CE 68: STRUCTURAL DESIGN I
(REINFORCED CONCRETE DESIGN)
COURSE PROJECT REPORT
Analysis of Reinforced Concrete
Bridge
DEPARTMENT OF CIVIL ENGINEERING
COLLEGE OF ENGINEERING
CENTRAL MINDANAO UNIVERSITY
Authors:
Lecturer:
Bongato, Pearl Arnie B.
Flores, John Aldin M.
Gevero, Grace Devon G.
Magarao, Dinamae D.
Roxas, Ronald Jr. R.
Engr. Richard J. Aquino
February 11, 2015
Certification
This is to certify that part or parts of our work was not copied from
somebody else work. A proper and full referencing was included for all ideas
including plans, drawings, pictures and diagrams taken from the internet and other
sources.
For the material which is quoted essentially word-for-word is given in
quotation marks and referenced.
Pearl Arnie B. Bongato .......................Signed ........................Date ..........................
John Aldin M. Flores ..........................Signed ........................ Date ..........................
Grace Devon G. Gevero .....................Signed ........................ Date ..........................
Dinamae D. Magarao .........................Signed ..........................Date .........................
Ronald R. Roxas Jr. ............................Signed ........................ Date ..........................
i
Executive Summary
The project proposal is about the Reinforced Concrete Maluos Bridge
situated along the Bukidnon-Davao City Road at Kabalansihan, Kitaotao,
Bukidnon. The said project is designed using the analysis for reinforced concrete.
Certain parameters for the reinforced concrete structure has been considered in
order to attain the objectives formulated in the project for better results.
Accordingly, the factors and parametric awareness that may affect the integrity of
the bridge was considered. The elements of the bridge, the materials and its
corresponding properties, the different types of loading including impact, and the
different design assumptions has been rigorously considered.
Portland cement, coarse and fine aggregates, water, admixtures, and
deformed bars are materials that made up the reinforced concrete has been
identified and defined according to its properties and specifications as base on
theoretical codes. Compressive and tensile strength, stress-strain curve, Modulus
of Elasticity, creep and shrinkage, and quality control of both concrete and the
reinforcing bars were further elaborated. Next, the strength design method, NSCP
designs assumptions and safety provisions, loads and load combinations as based
on AASHTO and NSCP, and software programs used in the calculations and
design were discussed thoroughly. Under the plans and specifications were the
architectural and structural drawings which were shown. Such architectural
drawings includes the top view, general elevation, and isometric view of the
bridge while on the structural drawings includes the detailed drawings of the
beam, slab, barriers, and footings. Followed by the plans and specifications are
the results and discussion of the project. This is where the important parameters
and factors in the analysis and assumptions of the design was discussed. After the
analysis is the conclusion and recommendation for the project.
The bridge is designed to support an MS18 (H20-44) vehicle. The bridge
is composed of eight reinforced concrete beam/girder with a dimension of
350mm x 620mm. Beams located on both ends, supporting sidewalk live loadings,
has 5-25mm reinforcements, while beams supporting the roadway has 11-25mm
reinforcements. Moreover, it is composed of a 200mm-thick slab with a 125mmthick wearing course made of asphalt. Lastly, a spread footing with a dimension
of 9.54m by 3.5m with a thickness 600mm and with a 25mm diameter
reinforced bars has been designed. More detailed and elaborated results are
presented in Chapter 5.
ii
Contents
1 Project Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Objectives of the Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Scope and Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
1.4 Project Outline/Work-flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
2 Reinforced Concrete Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
2.1 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Main Ingredients of Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Portland Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Coarse and Fine Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.3 Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.4 Admixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
2.2.5 Compressive Strength . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . 6
2.2.6 Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.7 Modulus of Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
2.2.8 Creep and Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.9 Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Deformed Steel Bars . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 10
2.3.1 Philippine Standard Bars . . . . . . . . . . . . . . . . . . . . . . . . . . .12
2.3.2 Stress-Strain Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.3 Yield Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.3.4 Modulus of Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Design Methods 9
3.1 Strength Design Methods (SDM) . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
3.1.1 Description of Strength Design Methods . . . . . . . . . . . . . .15
3.1.2 NSCP Design Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.3 Load and Load Combinations . . . . . . . . . . . . . . . . . . . . . .16
3.1.4 NSCP Safety Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Structural Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
3.2.1 Structural Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . .20
3.2.2 Structural Design Procedures . . . . . . . . . . . . . . . . . . . . . . . .20
3.2.3 Design of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.4 Design of Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
3.2.5 Design of Footings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Plans and Specifications
4.1 Architectural Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Structural Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 Results and Discussion
iii
5.1 Structural Analysis and Design Assumptions . . . . . . . . . . . . . . . . .28
5.2 Computed Design Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2.1 Dead Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
5.2.2 Live Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2.3 Factored Loads and Load Combinations . . . . . . . . . . . . . . 29
5.3 Structural Design Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
5.3.1 Beam Sizes, Bars, Stirrups, Sketches . . . . . . . . . .. . . . . . . 31
5.3.2 Slab Sizes, Bars, Ties, Sketches . . . . . . . . . . . . . . . . . . . . .31
5.3.3 Footing Sizes, Bars, Sketches . . . . . . . . . . . . . . . . . . . . . . 31
6 Conclusion and Recommendations
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
Appendix A Design Aids
A.1 Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .34
A.2 Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Appendix B Structural Analysis. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .36
Appendix C Design Computations. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 39
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
iv
List of Figures
2.1 Materials used for concrete mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2.2 Stress-Strain Curve at short term loading . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.3 Creep Curve
9
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.4 Marking system for reinforcing bars . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
2.6 Stress-strain diagram for steel
....................... .........
14
3.1 Standard HS Truck Weight Distribution . . . . . . . . . . . . . . . . . .. . . . . . . .
17
4.1 Top view . . . . . . . . . . . . . . . . . . .
26
. . . . . . . . . . . . . . . . . .. . . . . . . . . .
4.2 Isometric view .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Elevation
5.1 Beam I
5.2 Beam 2
27
. . . . ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .
...........................
5.3 Design for slab
30
. . . . . . . . . . . . . . . . . . . . . . .30
. . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 31
5.4 Design for footing
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
v
List of Tables
1.1 Required Average Compressive Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 ASTM and Philippine Standards of reinforcement Bars
vi
. . . . . . . . . . . .. . .12
Acknowledgments
We would like to express our gratitude to our dear professor in this subject,
Engr. Richard Aquino, for his valuable advice, efforts in molding us to become
engineers, ideas in the field of bridge engineering, and undying support in making
this project. Our deepest thanks for him, in helping us to experience more and to
explore things in finishing this book. To the different programs he introduced to
us, that we are able to do things in easy way.
To the DPWH - District III for giving us the general plans and
specifications of the Maluos Bridge II.
To all the Civil Engineering Department faculties who were able to
elaborate further computations and discussion in accordance to analysis of the
bridge.
To the members of this group for all the brain-storms, trust, efforts, and
patience in developing this book, and making great teamwork.
To all engineers who were able to share there knowledge on the design
and analysis of bridges, the factors and considerations in designing a bridge, and
referral of the different bridge design and analysis software.
We also thank our Almighty God for giving us wisdom, knowledge and
understanding and gave us life. Thank You Lord. You are our inspiration. Words
cannot express Your love for us for You are an amazing God.
Words are not enough to utter for how thankful we are to the people who
become part in making this project.
vii
Chapter 1
Project Background
Bridges along national roads support the country’s sustainable economic
growth by facilitating the transport of goods and services. Nonetheless, there are
still challenges in ensuring the structural integrity of national bridges.
Planning and designing of bridges is the most significant aspect of
structural engineering. It is the manifestation of the creative capability of the
designers and demonstrates their imagination, innovation, and exploration. Bridge
design is a complex engineering problem. The design process includes
consideration of other important factors, such as the choice of bridge system,
materials, dimensions, foundations, aesthetics, and local landscape and
environment. Thus, the importance of conceptual analysis in bridge-designing
problems cannot be emphasized strongly enough.
Factually, the structural design scheme of the bridge presents a complex
problem for the structural designer despite the presence of modern technology and
advance computer facilities. The scope of such problem encompasses the
determination of general dimensions of the structure, the span system, and the
choice of a rational type of substructure. Furthermore, there is a demand to find
the most advantageous solution to the problem in order to determine the
maximum safety with minimum cost that is compatible with structural
engineering principles. Fulfilling these demands will provide the proper solution
to the technical and economic parameters, such as the structural behavior, cost,
safety, convenience, and external view.
Reinforced concrete is the most important material used in the
construction of structures especially bridges. The raw materials of concrete,
consisting of water, fine aggregate, and cement, can be found in most areas of the
world and can be mixed to form a variety of structural shapes. The great
availability and flexibility of concrete material and reinforcing bars have made the
reinforced concrete bridge a very competitive alternative. Moreover, structures
made from reinforced concrete are very rigid and has a long service life which is
1
ideal for highway bridges. However, several factors such as span,
foundation conditions, loads, architectural considerations and others should be
considered.
Due to the different catastrophic events, such as typhoons and earthquakes,
that is currently happening in our country, reinforced structures should strongly be
considered. In relation to this, the study of design of reinforced concrete structure
is crucial especially on highway bridges. Bridge aesthetics may be a great issue in
the visual impact of the community, but its performance, efficiency and cost is
severely important.
1.1 Project Description
The Maluos Bridge II that will be located in Kabanlasihan, Sinuda, Kitaotao,
Bukidnon along the Bukidnon-Davao City road is made of reinforce concrete. It
has a span of 8m, and a width of 5m from the outer face of the barrier to the
center line of the road. It has a total number of 8 reinforced beams/girders at
1.346m apart. The reinforced bridge was designed to withstand the MS18 (HS2044) vehicular loading.
1.2 Objectives of the Study



To design a reinforced concrete bridge;
To compute and identify the different loadings applied on the bridge; and
To analyze and design the different structural members of the bridge.
1.3 Scope and Limitation



The bridge is only limited on the design of a reinforced concrete structure;
Piles supporting the footings are excluded in the design; and
Longitudinal loads, environmental loads, wing loads, earthquake loads,
thermal loads, and loads due to stream flow are excluded in the design.
2
1.4 Project Outline/Work-flow
1. Identifying Structural Parameters
2. Creating Structural Design
3. Computation of Structural Loadings
a) Computation of Live Loads
b) Computation of Dead Loads
4. Structural Design Analysis in MS EXCEL or WPS Spreadsheets
5. Constructing Written Report
3
Chapter 2
Reinforced Concrete Materials
2.1 Concrete
Concrete is a mixture of sand, gravel, crushed rock, or other aggregates held
together in a rock-like mass with a paste of cement and water, other times added
with admixtures to change the workability, durability, and time of hardening of
the concrete [McCormac and Brown, 2010]. Nowadays, concrete is widely used
due to its availability, durability and cost. Figure 2.1 shows the different materials
used for concrete.
Figure 2.1 Materials used for concrete mixture
4
2.1.1 Main Ingredients of Concrete
2.1.1.1 Portland Cement
Portland cement is a powdered, grayish material that consists chiefly of
calcium and aluminum silicates. The American Society for Testing and Materials
had classified five types of Portland cement that are manufactured from the same
raw materials but of different properties depending on its blend. Type I cement is
the common cement used in construction, but the other four types are used for
special situations were early strength or low heat or sulfate resistance is needed.
2.1.1.2 Coarse and Fine Aggregates
Three-fourths of the concrete volume is composed of aggregates. Section
403.4.1 of the NSCP Code states that the limiting values are as follows: one-fifth
of the narrowest dimensions between the sides of the forms, one-third of the depth
of slabs, or three-quarters of the minimum clear spacing between reinforcing.
Aggregates should be strong, durable and clean for it may interfere the bonding
between the cement paste and aggregate. Additionally, the strength of the
aggregate has an effect on the strength of the concrete, and its properties may
greatly affect the concrete’s durability.
2.1.1.3 Water
Natural water that is potable and has no pronounced taste or odor is
satisfactory as mixing water for concrete. Section 3.4.1 of ACI Code stipulates
that the water used in mixing concrete shall conform to ASTM C1602. In which,
it allows the use of potable water without testing and includes methods for
qualifying non-potable sources of water with consideration of effects on its setting
time and strength. To ensure water quality, testing frequencies are monitored. It
also includes optional limits for chlorides, sulfates, alkalis, and solids in mixing
water that can be invoked when appropriate.
5
2.1.1.4 Admixtures
NSCP defined admixture as a material, other than water, aggregate, or
hydraulic cement, used as an ingredient of concrete and is added to concrete
before or during its mixing to modify its properties. There are admixtures to
accelerate or retard setting and hardening, to improve workability, to increase
strength, to improve durability, to decrease permeability, and to impart other
properties. Different kinds of admixtures depending on its functions are used in
constructions, namely accelerating admixtures, set-retarding admixtures, and airentraining admixtures.
2.1.2 Compressive Strength
Concrete has a relatively high compressive strength that is determine by
testing to failure of 28-day-old concrete cylinder at a specified rate of loading.
Thus, the values obtained for the compressive strength of concrete are to a
considerable degree dependent on the sizes and shapes of the test units and the
manner in which they are loaded. ACI Section 5.3.1.1 requires that the basis of
the compressive strength of the concrete shall not exceed the specified 28-day
strength selecting the proportions at very large values. And that for concrete
production facilities that have a compressive strength test records of not older
than 24 months to enable them to calculate satisfactory standard deviations, a set
of required average compressive strengths to be used for selecting concrete
properties is specified in ACI Table 5.3.2.1. Different compressive standard
deviation values would be used as stated by ACI.
6
Table 1.1 Required Average Compressive Strengths (ACI, 2011)
2.1.3 Tensile Strength
The tensile strength of the concrete varies from 8% - 15 % of its
compressive strength. Tensile strength is neglected in design calculations and has
a definite reduction effect on their deflections.
Tensile strength in concrete does not vary in direct proportion to its
ultimate compression strength making it quite difficult to determine with direct
axial tension loads because of the problems in gripping test specimens so as to
avoid stress concentrations, and because of difficulties in aligning the loads. The
tensile strength of concrete in flexure is quite important when considering beam
cracks and deflections.
2.1.4 Stress-strain Curve
A typical relationship between stress and strain for normal strength
concrete is presented in a stress-strain curve. The non-linearity is primarily a
function of the coalescence of microcracks at the paste-aggregate interface
[PortalConcrete, 2012]. Thus, the ultimate stress is reached when a large crack
network is formed within the concrete, consisting of the coalesced microcracks
and the cracks in the cement paste matrix. Corresponding to the ultimate stress,
the strain is usually around 0.003 for normal strength concrete.
The descending proportion of the stress-strain curve can be obtained by a
displacement or a strain controlled machines. Thus any extra load beyond the
7
ultimate capacity leads to a catastrophic failure of the specimen. And that the
strain at failure is typically 0.005 for normal strength concrete. Below shows the
stress-strain curve figure 2.2.
Figure 2.2 Stress-Strain Curve at short term loading [McCormac and
Brown, 2010]
2.1.5 Modulus of Elasticity
The ratio of normal stress to conforming strain for tensile or compressive
stresses below proportional limit of material is known as the Modulus of
Elasticity. NSCP Section 408.6.1 specifies that it shall be permitted to be taken as
w1.5c0.043√f’c (in MPa) for values of wc between 1,500 and 2,500 kg/m3. For
normal weight concrete, Ec shall be permitted to be taken as 4,200√f’c.
8
2.1.6 Creep and Shrinkage
Concrete is a structural material with time-dependent properties, such as
shrinkage as well as creep and its associated stress relaxation, which significantly
affect the structural behavior.
Concrete continues to deform for long periods of time under sustained
compressive loads which results in an additional deformation called creep or the
plastic flow. The amount of creep is largely dependent on the amount of stress. It
is directly proportional to stress as long as the sustained stress is not greater than
one-half of f’c, otherwise creep will increase rapidly [Nilson, et al., 2012]. Figure
2.3 shows the typical creep curve for concrete loaded in 600 psi at 28-days old.
Figure 2.3 Creep Curve
The paste consisting of cement and water fills the voids between the
aggregate and bonds the aggregate together when the materials for concrete are
mixed. It should be sufficiently workable so that it can be made to flow in
between the reinforcing bars and through the forms. When this water evaporates,
it made the concrete shrinks reducing the shear strength of the member. It may
also permit the reinforcements to be exposed to the atmosphere or chemicals.
9
Moreover, the amount of shrinkage is heavily dependent on the type of exposure.
2.1.7 Quality Control
The quality of milled-produced materials, such as structural or reinforcing
steel, is ensured by the producer, who must exercise organized quality controls,
usually specified by relevant ASTM standards. Concrete, in contrast, is produced
or closed to the site, and its final qualities are affected by a number of factors,
which have been discussed briefly. Therefore, efficient quality control must be
established at the construction site.
2.2 Deformed Steel Bars
Deformed reinforcing bars are composed of ribbed projections rolled onto
their surfaces to provide better bonding between the concrete and the steel.
Minimum requirements for these deformations have been developed in
experimental research.
Accordingly, Section 3.5.3.1 of ACI Code specifies that deformed
reinforcing bars shall conform to the requirements for deformed bars following
the specifications for carbon steel (ASTM A615), low-alloy steel (ASTM A706),
stainless steel (ASTM A955), and rail steel and axle steel (ASTM A996). The
ASTM specifications require that fy at least 414 MPa shall corresponds to a
tensile strain of 0.35 % be at least fy. Table 2.1 shows the ASTM standards of
Reinforcement Bars and Philippine Standards of Reinforcement Bars with its
specific bar designation, nominal mass, and nominal area. Figure 2.4 shows the
marking system for the reinforcing bars meeting the ASTM Specifications A615,
A706, and A996.
10
Figure 2.4: Marking system for reinforcing bars
11
2.2.1 Philippine standard bars
Table 2.1
ASTM and Philippine Standards of Reinforcement Bars
[NSCP, 2008]
2.2.2 Stress-strain diagram
The main properties that determine the characteristics of reinforcing bars
are its yield point and Modulus of Elasticity, Es. The latter is practically the same
for all reinforcing steels and is taken as Es = 200,000 MPa. The yield point of
steel is the stress at which the yield plateau establishes itself. Figure 2.5 the ideal
for Grade-40, Grade-60, and Grade-70 reinforcing bars, and for welded-wire
fabric. High strength bars generally do not have a well-defined yield point.
12
Figure 2.5: Stress and Strain Diagram [Wight, K. ]
2.2.3 Yield strength
The yield strength or yield point of a material is defined as the stress at
which a material begins to deform plastically. The strength of steel differs on its
composition and due to its different heat treatment conditions. The stress-strain
diagram of steel in which rupture strength, yield point, elastic limit and
proportional limit are shown in figure 2.6.
13
Figure 2.6: Stress-Strain Diagram for Steel [Nilson, et al.]
2.2.4 Modulus of elasticity
Young’s Modulus or the Modulus of Elasticity describes the tensile
elasticity or the tendency of an object to deform along an axis when opposing
forces are applied, and it is the ratio of tensile stress to tensile strain. For steel, the
Modulus of Elasticity is equal to 200,000 MPa.
14
Chapter 3
Design Methods
3.1 Strength Design Methods (SDM)
3.1.1 Ultimate Strength Design Methods/ Load and Resistance Factor
Design(LRFD) and NSCP Design Assumptions
LRFD is a factor used in different load present in a building. These factor is
used depending on the type of loads like dead loads, live loads, seismic loads and
wind loads. The live load analyzed in bridges is the moving load. Moving load is
the live load projected in the analysis of highway bridge loadings. The following
combinations of loads with its factors as based on Section 409.3.1 of the NSCP
Code is shown below:
1.
1.4D
2.
1.2D + 1.6L
3.
1.2D + 1.6(Lr or S or R) + ((0.5 or 1.0)*L or 0.8W)
4.
1.2D + 1.6W + (0.5 or 1.0)*L + 0.5(Lr or S or R)
5.
1.2D + 1.0E + (0.5 or 1.0)*L + 0.2S
6.
0.9D + 1.6W + 1.6H
7.
0.9D + 1.0E + 1.6H
Load combinations 1 and 2, where D stands for dead load and l stands for the
live load, are used in this project. Higher values obtain from the load
combinations are considered.
15
Significantly, the design factors for moment , shear and axial compression
load are as follows:
Mu≤øMn
Vu≤øVn
Pu≤øPn
Where ;
øMn = is the design strength
Mu = is the required strength
Vu = is the required shear
øVu = is the design shear
The design strength is the product of the nominal strength and strength
reduction factor, where the strength reduction factor is always less than 1. The
reduction factors, ø, depends on the type of section whether it is compressioncontrolled, tension-controlled, and transition-controlled section.
Ø factors for tension-controlled sections are the following:
Flexure = 0.9
Shear = 0.85
Column = 0.7
3.1.2 Loads and Load Combinations
1. Dead load
The dead load load shall consist of the weight of the complete structure
including the sidewalks, barriers, roadway, and other public utilities. However,
when a separate wearing course is to be place or replaced during and after
construction, AASHTO Section 1.2.2 for Bridge Specification states that an
adequate allowance shall be made for its weight in the design dead load,
otherwise, provision for future wearing surface is not required.
16
2. Live load
The live load consist of the weight of the applied moving load of the
vehicles, and sidewalk loadings.
Additionally, the live load to be considered is the MS18 (HS20-44) truck
or its lane equivalent loading in accordance with the DPWH Design Guidelines.
Sidewalk loadings vary depending on site conditions and would further require
engineering judgement that would consider the given DPWH Design Guidelines.
Moreover, a conventional computation in obtaining the live loadings is by
adapting the percentage weight distribution of the truck. Figure 3.1 shows the
weight distribution of standard HS truck.
Figure 3.1 Standard HS Truck Weight Distribution
3. Impact
Live load stresses produced by MS loadings shall be increased, depending
on the type of group and by the allowance as stated for dynamic, vibratory and
17
impact effects. Impact is added to the live load as based on AASHTO
recommendations. The reduction in impact values can be made for bridges when
conditions.
4. Others
DPWH Manual Load Ratings emphasized that longitudinal, environmental,
wind, earthquake, and thermal loads may not be considered due to the fact that the
occurrence of extreme values during the relatively short duration live loading is
extremely small.
3.1.4 NSCP Safety Provisions
The NSCP provided safety provisions for the building to stand with the
effects of loading present in the environment. The design strength must be greater
than or equal to the required loads with corresponding load combinations. That is:
Mu≤øMn
Vu≤øVn
Pu≤øPn
The strength reduction factor,ø, is important in the design. It must be in
tension-controlled section which is 0.9.
3.1.5 Structural Analysis Methods
3.1.5.1Classical Methods
In this method, the knowledge from Statics of Rigid Bodies and Strength
of Materials is highly needed, since all the formulas are used in this method was
derived based on the concept in the subjects. Implication of all the equation was
possible through design assumptions presented in the NSCP. The Strength Design
Method is the assumptions of all of the materials where steel is to be under yield
condition and concrete is close to failure. In order to start the analysis, stress and
strain compatibility and equilibrium are the requirements.
18
1. Stress and strain compatibility.
It is the free body diagram that easily constructs and shows a
compatibility equation. The diagram of a compatibility equation on a stress
distribution is a second degree curve. Whitney suggested to change the curve to a
simpler rectangular uniformly distributed load with its maximum stress of 0.85f’c
at a 28-day compressive strength of concrete.
2. Equilibrium.
It is the summation of all the forces into zero, so that the internal forces
could balance the effect of its external loads.
3.1.5.2 NSCP Moment and Shear Coefficient
In order to require full analysis in order to get the value of the maximum
moment and maximum shear, the moment and shear coefficient must be based on
the clear span distance between face of the support.
Coefficients are all based from the total distributed factor load (Wu),
the sum factor of dead load and live load.
Wu = 1.2D + 1.6L
NSCP Eq - 409.2
The moments and shear coefficients are the requirements given in the
NSCP Code section 408.4.3 as:





There are two more spans;
Spans are approximately equal, with the larger of two adjacent spans not
greater than the shorter by more than 20 %
Loads are uniformly distributed;
Unfactored live load does not exceed 3 times unfactored dead load; and
The members are prismatic.
NSCP also developed these coefficients to directly compute its maximum
moment and shear of the structures. Once these condition are violated, full
analysis of structure must be taken.
Mu= Cm(wuLn2)
Eq - 1
Vu= Cv(wuLn/2)
Eq - 2
19
Where Cm, and Cv are shear and moment coefficient.
3.1.5.3 Computer Programs
AutoCAD 2014
To improve the quality of the drawing design for better communications
and understanding of the designer, AutoCAD was used for enhancement.
WPS Spreadsheet
The use of electronic spreadsheet was utilized in the computations for the
design and analysis.
3.2 Structural Analysis and Design
3.2.2 Procedures of Structural Design:
3.2.2.1 Design of beams:
In designing a beam, there are alternative approaches that are needed to be
considered. First, ρ, width of the beam, and the effective depth from the extreme
compression fiber are set. The alternative approach is to preset b and d where ρ, is
unknown.
Dimensions and reinforcements are need to be specified so that factored load
moment is resisted, thus, two possible approaches are considered.
1.
Compute the  min and  max with the following formula:
 min 
20
f ' c 1.4

4 fy
fy
Choose the higher value among the two ρ values for ρmin.
 max  0.75 bal
0.85 f ' c 1 600
(
)
 bal 
 max
fy
600  fy
0.85 f ' c 1  cu

(
)
fy
 cu   t
Use ρ value that ranges from  min ≤ρ≤  max
2. Compute the bd²
The flexural resistance is determine by using this formula:
Rn  fy (1  0.5 m)
m
fy
0.85 f ' c
bd 2 
Mu
Rn
3. Set the values of b (base of the beam) and d (the distance from the
compression fiber to the centroid of the steel).
With the use of different dimension of b, bd² must be divided with the
assumed b, and the square root of the quotient to get d. Next, d would then be
added to the clear cover to get h ( the height of the beam). Standard minimum
cover provided by the NSCP 407.8.1 of 40-mm plus the diameter or the stirrup
and half of the diameter of the bar is taken to obtain the clear cover. Using
economical sections which is:
1.5  h  2.0
b
21
Values that satisfies the stated expression should be the bases of the
economical section of the beam. bd² that has been provided and required should
be compared. Thus, the provided bd² should be greater than or equal to the
required bd².
4. Revision of the ρ must less than or equal to  max and greater than ρmin.
By using the formula, revised ρ can be determine:
1
2 Rn
  (1  1 
m
0.85 f ' c
First, the Rn(flexural resistance) is taken by the formula below:
Rnprovided 
Mu
bd 2 provided
5. The area of the reinforcing steel is computed using the revised ρ with the
formula:
Asrequired   revise bd
6. Reinforcement was selected using As (required). From this, the area of bars
25mm or 20mm diameter are obtained using the stated formula:
Asrequired
n
As25or 20 mm
7. Spacing of the reinforcements are obtained satisfying the requirement
provided that the spacing of the reinforcement must be greater than or
equal to Smin of the chosen bar (25mm diameter) by using this formula:
S
b  2ds  4ds  ndb
n 1
22
8. The section was checked with the conditions that if øMn≥Mu, then your
design is GOOD, Oh Yeah!
3.2.2.2 Slab Design
In designing, normally, the design of slab is the same although the base (b)
of the slab is one-meter-strip. The assumed thickness of the slab is to be referred
to the Table 409-1 - Minimum Thickness of Non-prestressed beams or one way
slab unless deflection are computed under the NSCP code section 409.6.2.3. Then
it was assumed also that the moment arm in getting the øMn is 0.95d. Compute
The spacing of the tension bars in a one-meter-strip was computed. And a
checking was enhance the section is good if øMn≥Mu.
3.2.2.3 Design of Footings:
Normally, the design footing of the bridge is complicated compare to the
vertical structures. So, values were assumed such as the allowable soil bearing
pressure(qa), the depth of the footing from the ground surface (df),unit weight of
the soil( s ) and thickness of the footing (hf) in the design. The base of the footing
was computed by using this formula:
A
Pdl  Pll
qe
A
b
L
1. Qu was computed using this formula:
qu 
1.2( DL)  1.6( LL)
Arequired
23
2. The shear was checked to assure that it is capable of resisting of one way and
two way shear.
Vc  Vu
For one way shear, this formula was used:
Vu  qu ( Aef )
b  a  2d
)( L)
2
1
Vc    f ' cbd
6
Vu  qu (
For two-way shear (punching shear), the formula below was used:
Vu  qu ( L2  (
b0 2
) )
4
d  hf  cc  db
b0  2(a  d )  2(b  d )
Vc    f ' cb0 d
1
3
Mu, Rn, and ρ was obtained using the following formula:
Mu  qu * B(
Rn 
Mu
bd 2

B  width 2 1
) ( )
2
2
1
2 Rn
(1  1 
m
0.85 f ' c
24
The reinforcements that would be used in the design of the footing was
obtained by using the same process like that of the beam. And that, the selected As
would be based on the following formula:
Asrequired   revise bd
Area and number of the bars could then be determined. The spacing of the
reinforcement was then checked.
Moreover, the spacing of the reinforcement must be greater than or equal
to Smin which is 25mm by using this formula:
S
b  2ds  4ds  ndb
n 1
The section was checked. If øMn≥Mu, then your design is GOOD, Oh Yeah!
25
Chapter 4
Plans and Specifications
4.1 Architectural Drawings
The isometric view, top view and the general plan of the Reinforced
Concrete Maluos Bridge are presented in the following subsections:
Figure 4.1 Top View
26
4.1.1 Isometric
The Maluos Bridge is an eight-meter span reinforced concrete bridge. it is
composed of a barriers, curbs, sidewalk, roadway with composed of wearing
course and reinforced concrete beams or girder.
Figure 4.2 Isometric View
4.1.2 General Elevation
Figure 4.3 Elevation
27
Chapter 5
Results and Discussion
5.1 Structural Analysis and Design Assumptions
In the structural design, specifically in the computation of loading, there
were many assumptions. It was assume in the computation of dead loads that the
unit weight of the concrete was 24 kN/m³, the slab thickness was 200 mm, the
beam dimensions were 600 mm x 350 mm, the unit weight of the asphalt was 22
kN/m³, the beam spacing from center to center was 1.364 m, the tributary width of
1.652 m, the sidewalk width of 1.11 m, the asphalt thickness of 125 mm, asphalt
width of 0.682 m, the railing height was 0.9 m, the railing width was 250 mm, the
vertical railing area was 0.0625 m², the horizontal railing area was 0.04 m², the
number of horizontal railing was 2, the number of vertical railings was 5, and the
length of the span was 8 m.
In the computation of live loads, the assume value were ; from the
AASHTO standards, the assumed weight (W) of the truck ( HS20-44/MS-18) was
33 metric tons or equivalent to 33000 kg. The load carried in the front wheel axle
was according to AASHTO was 0.1 W (P1), the center wheel was 0.4 W (P2) and
also 0.4 W (P3) of the rear wheel that is according to AASHTO standards. The
distance between P1 and P2 was also assumed to be 4.27 m and distance between
P2 and P3 was also assumed to be 4.87. It was also assumed that the live load in
sidewalk was 12 kPa from NSCP.
In the design of the beams in flexural and in shear, slabs and footing, the
assumed value were; the modulus of elasticity of the steel (E) was 200000 MPa,
the compressive strength of the concrete ( f’c) was 28 MPa and the yield strength
of the steel (fy) was 414 MPa.
In the design of the footing, there were some value that were needed to be
assumed. The allowable bearing pressure (Qa) was assumed to be 90 kPa. The
depth of the footing (Df) was assumed to be 2 m. The thickness of the footing (Hf)
was also assumed to be 600 mm. The average unit weight of the soil and the
concrete was also assumed to be 20 kN/m³.
28
5.2 Computed Design Loads
5.2.1 Dead Load
In the bridge, there were eight beams in a width of it. The edges
beam were assumed to be Beam1 and the remaining six beams were also
assume to be Beam2. For Beam1, the total computed dead load was
24.269 Kn/m. For Beam 2, the total computed dead load was 15.338
Kn/m. There was great difference between the magnitude of the total dead
loads carried by Beam 1 and Beam 2. This was due to the fact that Beam 1
carried the railings, the sidewalk slab and the beam.
5.2.2 Live Load
The live load computation have to parts the computation of the live
load for Beam 1 and Beam 2 just like in the dead load. For Beam 1, the
total computed live load was 13. 32 kN. And for Beam 2, the total live
load computed was 311.96 kN-m including the addition factor due to
impact.
5.2.3 Factored Loads and Load Combinations
Normally in the design of the any building structure with high
percentage of live load. The load combination usually 1.2 of the dead load
and 1.6 of the live load. The other solution is to get each moment
combinations just like the students did. For beam 1, the computed 1.2
moment due to dead load was 232.98 kN-m and for 1.6 moment due to
live loads was 170.496 kN-m. For Beam 2, the 1.2 moment due to dead
load was 147.25 kN-m, and the 1.6 moment due to live load including the
impact load added was 499.136 kN-m.
5.3 Structural Analysis Results
For Beam 1, the computed 1.2 of the dead load and 1.6 of the live
load moment was 403.48 kN-m. Normally the load factor of 1.2 for dead
load and 1.6 for live load was used because it is always greater to the
combination 1.4 of the dead load in the design of the bridge. For Beam 2,
the computed values with their load factors was 646.386 kN-m.
5.4. Beam Sizes, Bars, Stirrups, Sketches
29
Figure 5.1 Beam I
The design of the beam was computed in the help of a computer
program called WPS SpreadSheet. The dimension of the Beam 1 was 620
mm by 350 mm. The number of the bars of 25 mm diameter bar which
was from the spreadsheet was five with two layers. The spacing of the
stirrups from the distance d from the face of the support was 270 mm. So,
it assumed that the spacing of a 8 meter span of the stirrups from the face
of the support was 1-50 mm, 5-200mm, 8-270mm and the remaining
reinforcements at 300mm.
Figure 5.2 Beam 2
The dimension of the Beam 2 was 620 mm by 350 mm. 8-25mm
diameter bars designed at two layers was calculated using WPS
Spreadsheet. The spacing of the stirrups from the distance d from the face
of the support was 150 mm. So, it assumed that the spacing of an 8 meter
span of the stirrups from the face of the support was 1-50 mm, 5-100mm,
8-150mm and the rest reinforcements are 300mm.
30
5.5 Slab Sizes, Bars,Sketches
Figure 5.3 Design for Slab
In this design of the slab in flexure, a one meter strip by the thickness of
the slab of 200 mm. Still 25 mm diameter bar with 16 bars, the numbers of bars,
spaced with 37.33 mm. The student was not able to design the slab in shear.
5.6 Footing Sizes, Bars, Sketches
Figure 5.4 Footing Design
In the design of the footing, there were values that were assumed. And the
results from the assumed value were; the dimension of the footing was 9.54m by
3.5 m, the number of bars for the longitudinal reinforcements with 25 mm
diameter of the bar was 47 bars spaced with 91 mm spacing. And in the transverse
reinforcements, the number of bars with 25 mm diameter of the bar was 28 bars
spaced with 321.85 mm spacing.
31
Chapter 6
Conclusions and Recommendations
6.1 Conclusion
The Reinforced Concrete Bridge was located at Maluos, Kitaotao,
Bukidnon with a span of 8 meters and a width of 9.54 meters designed as
reinforced concrete. There are 8 beams distributed equally at 1.364 to the whole
width of the bridge. All beam 1, were located from edge to edge. Six beam 2 were
located at the center between the two beam 1.
The flexural design of beam 1 and beam 2 were different because the load
carried by beam 1 was different from that of the load carried by beam 2. In beam
1, loads are composed of the dead load (beams, slab, sidewalk slab, railings) and
live load such as human. In beam two, it has a dead load composed of the beam,
slabs, asphalt/wearing course, and its live load. The dimensions of the beams are
all through-out the same, 620mm by 350mm. They only differ on the number of
bars present in beam 1 and beam 2. The number of bars in beam 1 was 5 and in
beam 2, was 8. The shear design of the beam 1 and the beam 2 were differentas
well as its required shear. The spacing of the stirrups from a distance d from the
face of the support of the beam 1 was 270 mm of the beam 1. The spacing of
stirrups from the distance d from the face of the support was 150 mm of the beam
2. It was concluded the bigger the shear the lesser its spacing and the bigger the
moment the more number of bars were used.
The design of the slab was 1 meter strip and only for the slab of the
roadway. The design of the slab was the same as the beam. From NSCP table
409-1, the minimum thickness of the slab with an assumed value was taken, then
the design was complete. 25 mm diameter bars were used with with a spacing of
37.33 and it was good because it was bigger than the minimum spacing which is
25 mm.
The design of the footing of the bridge was very difficult without conduct
a study of the typical soil profile of the location. Thus, there were so many
assumptions to be made. The computed overall load reactions was carried by
each support. Then, qa (allowable bearing pressure) was assumed as well as the
32
dimensions of the piers. The depth from the base of the footing to the ground
surface was also assumed. Then, results were computed. In the longitudinal
reinforcements, 25mm diameter of the bar with a spacing of 91mm was adopted,
and in the transverse reinforcements, 25mm diameter of bar with a spacing of
321.85 mm was used.
6.2 Recommendations
Reinforced concrete bridge is one of the featured structure in the society.
Moreover, the design of the bridge should be critical to ease integrity and cost on
the structure. Thus, it is recommended to make and follow exact and accurate
values, and design codes and methods according to the NSCP and ACI.
Furthermore, the use of structural bridge designers would truly be appreciated to
elaborate more of the parameters, such as the finite element analysis of the bridge.
Additionally, the assumptions of values considered in designing should be
approximate to the actual values, otherwise iterative calculations are extensively
observed.
In this analysis, live loads and dead loads are only considered. Thus, it is
important to include the seismic, longitudinal, uplift, and wind loads for further
analysis.
33
Appendix A
Design Aids
A.1 Table
34
Table 2.1
ASTM and Philippine Standards of Reinforcement Bars
[NSCP, 2008]
35
A.2 Chart
Figure 2.5: Stress and Strain Diagram [Wight, K. ]
Figure 2.6: Stress-Strain Diagram for Steel [Nilson, et al.]
36
Appendix B
Structural Analysis
37
38
39
Appendix C
Design Computations
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
ANALYSIS OF DESIGN FOR BEAM 1
55
56
ANALYSIS OF DESIGN FOR BEAM 2
57
58
References
AASHTO (1973). Standard specifications for highway bridges.
ACI 318-11. (2011). Building code requirement for structural concrete.
Bernas, A. (2006). Heavy impacts on bridge restraint systems. International
conference on bridges. Retrieved from www.deltabloc.com
Chen, W.F. And Duan L. (1999). Bridge engineering handbook. CRC Press (08493-7434-0).
Grahn, M. (2012). Structural analysis and design of concrete bridges: current
modelling procedures and impact on design. Master’s Programme
Structural Engineering and Building Performance Design. Sweden.
McCormac, J., and Brown, R. (2012). Design of reinforced concrete, 9th ed. Wiley
and Sons, Inc.
Nilson, A., Darwin, D., and Dolan, C. (2010). Design of concrete structures, 14th
ed. McGraw Hills, NY.
NSCP. (2008). Chapter 4: Structural concrete.
Swanson, J.A. & Miller, R. A. (2007). LRFD bridge design: AASHTO LRFD
bridge design specifications.
59