver needs to know the cells where
the adjustable parameters are located. Enter the
cell locations in the text box following: By
Changing Cells:.
Fourth, constraints (if any) are entered by
clicking the Add button under Subject to the
Constraints:. The addition and use of constraints will be discussed in Section 5.4.3.
Solver can be used in two ways. First, Solver
can be used to find model parameters that best fit a
model. The use of Solver in model fitting is discussed in Section 5.4.2. Second, Solver can be
used to solve constrained optimization problems.
This use is illustrated in Section 5.4.3.
5.4.2 Using Solver for model fitting
Solver is a very powerful tool for finding the
“best-fit” adjustable parameters in a model. The
use of Solver to fit model parameters will be illustrated with data and a linear model (y = mx + b),
where m and b are adjustable parameters. (To use
Solver, it is not necessary that the model be linear.)
To use Solver, first set up your spreadsheet
with four areas. First, enter the data. The data are
shown in cells B2:C5 in Figure 5.3.
Figure 5.3: Spreadsheet Set-Up for Model Fitting with Solver
Second, establish cells for the adjustable
rameters. It is a little easier to use Solver if
cells containing the adjustable parameters are
jacent to one another. Enter a guess for each
pathe
adpa-
rameter in its cell. The guesses can be pretty
crude. In the example, the parameters m and b are
in cells B7 and B8, respectively. Note that the
cells are labeled (in cells A7 and A8) and contain
initial guesses.
Third, use your model to calculate the predicted value of y (ŷi) for each measured value of y
(yi). In the example, the model is: ŷi = mxi + b.
The predicted values of y are in column E. For
example, cell E2 contains the formula:
=B2*$B$7+$B$8.
Fourth, create a cell containing the objective
function. For most models, an appropriate objective function is the sum of the squares of the errors
(SSE). In the example, the squares of the errors [=
(yi – ŷi)2] are calculated in cells F2 to F5. For example, the formula in cell F2 is: =(C2-E2)^2. The
objective function is simply the sum of the values
of (yi – ŷi)2. In Figure 5.3, SSE is in cell F7, which
contains the formula: =SUM(F2:F5). Cell F7 is
the target cell, since it evaluates to the objective
function. Figure 5.3 shows the completed spreadsheet, with the value of the objective function
equal to 4.59 for the initial guesses of m and b.
With the spreadsheet set up, access Solver.
For most models, you seek to minimize SSE.
Therefore, set up Solver as follows. First, enter
the cell containing SSE in the Set Target Cell:
text box. This can be accomplished by typing the
cell location in the text box (e.g., typing F7) or by
clicking inside the Set Target Cell: text box and
then clicking the target cell in the spreadsheet.
Second, click the Min radio button (to minimize
SSE). Third, enter the cell(s) containing the adjustable parameter(s) in the By Changing Cells:
text box. This can be accomplished by typing the
cell (or range) location in the text box (e.g., typing
B7:B8) or by clicking inside the By Changing
Cells: text box and then clicking and dragging
across the cells containing the adjustable parameters in the spreadsheet. The final version of the
Solver window will look like Figure 5.4.
To find the values of the adjustable parameters
that minimize SSE, click the Solve button on the
Solver window and accept the answer. The final
spreadsheet will look like Figure 5.5.
Note that the minimum value of SSE in this
case is about 0.107 (with units of the square of the
units of y). You can calculate the correlation coefficient (r2) easily from the equation in Section E.3,
repeated here for convenience:
CHAPTER 5: TOOLS
40
cannot produce particles with a volume less that
5×10–3 mm3. An analysis reveals:
n
r2 1
2
  y i  yˆ i 
i 1
n
2
  yi  y 
i 1
The numerator in the second term is SSE (already
in your spreadsheet). You can calculate the denominator in the second term by adding a column
to your spreadsheet.
total particle surface area = A = (number
of particles)×(surface area per particle)
so: A = 4πr2N
where: N = number of particles and r = particle
radius. The number of particles is given by:
N
= (total volume of the
ticles)/(volume of one particle)
par-
The total volume of the particles is the total mass
of the particles, m, divided by the density of the
particles, ρ. If m is in grams and ρ is in g/cm3,
then m/ρ is in cm3 and the total volume in mm3 is
1000m/ρ. Thus:
Figure 5.4: Sample Spreadsheet with Solver
Window
1000
N
m

4 3
r
3
(for m in g, ρ in g/cm3, and r in mm)
Figure 5.5: Final Spreadsheet with Optimal Parameter Values
5.4.3 Using Solver with constraints
Solver also can be used to optimize an objective
function subject to constraints. The use of Solver
with constrained optimization will be illustrated
with the following problem. Suppose you have
designed a catalyst to minimize byproducts from
the manufacture of a solvent. The catalyst is to be
made into spherical particles. You wish to maximize the total surface area of the particles. However, the equipment you have at your disposal
The mathematical statement of the problem is:
find the value of r that maximizes A = 4πr2N subject to V = (4/3)πr3 < 5×10–3 mm3. For your catalyst, use m = 10 g and ρ = 2.3 g/cm3.
A spreadsheet for this problem is shown in
Figure 5.5. The formulas for V, N, and A are
shown in cells D5 through D8, respectively. A
guess for r of 1 mm has been entered in cell B4.
In Solver, you can find the value of r that maximizes A by selecting cell B8 as the target cell,
choosing to maximize it, and selecting cell B4 as
the cell to change. You now need to enter the
constraint that V < 5×10–3 mm3. To enter the constraint, click the Add button under Subject to
the Constraints:. In the Cell Reference: text
box, enter (or click on) the cell you want to constrain (B5 in the example). In the drop-down box
in the middle of the window, select >= (since the
constraint is a “greater than or equal to” constraint). In the Constraint: text box, type a cell
41
CIVIL ENGINEERING LAB REPORT MANUAL
reference or value. In the example, type the value
5e-3 (see Figure 5.7).
Figure 5.5: Example Spreadsheet for the Constrained Optimization Problem
Figure 5.8: Example Spreadsheet with Constraint
Click Solve to solve. If you try this on your
own, you will find that r is about 0.105 mm, V is
just about at its limit of 5×10–3 mm3, and the total
surface area is about 1.23×105 mm2.
5.5 SUMMARY
Figure 5.7: Example of the Add Constraint Dialog Box
To add the constraint, click the Add button.
Then click the Cancel button to return to the
main Solver window. The spreadsheet should look
like Figure 5.8.
With Microsoft Word, you can create documents,
make tables, spell- and grammar-check a document, and use the equation editor to make equations more readable. Group tools allow you to
create documents with more than one author will
less effort.
You are used to using Microsoft Excel to manipulate data. Microsoft Excel also can be used to
produce high-quality tables and figures.
Linear models (y = mx + b) are very common
in engineering. You can find the slope and intercept using formulas, Microsoft Excel built-in functions, or Microsoft Excel plotting functions.
Non-linear optimization also is common in
engineering. Use Microsoft Excel’s Solver to
solve simple linear or non-linear optimization
problems. Parameters that minimize, maximize,
or fix the objective function can be determined
with or without constraints.
Chapter 6
Other Engineering Documents
T
hus far in this manual, you have been exposed to the organization of lab reports.
Engineering reports in general are used to
present the results of a study. A report may
transmit the results of the entire project (called a
final or full report), transmit the results of a portion of the project (called a progress report), or
transmit a small piece of a report in a short form
(often called a letter report).
In addition to reports, engineers write several
other kinds of documents. Common document
types include letters, memorandums, and email.
6.1 REPORTS
The general outline of an engineering report is
similar to the lab report outline discussed in Section 2.1.3. Two other elements of a report deserve
mention. First, every report should have a title or
cover page. The title page for your lab reports was
discussed in Section 2.2.
Second, most reports have a transmittal letter
(also called a cover letter). The transmittal letter
is a short letter that accompanies the report. The
format of letters is presented in Section 6.2.
6.2 LETTERS
Engineers use letters as a way to document the
transmission of ideas to the client or other agency.
Letters must have structure. The heading of a letter includes the date and recipient’s name and title.
The first paragraph of a letter should summarize
previous correspondence and state the purpose of
the letter. In the next paragraph or paragraphs,
supporting information should be presented. The
last paragraph of the letter should summarize the
main points and state the required actions or follow-up communication. In the closing information of a letter, include your name, title, and signature. An example letter is shown in Illustration
6.1.
Note the heading information; introductory, supporting, and concluding paragraphs; and closing
information.
6.3 MEMORANDUMS
A memorandum (plural: memorandums or memoranda) is a short note. Similar to letters, memorandums are used for short documentation of engineering work. In fact, the word “memorandum” is
a shortened form of memorandum est – Latin for
“it is to be remembered.” Memorandums frequently are used for messages inside an organization (called internal memorandums).
Memorandums (or memos) are structured
similarly to letters (see Section 6.2), but without
the heading and closing information of a letter.
Heading information in a memo tells you to whom
the memo is written, who wrote the memo, the
memo topic, the date, and the word “Memorandum.”
Memo paragraphs are similar to those of letters: previous correspondence and memo purpose
summarized in the first paragraph, supporting information in the following paragraphs, and main
points summarized in the last paragraph.
An example of a memo is given in Illustration
6.2. Note the heading information and purpose of
each of the three paragraphs. A copy of this
memo likely would be placed in the project file to
document the internal communication of the consulting firm.
6.4 EMAIL
Nearly every college student in the twenty-first
century has used email, usually for informal conversation. Email also can be used in formal business correspondence, sometimes in place of a letter or memo.
AZA Engineers
Warsaw • Milton • Cleveland
March 10, 2006
Mary J. Bremer, PE
Director of Public Works
Rivertown Public Works Department
1120 Bank Road
Rivertown, Ohio
Dear Ms. Bremer,
As per our telephone conservation of March 9th, I am writing to summarize your comments on the
draft stormwater report. Our responses to your comments also are included in this letter.
My notes indicate that your staff had three main comments on the draft report. First, the name of the
Bilmore Pump Station was misspelled on page 6-2. Second, the flow calculations for the West
Branch were based on 1980-2000 rainfall data, while all other system design calculations were based
on 1970-2000 rainfall data. Third, your staff requested that the cradle design for Option 4 use a
smaller factor of safety than the 2.5 safety factor in the report (p. 7-7).
We will correct the spelling error on page 6-2 and update the design calculations for the West Branch
with rainfall data from 1970-2004. However, we feel best engineering practice requires the safety factor of 2.5 in the pump cradle design. Based on conversations with the pump manufacturer, lower
safety factors will increase the chance of catastrophic failure. Therefore, we wish to retain the 2.5
safety factor in the design of Option 4.
To summarize, we plan to resubmit the report before March 31, 2006 with the spelling error corrected and with the design calculations for the West Branch updated to use rainfall data from
1970-2000. We will retain the safety factor of 2.5 in the pump cradle in Option 4.
Thank you for your thoughtful comments. I will call you next week to confirm the changes. We
look forward to delivering you the final report on this project.
Sincerely,
John H. Seal, PE
Senior Associate Engineer
12 Cunningham Pkwy, Suite 114, Warsaw, Ohio
Illustration 6.1: Example of a Technical Letter
44
CIVIL ENGINEERING LAB REPORT MANUAL
MEMORANDUM

Double-check the names on the “To” list
before you send the email. “Replying to
All” with the results of your recent medical check-up (when you intended to forward the results only to your roommate) is
a serious breach of business protocol.

Emails are as much a part of the technical
and legal record as are other documents.
Do not include anything in an email that
you would not include in other business
documents.
To: Yvonne Ringland
From: J.H. Seal, PE
Re: Comments on Rivertown stormwater
report
Date: March 9, 2006
I spoke with Mary Bremer at the Rivertown
DPW today about the draft stormwater report. She requested that we use the same
rainfall data for the West Branch design
calculations as we did for the rest of the
report. We used 1970-2000 rainfall data
for the majority of the report.
Please redo the West Branch design with
1970-2000 rainfall data. The final report is
due by March 31st. Please have the revisions to me by March 25th so we can get
the changes to the word processing staff.
If you have questions about the requested
changes, please call me at extension 36.
Illustration 6.2: Example of a
Memorandum
An example of a business email message is shown
in Illustration 6.3.
To: Roger Yee (rty@azaengineers.com)
From: John H. Seal
(jhs@azaengineers.com)
Subject: Pump cradle design for Rivertown
Cc: Cynthia Cronin
(cronin@rgoldpumps.com)
Bcc:
Attached: Draft Rivertown report.doc
Roger –
Although email is less formal that other forms
of written communication, it is easy to let an
overly familiar style creep into your formal email
correspondence. You use different words in
speaking to your professor, clients, and colleagues
that you use to speak to friends at a party. Similarly, use more formal language in business email.
Some rules for business email correspondence include:



Avoid email contractions (e.g., “RU” for
“are you” and “*s*” for “smile”)
Avoid “emoticons” – text characters used
to express emotions (e.g., “:-)” for a
smiley face)
Proofread carefully before you hit Send.
Look for language that may be offensive
or inappropriate
Rivertown has questioned our use of a 2.5
safety factor for the cradle design in Option 4 of the stormwater project. Attached
is the draft report.
Are we sure about this safety factor? If
so, please help me to justify it. I am copying Cindy Cronin at Rheingold Pumps on
this message. We are specifying Rheingold Pumps and Cindy might be able to
help.
Please get back to me by the end of the
day on this, Roger.
Thanks,
John H. Seal
Senior Associate Engineer
AZA Engineering
Illustration 6.3: Example of a Business Email
45
CIVIL AND ENVIRONMENTAL ENGINEERING LAB AND TECHNICAL REPORT MANUAL
6.5 SUMMARY
In addition to reports, engineers produce letters,
memos, and emails almost daily in their working
lives. Both letters and memos have a heading,
closing, and structured paragraphs. The first paragraph summarizes previous correspondence and
states the purpose of the letter or memo. The next
paragraphs present supporting information. The
last paragraph summarizes the main points and
state the required actions or follow-up communication. Business emails are part of the business
record and should be created and sent in a professional manner.
45
Glossary
accuracy: a measure of closeness to the true value
adjective chain: a long list of modifiers to a noun
(to be avoided)
bar chart: a type of plot using bars that is employed when the independent variable is not continuous
bibliography: a list of useful sources of information, including sources not cited in the text (as
contrasted with a list of references, in which only
cited material is listed)
pie chart: a type of plot using pie slices that is
employed to show the relative contributions of
several factors to a whole
precision: a measure of similarity in a set of values
rounding: adjusting the value of certain digits to
comply with the appropriate number of significant
digits
run-on sentence: a sentence containing more than
one idea (usually having one or more conjunctions)
correlation coefficient (r2): a dimensionless
measure of the degree of fit of a model to data (r2
> 0.9 is good)
scatter plot (or x-y plot): a type of plot using
symbols or lines that is employed when the independent variable is continuous
dimensional analysis: the manipulation of units to
check if the units “balance”
sentence fragment: an incomplete sentence
(usually lacking a subject or verb)
error analysis: the study and evaluation of measurement and calculation uncertainties
significant digits (significant figures): the number of digits justified by the precision of the data
legend: a listing of the property represented by
each symbol, bar, or line
model calibration: the process of finding the values of the adjustable parameters so that the model
output matches the experimental data as closely as
possible
signposting: indicators used to show the audience
where they are in presentation
split infinitive: insertion of a word between “to”
and the verb (to be avoided)
model fits: comparison of model output to the calibration data set
sum of the squares of the errors (SSE): the
square of the differences between the model output and data
model predictions: comparison of model output
to data outside the calibration data set
Système Internationale d’Unitès (SI units): a
standardized set of units (see Appendix E)
objective function: a mathematical statement of
the success of the project
target audience: the intended recipients of the
information to be presented
outline: a list of the major headings and subheadings in the presentation, showing the order of the
main ideas and showing the secondary topics supporting the main ideas
topic sentence: the first sentence in a paragraph in
which the purpose of the paragraph is stated
voice: person or people doing the action
GLOSSARY
white space: blank space on the page in a document
G-2
References and Bibliography
mation are listed below. This list is by no means
exhaustive.
REFERENCES
Alley, M. The Craft of Scientific Writing. 3rd
ed., Springer-Verlag, New York, NY, 1996.
Finkelstein, Jr., L. Pocket Book of Technical
Writing for Engineers and Scientists, 2nd ed.,
McGraw-Hill Co., Inc., New York, NY, 2005
Jensen, J.N.. A User’s Guide to Engineering.
Pearson/Prentice-Hall, Upper Saddle Rover, NJ,
2006.
McNeill, B., L. Bellamy, and S. Foster. Introduction to Engineering Design, Arizona State Univ.,
Tempe, AZ, 1995. As found in: K.A. Smith.
Teamwork and Project Management. 2nd ed.,
McGraw-Hill, New York, NY, 2004.
Paradis, J.G. and M.L. Zimmerman. The MIT
Guide to Science and Engineering Communication. The MIT Press, Cambridge, MA, 1997.
Smith, J.G. and P.A. Vesiland. Report Writing
for Environmental Engineers and Scientists.
Lakeshore Press, Woodsville, NH, 1996.
Strunk, Jr., W. and E.B. White. The Elements of
Style, 3rd ed. Allyn and Bacon, Needham Heights,
MA, 1979.
Taylor, J.R. An Introduction to Error Analysis,
The Study of Uncertainty in Physical Measurements, 2nd ed. University Science Books,
Sausalito, CA, 1997.
nd
Wright, P.H. Introduction to Engineering, 2 ed.
John Wiley and Sons, New York, NY, 1994.
ANNOTED BIBLIOGRAPHY FOR
TECHNICAL COMMUNICATION
There are a number of excellent books on technical communications. A few good sources of infor-
Alley, M., L. Crowley, J. Donnell, and C. Moore
(eds.). Writing Guidelines for Engineering and
Science Students.
An excellent on-line guide available at
http://filebox.vt.edu/eng/mech/writing/index.html
(visited June 6, 2003)
Dodd, J.S. The ACS Style Guide. American
Chemical Society, Washington, DC, 1986.
Although the emphasis is on technical writing in
chemistry, this official guide of the American
Chemical Society is a good general reference on
technical writing.
McMurrey, D.A. Online Technical Writing Online Textbook
This is a fine guide to technical writing. It can be
found online at:
http://www.io.com/~hcexres/tcm1603/acchtml/acc
toc.html (visited May 28, 2003)
Paradis, J.G. and M.L. Zimmerman (see References for details)
This is a good reference with many examples of
technical writing.
Sageev, P. Helping Researchers Write ... So
Managers Can Understand. Batelle Press, 1968.
The emphasis here is on technical writing in the
corporate setting (written by Ms. Sageev, of UB’s
Center for Technical Communication (CTC).
Smith and Vesiland (see References for details)
Smith and Vesiland cover most aspects of technical writing, with many examples from environmental engineering.
Strunk and White (see References for details)
This is a classic reference and very inexpensive.
This book should be on your reference shelf, along
with a good dictionary.
REFERNCES AND BIBLIOGRAPHY
Tufte, E.R. The Visual Display of Quantitative
Information. Graphics Press, Cheshire, CT, 1983.
Tufte, E.R. Envising Information. Graphics
Press, Cheshire, CT, 1990.
Tufte, E.R. Visual Explanations: Images and
Quantities, Evidence and Narrative. Graphics
Press, Cheshire, CT, 1993.
These three books by Tufte will change your ideas
about the beautiful and innovative ways that technical information can be communicated.
RB-2
Appendix A
Example Lab Reports
T
his appendix contains sample report for a
laboratory on the tension testing of glass
fiber reinforced polymers and a BOD laboratory. The report on reinforced polymers is
discussed in detail in Chapter 2.
CIE 360 – Environmental Engineering Laboratory
Fall 2005
Lab Exercise 1
BOD Analysis of Amherst Wastewater Treatment
A submittal to
Todd Snyder
Civil, Structural, and Environmental Engineering
University at Buffalo
Presented by
Group leader: Todd Snyder
Team member #2:
Team member #3:
September 19, 2005
1
Abstract
Biochemical oxygen demand (BOD) is an established measurement of wastewater
strength. Standard Method 5210 was used to measure the BOD of wastewater influent to
the Amherst, NY treatment plant, effluent from the plant, and the receiving water
(Tonawanda Creek). Based on this analysis, the effluent is predicted to increase the BOD
of the creek 11% to 1.0 mg/L. Without treatment, the wastewater is predicted to increase
the creek BOD over 250%. A kinetic study performed on the influent found that the
BOD of the wastewater is exerted according to: BOD = 37.7(1 – 10–0.12t), with BOD in
mg/L as O2 and t = time in days.
Introduction
BOD is the measurement of oxygen consumed by living microorganisms (primarily bacteria)
while consuming organic matter present in a water or waste sample. Nitrification will also
contribute to BOD. Non-biodegradable (or refractory) organic compounds will not
contribute to BOD (Tchobanoglous and Schroeder, 1987). Wastewater treatment plants
such as the Amherst Water Pollution Control Facility (AWPCF) remove BOD to minimize
the impact of manmade wastewater on the environment. Typically, BOD is measured after
five days and is called BOD5.
The primary purpose of the laboratory exercise was to measure the BOD removal efficiency
of the wastewater treatment plant and to predict the impact on Tonawanda Creek. To
accomplish this we measured the BOD of 3 samples:
1. AWPCF Influent
2. AWPCF Effluent
3. Tonawanda Creek
Samples (1) and (2) were used to determine the BOD5 removal efficiency of the AWPCF.
Samples (2) and (3) and a mass balance were used to determine the effect of the AWPCF
effluent on Tonawanda Creek downstream BOD5. A secondary purpose of this lab was to
determine BOD exertion kinetics.
Theory
In the aquatic environment, dissolved oxygen (DO) typically decreases by first-order
biologically-mediated kinetics. In other words:
dDO
 k t
dt
Integrating:
DO = DO0e– k’t
2
where: DO0 is the initial DO, t is time and k’ is a first-order rate constant. BOD is equal
to DO0 – DO, so:
BOD = DO0 – DO = DO0(1 – e– k’t) = L(1 – 10– kt)
eq. 1
where: L = DO0 and k = k’/ln(10). The parameter L also is called the ultimate BOD.
Method
5 day BOD test:
Analyses were performed in accordance with Standard Method 5210B: 5 Day BOD Test
(APHA et al., 1998). A YSI Model 5000 dissolved oxygen meter equipped with a Model
5750 non-stirring BOD probe was used to measure dissolved oxygen. The meter was
calibrated in accordance with its manual. Standard 300 mL BOD bottles were incubated
in a Fisher Scientific incubator at 20.0 degrees Celsius. Five replicates were analyzed for
BOD5 values for the effluent and creek samples using no dilution of the samples. The
influent was analyzed in duplicate at two dilutions: 1:15 and 1:50 strengths.
Deviations from the method included the following:



No glucose-glutamic acid check was performed
The pH was not checked. It was assumed suitable for bacterial growth.
Only 2 dilutions were used for the high BOD influent.
Kinetics test (0-5 day BOD):
The BOD of the influent was measured in duplicate at two dilutions, 1:15 and 1:50, after
1, 2, 3, 4, and 5 days of incubation at 20 degrees Celsius. All the BOD bottles for the test
were filled and measured for initial dissolved oxygen at the same time. Dilution water
blanks were also prepared in duplicate.
The bottles used for the BOD5 analysis were immediately placed in the incubator. The
others were refrigerated. Duplicates were removed from the refrigerator and placed in
the incubator at approximately the same time on each day for the next 4 days. It was
assumed that almost no biological action took place in the refrigerator because of the low
temperature. For consistency, all the BOD bottles were prepared at the same time and all
the bottles were analyzed for final dissolved oxygen at the same time.
Results and Discussion
Measured BOD5 values were 29, 2.3, and 0.9 mg/L for the influent, effluent, and
upstream Tonawanda Creek samples, respectively. Based on these values, AWPCF
decreases the wastewater BOD by 92%.
3
A mass balance was performed using a flow rate of 24 million gallons per day (mgd) from
the AWPCF and 420 cfs (271 mgd) for the creek. The mass balance is (all terms in lb/d)
rate of BOD5 from Tonawanda Creek upstream of the AWPCF
+ rate of BOD5 from Tonawanda Creek upstream of the AWPCF =
rate of BOD5 in Tonawanda Creek downstream of the AWPCF
Or:
8.34QTCUSBOD5,TCUS + 8.34QAWPCFBOD5,AWPCF = 8.34QTCDSBOD5,TCDS
Where: Q = flow in mgd and the subscript TCUS and TCDS refer to Tonawanda Creek
upstream and downstream of the AWCPF, respectively. Assuming that QTCDS = QTCUS +
QAWPCF = 295 mgd, the BOD5 in Tonawanda Creek downstream of the treatment plant can be
calculated.
Based on the mass balance, BOD5,TCDS is 1.0 mg/L. Therefore, the wastewater effluent is
predicted to increase the creek BOD from 0.9 to 1.0 mg/L (an increase of 11%). If raw
wastewater were to be released without treatment by the plant, the BOD5 downstream in the
creek would be 3.2 mg/L, an increase of over 250% from its upstream value.
The BOD exertion curve for the influent is presented in Figure 1. As shown in Figure 1,
the BOD exerted increases with time. The increase in BOD exertion with time is
consistent with eq. 1.
35
30
BOD exerted (mg/L)
25
20
Observed BOD
Model BOD
15
10
5
0
0
0.5
1
1.5
2
2.5
Time (d)
4
3
3.5
4
4.5
5
Figure 1: Measured and Predicted BOD Exertion Curves for Plant Influent
The model in eq. 1 was fitted to the data. The model parameters L and t were estimated
using Solver in MS Excel by minimizing the sum of the squared residuals. (See the
attached spreadsheet in the appendix for details.) Fitted values of L and k were 37.7
mg/L and 0.12 d–1, respectively. The predicted BOD exertion curve is plotted with the
observed BOD data in Figure 1. The predicted BOD exertion curve compares well with
the observed data. The calculated r2 value is $$$.
Typical values of k’ are 0.2 to 0.3 d–1 (Tchobanoglous and Schroeder, 1987). The
resulting k values are 0.09 to 0.13. The predicted value of k is in the range. The predicted
value of L, about 38 mg/L, is typical of the AWPCF influent (Snyder, 2005).
Conclusions
The Amherst wastewater treatment plant removes 92% of BOD5 from the Town’s
wastewater. As a result, the BOD downstream in Tonawanda Creek is predicted to
increase by only 11% as a result of the discharge of the treated wastewater. Without
treatment, the town’s wastewater would increase the BOD downstream in the creek by
over 250%. Based on a first-order model of BOD exertion, the fitted first-order rate
coefficient for BOD exertion in wastewater influent is 0.12 d–1 and the fitted ultimate
BOD for the influent is 37.7 mg/L.
References
American Public Health Association, American Water Work Association, and Water
Environment Federation. Standard Methods for the Analysis of Water and Wastewater,
20th Edition, APHA, AWWA, WEF, Washington DC, 1998.
T.M. Snyder. Personal conversation, 2005.
G. Tchobanoglous and E.D. Schroeder. Water Quality. Addison-Wesley Publishing
Company, Reading, MA, 1987.
5
Appendix
A: Lab handouts
B: Copies of lab notebook
C: Calculation sheets
8
12
13
6
CIE 360 - Environmental Engineering Laboratory
Theme 1: Wastewater Treatment and Environmental Impact of Effluent
Investigate the treatment of wastewater at the Town of Amherst Water Pollution Control
Facility (AWPCF), measure the removal efficiency of several pollutants, and determine the
impact on water quality in the receiving water body, Tonawanda Creek.
Lab 1: BOD Startup
Friday, 9/2/05 from 12-2pm (not normal lab time)
Background
Biochemical oxygen demand (BOD) is the measurement of oxygen consumed by living
microorganisms (primarily bacteria) while consuming organic matter present in a water or
waste sample. Nitrification will also contribute to BOD. Non-biodegradable (or refractory)
organic compounds will not contribute to BOD. We will measure the BOD of 3 samples:
4. AWPCF Influent
5. AWPCF Effluent
6. Tonawanda Creek
Using samples (1) and (2) we will determine the BOD removal efficiency of the AWPCF.
Using samples (2) and (3) and a simple mass balance, we will determine the effect of the
AWPCF effluent on Tonawanda Creek downstream BOD.
Method
We will use AWWA Standard Method 5210 to measure BOD. It involves placing samples in
closed bottles followed by incubation for 5 days. After incubation the change in dissolved
oxygen (DO) will be measured.
Initial DO is limited by the saturation value of oxygen in water at room temperature, about 8
mg/L. This limited supply of oxygen is easily depleted by high concentration wastes such as
the wastewater influent; therefore such samples must be diluted to ensure that oxygen will be
present throughout the test duration. There should be very little BOD remaining in the
AWPCF effluent samples so it and the Tonawanda Creek water will not need to be diluted.
Hopefully, our samples will express a 5 day DO drop of more than 2 mg/L but still end up
with a residual DO greater than 0.5-1 mg/L.
It is important that the environmental conditions during the test be suitable for the living
organisms. Therefore, nutrients are added to the dilution water. Dilution water blanks must be
included in the test to correct for any BOD contribution by the dilution water. Seed bacteria
are also included in the dilution water, although they are probably not necessary for our
particular samples.
The rate of biological reactions is affected by temperature. For this reason BOD tests are
carried out at a constant temperature of 20C in the laboratory incubator.
Lab Exercise
7
This portion of the lab exercise will be conducted by the instructor. The BOD bottles will be
filled on Friday, 9/2/05 from 12-2. Please stop by 120 Jarvis hall to lend a hand or observe.
Bottles to be used for 5 day BOD tests will be placed in an incubator at 20 degrees C. The
rest will be refrigerated and eventually placed in the incubator to simulate incubations of 4, 3,
2, and 1 day BOD values.
Note: This is not a standard method of performing this test for intermediate times, however it
should be more consistent than trying to set up daily BOD bottles.
The method of setting up the BOD bottles is as follows:
 Fill 10 BOD bottles with Dilution water. Refill the bottles if necessary, insert a stopper
verifying there are no bubbles in the bottle, apply a water seal and apply a cap to prevent
evaporation of the water seal.
In the same manner,
 Fill and cap 5 BOD bottles with AWPCF effluent
 Fill and cap 5 BOD bottles with Tonawanda Creek water
 Dilute 200 mL of AWPCF Influent to a volume of 10 L using dilution water. Fill and cap
10 BOD bottles (Note that this is a 50:1 dilution)
 Similarly, fill and cap 10 BOD bottles with a 15:1 dilution of the influent
We will be analyzing Tonawanda Creek water and AWPCF effluent for BOD after 5 days.
This may be referred to as BOD5 (note that this is the standard BOD test). It is customary to
test duplicate samples. Triplicates would be typical; however we will run 5 duplicates
instead.
Duplicate AWPCF influent samples will be analyzed for DO after 1-5 days of incubation to
study the kinetics.
Safety
The primary hazards in this lab exercise are the sanitary waste water samples which may
contain human pathogens and the risk of electrical shock from working with water near
electrical receptacles.
Take note of location of the eye wash station, turn the water on and verify its operation. Take
note of the location of the emergency shower outside the entrance to 120 Jarvis. Always
wear your safety glasses. Do not eat or drink in the lab.
Unsafe behavior including failure to wear safety glasses, eating, drinking, or horseplay will
be addressed in the "Attendance / Participation" portion of your grade.
8
CIE 360 - Environmental Engineering Laboratory
Theme 1: Wastewater Treatment and Environmental Impact of Effluent
Investigate the treatment of wastewater at the Town of Amherst Water Pollution Control
Facility (AWPCF), measure the removal efficiency of several pollutants, and determine the
impact on water quality in the receiving water boy, Tonawanda Creek.
Lab 1: BOD
9/14/2003
This week we will be finishing our work with BOD. The data collected are:





Days 0-5 dissolved oxygen (DO) data for 50:1 dilute AWPCF Influent
Days 0-5 dissolved oxygen (DO) data for 15:1 dilute AWPCF Influent
Days 0-5 dissolved oxygen (DO) data for the dilution water
Days 0 and 5 DO data for full strength AWPCF Effluent
Days 0 and 5 DO full strength Tonawanda Creek water
Lab Exercise
Become familiar with the BOD meter manual; use it to calibrate the meter. Measure the
residual DO in all of the BOD bottles and record the data in your lab notebooks.
Safety
The primary hazards in this lab exercise are the sanitary waste water samples which may
contain human pathogens and the risk of electrical shock from working with water near
electrical receptacles.
Take note of location of the eye wash station in the lab and the emergency shower just
outside the door of Jarvis 120. Always wear your safety glasses and gloves. Do not eat or
drink in the lab.
Unsafe behavior including failure to wear safety glasses, eating, drinking, or horseplay will
be addressed in the "Attendance / Participation" portion of your grade.
Waste Disposal
Waste from the BOD bottles can go down the drain in accordance with University guidelines
for drain disposal of laboratory waste.
Report
This is a group report, due in one week. Divide the work as defined in the course syllabus
and follow the lab manual guidance closely. Email the report to tmsnyder@buffalo.edu by
midnight for full credit. Each day after that will result in a 20% decrease in the grade.
Show the 0-5 day BOD exertion curves for the influent. Note that according to the standard
method a DO drop of at least 2mg/L with at least 1mg/L DO remaining is preferable. So you
may end up using the data from the 1/15 dilutions in some cases and the 1/50 dilutions for
others to determine the BOD expressed at each time interval.
9
Apply a simple 1st order reaction model to your data and fit the model, solving for the
reaction rate coefficient, k, and ultimate BOD, L.
Calculate the influent, effluent, and creek water BOD5 values and display them in a bar
graph.
Calculate the BOD removal efficiency of the plant.
Use a mass balance to calculate the effect of AWPCF effluent on downstream BOD in the
creek. The AWPCF treats an average of 24 million gallons per day (MGD). Tonawanda
Creek has an average flow of 420 cfs.
Attach your lab notes in an Appendix, including this handout. Please bring your report to me
early for feedback and revisions prior to the due date.
10
(Scan lab notebook sheets and place images here)
11
Calculation sheets:
12
13
CIE 361
Fall 2004
Lab #6
Tension Testing of
Glass Fiber Reinforced Polymer
Submitted to:
Professor Anderson
Ketter Hall
University at Buffalo
Submitted by:
John Peters
Susan Jones
Mark Whittaker
September 15, 2004
Abstract
An experiment laboratory was conducted to test whether a glass fiber reinforced polymer
(GFRP) had better mechanical properties than its component polymer. In addition, the
mechanical properties of the GFRP in the fill and warp directions were compared. Tensile
tests were performed according to ASTM methods by displacement control using an MTS
universal testing machine and a data acquisition sampling rate of 1.0 Hz. Test coupons were
cut from a ten–layer laminate of a polymer (vinyl ester resin DERAKANE 411) and a woven
glass fiber fabric. Results showed that eTest coupons were cut from a ten–layer laminate of a
polymer (vinyl ester resin DERAKANE 411) and a woven glass fiber fabric. Embedding the
woven glass fiber fabric within the polymer increased both the stiffness and strength of the
material (modulus of elasticity increased from 3.38 GPa to about 17 GPa and the tensile
strength increased from 80 MPa to about 300 MPa). However, the composite was more
brittle than the polymer (as indicated by a lower percent elongation). There was a slight
variation in mechanical properties in the warp and fill directions, presumably due to the
different number of fibers in the two directions.
Introduction
Fiber-reinforced composite materials are formed by embedding fibers of a strong, stiff
material into a weaker, softer material, known as the matrix. The resulting composite
material has superior mechanical properties to the two individual materials. The mechanical
properties of the composite are dependent on the number and orientation of the fibers.
In this labexperiment, a glass fiber reinforced polymer (GFRP) was tested. The GFRP was
made from layers of woven glass fiber fabric embedded within a vinyl ester resin matrix.
The fabric used had slightly more fibers in the warp direction than in the fill direction. The
lab testing had two objectives. The first objective was to compare the mechanical properties
of the GFRP composite to the properties of its component polymer. The second objective
was to compare the mechanical properties of the GFRP in the fill and warp directions.
Background
Definition of stress and strain
Mechanical properties of materials
When a tensile force is applied to a specimen, the engineering stress acting on the specimen is
determined by dividing the applied force by the original cross-sectional area.

F
A0
(1)
1
where σ is the engineering stress
F is the applied force
A0 is the initial cross-sectional area
As the applied force is increased, the specimen will elongate. The engineering strain is
defined as the elongation (change in length) divided by the original length
l
l0
where ε is the engineering strain
Δl is the elongation
l0 is the original length

(2)
Certain mechanical properties of the material can be determined from a plot of stress against
strain.
Mechanical properties of materials
The modulus of elasticity, E, is a measure of the materials stiffness, or its ability to resist
deformation while remaining elastic. The modulus of elasticity is determined by finding the
slope of the initial straight-line portion of the stress-strain curve and is equal to the change in
stress divided by the change in strain.
E


(3)
The tensile strength is the maximum stress a specimen can withstand in tension. It is equal to
the maximum point on the stress-strain plot. The tensile strength does not necessarily
correspond to the ultimate strength, or stress at which the specimen breaks.
The percent elongation (%EL) is a measure of the material ductility; the amount of
deformation before failure
%EL 
l
 100   f  100
l0
(4)
where εf is the strain at failure.
Formatted: Font: Italic
Formatted: Font: Italic, Subscript
A material with a low percent elongation, less than 5%, is said to be brittle. Ductile materials
have much higher values of percent elongation.
Poisson’s ratio (ν) is the ratio of the lateral strain (εL) to the axial strain (εa) and is defined by
Formatted: Font: Italic
Formatted: Font: Italic, Subscript

  L
a
(5)
2
Formatted: Font: Italic
Formatted: Font: Italic, Subscript
Poisson’s ratio is always positive and ranges in value from 0 to 0.5.
Published mMechanical properties of the individual materials
Polymer Matrix
Vinyl ester resins are typically used when high durability, thermal stability, and
extremely high corrosion resistance are required. In this study DERAKANE 411, which
is one of vinyl ester resins produced by the Dow Plastics (1999), was used. Typical
room temperature properties of the DERAKANE 411 resin are shown in Table 1.
Table 1: Typical Properties of DERAKANE 411 at Room Temperature
(Dow Plastics, 1999)
Property
Modulus of elasticity (GPa)
Tensile strength (MPa)
Percent elongation (%)
Poisson’s ratio
Value
3.38
75.8-82.7
5-8
0.35-0.38
Woven Glass Fiber Fabric
The fabric used in the study weighed 0.295 kg/m2 and had 213 and 224 yarns per meter
in the fill and warp directions, respectively. The thickness of the fabric was 0.226 mm.
The breaking strengths in the fill and warp directions were 40.5 and 42.4 kN/m,
respectively.
Methods
To quantify the effects of glass fiber reinforcement, standard mechanical properties (modulus
of elasticity, tensile strength, percent elongation, and Poisson’s ratio) were measured on
coupon samples of a GFRP. Since the glass fiber fabric used in this study has slightly more
fibers in the warp direction than in the fill direction, it was expected that two directions
would have slightly different mechanical properties.
3
Tensile tests were performed according to ASTM D3039–76, Standard Test Method for
Tensile Properties of Fiber-resin Composites, using an MTS universal testing machine. All
the tests were performed by displacement control. The rate of loading was 0.0847 mm/sec.
Data were collected using a data acquisition system with a sampling rate of 1.0 Hz. The test
setup is illustrated in Figure 1.
Test coupons were cut from a ten–layer laminate. The laminates were made by a hand lay–
up process. Dimensions of the test coupons are shown in Figure 2.
Figure 1: Tensile Test Fixture
Figure 2: Material Test Coupons (dimensions in mm)
Three coupons were prepared and tested for eachin both the fill and warp directions.
4
Results
Figures 3 and 4 show the stress-strain plots for the specimens tested in the fill and warp
directions, respectively. Note that the stress-strain plots are nearly linear, indicating a
constant modulus of elasticity (eeq. 3).
Figure 3: Stress-strain Curves in the Fill Direction
5
Figure 4: Stress-strain Curve in the Warp Direction
Table 2 gives a summary of the mechanical properties of the GFRP in both the fill and warp
direction. The modulus of elasticity was determined in the strain range of 0.001 to 0.003, as
specified in ASTM standards. Note that the variability between replicates was low.
Table 2: Tensile Properties of GFRP
Direction
Fill
Warp
Coupon
Modulus of
Elasticity
(GPa)
Tensile
Strength
(MPa)
%EL
Poisson’s
Ratio
T0-1
T0-2
T0-3
Average
T90-1
T90-2
T90-3
Average
16.83
16.27
16.80
16.64
17.69
18.39
17.68
17.92
289.7
288.2
275.7
284.5
339.9
337.7
328.5
335.4
2.21
2.27
2.07
2.18
2.36
2.38
2.32
2.35
0.125
0.136
0.126
0.129
0.127
0.143
0.122
0.131
6
Photographs of the specimens after failure are shown in Figure 5. Note the brittle nature of
the material at the point of failure.
(b) Warp Direction
(a) Fill Direction
Figure 5: Failure Modes of Tensile Test Coupons
Discussion
The test results show that the material behavior was very consistent. All three samples tested
in each direction yielded very similar values of modulus of elasticity and tensile strength (see
Figures 3 and 4). The mechanical properties are summarized in Table 2. TAgain, the
consistent nature of the material behavior is also apparent from the summary of mechanical
properties shown in Table 2. For example, the modulus of elasticity in the fill direction
varied from 16.27 to 16.83 GPa across the three samples, a variation of less than 5%.
Comparing Comparison of the measured mechanical properties of the GFRP (from Table 2)
with the published mechanical properties of the polymer matrix (given in Table 1), shows the
large increase in both stiffness and strength of the GFRP due to the embedment of the woven
glass fiber fabric, which act to reinforce the softer polymer matrix. it is apparent that
embedding the woven glass fiber fabric within the polymer increases both the stiffness and
strength of the material. The modulus of elasticity increased from 3.38 GPa to about 17 GPa
and the tensile strength increased from 80 MPa to about 300 MPa. However, the strain to
failure (%EL) decreased from 5-8% for the resin polymer alone to around 2% for the
composite material. This decrease is significant and indicates brittle failure. The brittle
nature of the composite material is illustrated in Figure 5.
There are about 5% more threads in the warp direction than the fill direction. The test results
show a 7.7% increase in elastic modulus and 17.9% increase in tensile strength in the warp
7
direction compared to the fill direction. These results imply that the increase in stiffness and
strength is not linearly proportional to the number of fibers.
Conclusions
Tensile tests were performed on GFRP and its mechanical properties were determined. The
findings are summarized below.

GFRP has superior properties to the individual materials.

Embedment of a woven glass fiber fabric within a polymer matrix increased both the
stiffness and strength of the material when compared to the mechanical properties of
the polymer alone.

Inclusion of the glass fibers produced a more brittle material

There is a slight variation in mechanical properties in the warp and fill directions,
presumably due to the different number of fibers in the two directions.
References
Dow Plastics (1999) DERAKANE Epoxy Vinyl Ester Resins – Chemical Resistance and
Engineering Guide, The Dow Chemical Company
Kitane, Y. Development of Hybrid FRP-Concrete Bridge Superstructure System. Ph.D.
dissertation, Dept. of Civil, Structural and Environmental Engineering, University at Buffalo,
2003.
8
Appendix B
Rules for Civil and Environmental Engineering
Lab Notebooks
Important rules for keeping your lab notebook:

















Use an appropriate notebook. Composition books are fine for this class but may not be appropriate later on
in your career.
On the cover, write your name and contact information (in case you lose it).
Reserve the first two pages for a table of contents which you will fill in as you fill in your notebook
For each experiment, complete the sections Title, Statement of Purpose, Background, Procedural Outline,
Data Collection, Results
Make all your notes directly into your lab notebook.
Never transfer your notes from another source into your notebook. You could make an error while transcribing and not realize it.
Number each page in the upper right corner in advance.
Do not skip any pages while taking notes. Take notes in chronological order.
Take notes on one side only. Leave other side blank for hand calculations or unimportant notes. (This becomes obvious if using carbon paper to make copies of your notes.)
Write only in black or blue ball point pen, never pencil.
Make corrections only by striking out writing with a single line, without obscuring the underlying text.
Note standard methods and describe your overall method.
Note any deviations from standard methods.
Note all instruments, model numbers, and calibration details.
Collect data in an organized manner. Use tables to organize the data.
Make sketches of lab setups if they will assist the reader in understanding what was done. For example,
sketch the locations where you took measurements from a pipe system.
Sign and date each page.
Appendix B
Group Self-Evaluation Form
Department of Civil, Structural and Environmental Engineering
University at Buffalo
Lab Group Self-Evaluation Form
Group Member
Percent
Contribution
Tasks Performed
Total =
100%
Course (circle one): CIE 360 CIE 361 CIE 362
Group ID: __________________________________
Group Leader: _______________________________
Date: ______________________________________
This form is to be completed by the Group Leader and attached to back of each lab report.
It will not be used to assign credit or grades unless obvious trends occur and identify a problem with one or
more of the group members.
Appendix C
Checklist for Civil and Environmental
Engineering Lab Reports
Purpose of the document:
Target audience:
Has the lab report been proofread?
Has the lab report been spell-checked?
Content
□ Title page complete
□ Introduction orients the reader
□ Objective clearly stated
□ Relevant theory included
□ Sufficient detail for duplication
□ Results are reasonable
□ Results are interpreted in discussion
□ Conclusions stem from discussion
□ Abstract summarizes entire document
Overall Document
□ Appropriate for target audience
□ Within page limit constraints (if any)
□ Well organized
□ Sections identified with headings
□ Consistent font, heading style, and voice
□ Good flow, reads as one document
□ Document paginated
Paragraph and Sentence Structure
□ Each paragraph contains one idea
□ Content of paragraph supports topic sentence
□ No run-on sentences or sentence fragments
Figures and Tables
□ Figures used for trends; tables used to show numbers
□ Figures and tables have numbering scheme and titles
□ Figures and tables are cited in the text by number
□ Figures have axes labeled with units
□ Figures have a legend (only if >1 series present)
□ Figure type (x-y, bar, etc.) is appropriate
□ Table column order is correct (indep. var. leftmost)
Data
□ Data have units, where appropriate
□ Number of significant figures makes sense
□ Precision and accuracy noted where appropriate
Equations
□ Equation editor used
□ Equations numbered
Appendix D
Common Problem Areas in Technical Writing
I
n addition to the rules of grammar discussed in
Chapter 3, several other words and phrases
cause problems in technical writing. Common
words and phrases that are misused in technical
writing are given below. Most of the words and
phrases listed below were found in Strunk and
White (1979) or Smith and Vesiland (1996).
affect/effect: These two words cause many difficulties in technical writing, but the rule regarding
their use is simple. The word “affect” is almost
always a verb. The word “effect” is almost always
a noun. Thus, write: “The effects of viscosity
were noted” (“effects” is a noun) and “Viscosity
affected the results” (“affected” is the verb).
Note: While “affect” is usually a verb, it is used in
psychology as a noun: for example, the Jones Affect. The word “effect” almost always is a noun,
but is used very rarely as a verb, as in: “Temperature effected a change in elasticity” (meaning temperature brought about a change in elasticity).
among/between: Use “between” when two people
or things are involved and “among” when more
than two or more people or things are involved.
For example: “The flow was split between two
pipes,” but “The work was divided among four
engineers.”
comprise: “Comprise” means “to consist of”:
“The frame comprises four steel rods” (i.e., the
frame consists of four steel rods) and “Four steel
rods make up the frame” (not: “Four steel rods
comprise the frame”).
double negatives: Avoid the use of two or more
negatives (“not” or words starting with “un-”) in
the same sentence. Rewrite by canceling out pairs
of negatives: “The lab was like our previous work”
(not: “The lab was not unlike our previous work”)
farther/further: “Farther” refers to distance,
while “further” refers to time or quantity. Thus:
“The beam was displaced farther on the shake table,” while: “Further studies are necessary to
quantify the results.”
fewer/less: “Fewer” is used in reference to the
number of things, while “less” refers to the quantity (or amount) of an object. For example: “Our
model has fewer adjustable parameters” (i.e., fewer number of parameters) and “The high efficiency
pump drew less current” (i.e., less amount of current).
irregardless: “Irregardless” is an example of a
double negative. The prefix ir- and the suffix -less
both negate regard. Please write “regardless” anytime you are tempted to write “irregardless.”
its/it’s: Here is a nagging exception to the rule that
you add an apostrophe to indicate the possessive
form. The word “its” is the possessive form: “Its
color was red”. The word “it’s” is a contraction of
“it is”: “It’s hot today.” In general, avoid contractions in formal writing.
personification: Personification is the assignment
of human characteristics to nonhuman objects, as
in: “The day smiled on me.” Personifications
should be avoided in technical writing. Some
people dislike the assignment of any active verb to
inanimate objects. In this view, some say you
should avoid statements such as: “The data
show...” or “The experiments demonstrate.…”
Although there is a difference of opinion on this
matter, it is best to avoid egregious examples of
personification in your technical writing (such as:
“The data really grabbed me by the throat,” which
is too informal as well!).
APPENDIX C: COMMON PROBLEM AREAS IN TECHNICAL WRITING
precede/proceed: “Precede” means “to come before,” while “proceed” means “to continue or
move forward.” Thus: “The structures labs preceded the fluids labs.” (meaning, the structures lab
was conducted first) and “The work proceeded
without interruption.” (meaning, the work continued without interruption).
presently: “Presently” means both “soon” and
“currently”. Strunk and White (1979) suggest that
“presently” be used only in the sense of “soon.”
D-2
Appendix E
SI Units
Quantity
Length
Mass
Time
Electric current
Temperature
Amount of substance
Luminous intensity
Plane angle
Solid angle
Unit(s)
Symbol and/or Formula
Base Units
meter
kilogram
seconds
ampere
kelvin
mole
candela
m
kg
s
A
K
mol
cd
Supplementary Units
radian
steradian
rad
sr
Common Derived Units with Special Names
Hz (= s-1)
hertz
Frequency
newton
Force
N (= kg-m/s2)
pascal
Pressure or stress
Pa (= N/m2)
joule
Energy or work
J (= N-m)
watt
Power
W (= J/s)
coulomb
Quantity of electricity
C (= A-s)
volt
Electric potential
V (= W/A)
farad
Capacitance
F (= C/V)
ohm
Electric resistance
Ω (= V/A)
siemens
Conductance
S (= A/V)
weber
Magnetic flux
Wb (= V-s)
telsa
Magnetic flux density
T (= Wb/m2)
henry
Inductance
H (= Wb/A)
lumen
Luminous flux
lm (= cd-sr)
lux
Illuminance
lx (= lm/m2)
Common Derived Units without Special Names
m2
Area
Volume
m3
Velocity
m/s
Acceleration
m/s2
Density
kg/m3
Specific volume
m3/kg
Entropy
J/K
Radiant intensity
W/sr
Bending moment (or
N-m
torque)
Heat capacity
J/kg-K
Adapted from Wright (1994)
Appendix F
Engineering Models
F.1 FITTING A MODEL TO DATA
  y i  yˆ i   3  2  0  1 .
3
n
SE    y i  yˆ i 
i 1
An example of computing SE is given in Figure
F.1. For the data in Figure F.1:
i 1
15
y–ŷ=0
10
y
y – ŷ = +2
5
{
} y – ŷ = –3
0
0
2
4
x
Data
6
8
Model
Figure F.1: Example of Computing SE
Is SE a good measure of the differences between
the model predictions and the experimental data?
SE is not a good measure of how well the model
fits the data. Why? In the SE, the “negative” errors (i.e., yi – ŷi less than zero) will cancel out
“positive” errors (i.e., yi – ŷi greater than zero).
For example, consider the data and model output
in Figure E.2. The model is: yi = mxi. Model output is shown for m = 2. For this value of m, SE =
0 because the negative errors and positive errors
cancel out. Even though SE = 0, it is clear from
Figure E.2 that the model yi = 2xi is not a “perfect”
model for the data.
y
As an engineer (and as a student in the lab
courses), you will compare model output to measured values. It is critical at this stage to fit the
model to the data rather than the data to the model. Never exclude data because they do not fit
your preconceived notions of what the data should
look like. In other words, do not reject data just
because the data does not match the model.
What is meant by “fitting the model to the data?” Fitting a model means finding the values of
the adjustable parameters so that the model output
matches the experimental data as closely as possible. This process is called model calibration.
There are a number of fitting tools used by
engineers to calibrate models. In this manual, a
numerical approach will be introduced. Before
discussing the fitting method, it is necessary to
think about how you will know when the model
output matches the data satisfactorily. A common
approach is to formulate a function that describes
the error in the model prediction and then pick
adjustable parameter values to minimize the function. The function describing the error sometimes
is called the objective function. Say, for example,
that the deterministic model has one independent
variable x, one dependent variable y, and one parameter m. From experiments, you have n pairs of
x and y values. The x values are denoted x1, x2, …,
xn and the y values are denoted y1, y2, …, yn. Since
the model is deterministic, each value of x (i.e.,
each xi) will give one predicted value of y (usually
denote ŷ i and pronounced “why eye hat”).
One possibility for an objective function is the
sum of the differences between the model predictions and the data. This is called the sum of the
errors (or SE). For the n data points (i.e., n pairs
of xi and yi), SE is given by:
14
12
10
8
6
4
2
0
Data
Model
0
2
4
x
6
8
Figure F.2: Example Model and Data to Illustrate Model Fit
F-2
APPENDIX F: ENGINEERING MODELS
There are many possible objective functions
where the positive and negative errors do not cancel out. A commonly used objective function is
the sum of the squares of the errors, SSE:
spreadsheet. Values of SSE are plotted against n
in Figure E.4. Note that the units of SSE are the
units of the dependent variable squared. What is
your estimate of n from Figure F.4?
n
2
SSE    y i  yˆ i 
4
SSE (cm )
i 1
To fit a model to data, the mathematical problem
becomes: find the set of adjustable parameter values that minimize the SSE.
To illustrate the use of SSE, consider an exciting new field of engineering: the use of fractal
geometry to describe the dimensions of irregular
objects. In common objects, the area (A) increases
proportionally to the square of a characteristic
length (l). Examples include circles (where A =
r2; r = radius), spheres (where the surface area =
4r2), squares (where A = s2; s = side), cubes
(where the surface area = 6s2), and equilateral tri3
s ). With fractal objects, A
angles (where A =
4
increases proportional to l raised to the power n,
where n is not necessarily equal to 2. Suppose you
measure the area of a family of fractal objects and
plot the area against the characteristic length (see
Figure F.3).
2
Area (cm )
400
300
200
1000000
800000
600000
400000
200000
0
0
1
2
3
4
n
Figure F.4: Variation of SSE with n in the Fractal Problem
From Figure F.4, SSE is minimized at n = 2.2-2.3.
As shown in this example, the values of the adjustable parameters should be selected so that SSE
is minimized.
The graphical approach of determining the
values of the adjustable parameters that minimize
SSE works well when your model has one adjustable parameter. The approach becomes more cumbersome with two adjustable parameters and virtually impossible to visualize with more than two
adjustable parameters. A common approach to
calibrating models containing more than one adjustable parameter is called regression analysis.
An example of regression analysis, linear regression, is presented in Section 5.3.
100
E.2 USING CALIBRATED MODELS
0
0
5
10
15
Characteristic length (cm)
Figure F.3: Data for Fractal Example
A reasonable model for the relationship between l
and A is: A = (proportionality constant)ln. Suppose
you know from other data that the proportionality
constant is equal to 1. Thus: A = ln. How would
you find n? One approach would be to vary n and
calculate the SSE. You can do this easily with a
During model calibration, the values of the adjustable parameters are determined. In this process,
the values of the dependent variables are calculated where data exist. These data sometimes are
called the calibration data set. The model outputs
for the calibration data set are called model fits.
You expect the model fits to be close to the data,
because you are using the data to fit the adjustable
parameters.
If you compare the calibrated model output to
other data (i.e., data outside the calibration data
set), the model outputs are called model predic-
F-3
CIVIL ENGINEERING LAB REPORT MANUAL
tions. Be sure to differentiate between model fits
and model predictions in your engineering work.
We want our models to be predictive; that is, to
predict data outside the calibration data set (but be
careful about extrapolation to values outside the
range of the calibration data set).
F.3 DETERMINING MODEL FIT
Another important issue in using models is determining how well the model fits the data. In fact,
you already know one way to look at model fits:
SSE. Unfortunately, SSE has a problem. It has
units of (units of y)2, so the magnitude of SSE depends on the units of y. SSE would be more useful
if it was dimensionless. One way to make SSE
dimensionless is to compare your model with the
simplest model for your dependent data. What is
the simplest possible model for any data? The
simplest model for a dependent variable y is: y =
constant. A reasonable value of the constant is the
arithmetic mean of the y values. Thus, the simplest model is:
yy
A more useful measure of model fit would be:
(SSE for your model)/(SSE for the simplest model), or:
(SSE for your model)/(SSE for the model y
= mean y)
In mathematical terms, this new measure is:
n
2
  y i  yˆ i 
i 1
n
2
  yi  y 
i 1
This new measure is equal to zero when the model
is perfect (SSE = 0) and is equal to one when the
model is no better than the simplest model (y =
mean y). This is ok, but it would be nice to have a
measure that was equal to one when the model is
perfect and was equal to zero when the model is
no better than the simplest model. This is accomplished by defining the correlation coefficient, r2:
n
r 2 1
2
  y i  yˆ i 
i 1
n
2
  yi  y 
i 1
The correlation coefficient is a very valuable
measure of the degree of fit of any model. It is
dimensionless and near one if the model fits the
data well. You can verify for the data in Figure
F.1 that r2 is equal to 0.98, indicating a good fit (r2
> 0.9 generally represents a good fit of the model
to the data).
F.4 SUMMARY
Engineers often rely on models to analyze data.
Always fit the model to the data, not the data to
the model. A common objective is to minimize
the sum of the squares of the errors (sum of
squares of the differences between the measured
and model-predicted values). Make sure to differentiate between model fits (model output for the
calibration data set) and model predictions (model
output for another data set). The correlation coefficient can be used to indicate model fit for any
model.