INTRODUCTION TO PRC II
1
CE-401 PLAIN & REINFORCED CONCRETE-II 3+0
•
•
•
•
Schedule: Tuesday and Thursday 08:00 am to 9:30 am
Venue:
Computer Lab-4
Objective:
To give concept to students about the conventional and advanced
designing approaches for various structural elements.
• Course Contents
• Flat Slab, Flat Plate and Waffle Slab: Analysis and design of flat
plate, flat slabs and waffle slabs, for flexure and shear under gravity
loading.
• Slender Columns: Analysis and design of slender columns subjected
to combined flexure and axial loading, Guidelines for design of
shear walls-an over view.
• Design of Different Types of Foundations: Analysis and design of
eccentric, strap, strip and mat footings, piles and pile caps, Buoyant
Footings.
• Stairs: Analysis and Design of Various Types of Stairs and Staircases.
2
Pre-stressing
• Principles & Design Philosophy: Principles of prestressing, properties of high strength materials,
Importance of high strength concrete and steel used in
pre-stressing, Behavioral aspects of pre-stressed beams
and comparison with reinforced concrete beams, posttensioning and pre-tensioning techniques, Profiles of
post-tensioned tendons, bonded and non-bonded
tendons, comparison and hard-ware requirements.
• Pre-stress Losses: Pre-stress losses, immediate and
time dependent losses, lump sum and detailed
estimation of pre-stress loss.
• Analysis and Design: Simply supported pre-stressed
beams for flexure and shear.
3
Books Recommended
• Nilson, A.H., Darwin, D. and Dolan, C.W.,
Design of Concrete Structures Fourteenth
Edition
• McCormac, J.C. and Nelson, J.K., Design of
Reinforced Concrete Sixth Edition
• Nilson A.H., Design of Pre-stressed concrete,
John Wiley and Sons.
• Gregor, J.G.M. Reinforced Concrete Design,
Prentice Hall
4
Weekly Course Distribution
Week
01
02
Topics to be covered
Overview one-way slab. Analysis and design of flat plate
for flexure and shear under gravity loading.
Analysis and design of flat slab for flexure and shear under
gravity loading, Overview of waffle slab.
03
Introduction to columns, overview of short columns.
Introduction to slender columns.
04
Analysis and design of slender columns.
05
Overview of various types of staircases.
06
Overview of shear wall design, isolated footing and
rectangular footing.
07
Design of combined footing.
08
Analysis and design of strip and strap footings.
09
Comments
Assignment: 01
Quiz: 01
Assignment: 01 (DD)
Assignment: 02
Assignment: 02 (DD)
Assignment: 03
Quiz: 02
Mid Semester Exams
5
Week
Topics to be covered
Comments
10
Analysis and design of eccentric, mat footings, and Assignment:03 (DD)
buoyant footings.
Assignment: 04
11
Overview of piles and pile caps.
12
Principles of pre-stressing, Properties of high strength
materials, Importance of high strength concrete and steel
Assignment:04 (DD)
used in pre-stressing, behavioral aspects of pre-stressed
beams and comparison with reinforced concrete beams.
13
Post tensioning and pre-tensioning techniques, profiles of
Quiz: 04
post tensioned tendons, bonded and non-bonded tendons,
Assignment: 05
comparison and hardware requirements.
14
Pre-stress losses, immediate and time dependent losses,
lump sum and detailed estimation of pre-stress force, Quiz: 05
simply supported pre-stressed beams for flexure and shear.
15
Design of Pre Stressed Beams
16
Quiz: 03
Assignment: 05(DD)
Introduction to seismic design / Revision
6
Letter Grades and Numerical Value
• Letter Grade
Numerical Value
A
AB+
B
BC+
C
F
4.00
3.67
3.33
3.00
2.67
2.33
2.00
0.00
7
Course Grading System
Grades will be determined on the basis of
•
•
•
•
•
5 Assignments
5 Quizzes
Mid-term test
Term Project
End Semester Exam
10%
10%
20%
15%
45%
8
Rules for Class
• Start with Talawat/translation
• TA/Grader:
Ms Siddique
• Office Hours:
MW 11-30 to 13-00
• All material shall be available in advance on the website/ through
Group Mail ce2011@wecuw.edu.pk
• Students are expected to come prepared for the class
• Solving of home assignment in class will contribute towards the
student’s grading of the course
• Disclaimer / Seating Plan
9
Flat Plate/Slabs
Two Way Slabs
10
TYPES OF SLABS
• Gen broad flat plate, usually horizontal with top
and bottom surfaces parallel or nearly so
• May be supported by:
– RC beams, masonry or RC walls, structural steel cols,
directly by columns, or continuously by the gr
• Support conditions:
–
–
–
–
–
Two opposite sides
Beams on all four sides
Intermediate beams
Directly by columns
Directly by columns with thick ended region near
columns
– Ribbed construction
– On ground continuously
11
INTRODUCTION
In general, slabs are classified as being one-way or two-way.
Slabs that primarily deflect in one direction are referred to
as one-way slabs. Simple-span, one-way slabs have
previously been discussed; while the design of continuous
slabs so that the slabs can deflect in two directions, referred
to as two-way slabs will be discussed in detail.
Depending on load conditions and other requirements slabs
may be strengthened by the addition of beams between the
columns, by thickening the slabs around the columns (drop
panels), and by flaring the columns under the slabs (column
capitals). These situations will be shown and discussed in the
lecture.
12
TYPES OF SLABS
13
TYPES OF SLABS
14
TYPES OF SLABS
Flat plates are solid concrete slabs of uniform depths that transfer
loads directly to the supporting columns without the aid of beams
or capitals or drop panels. Flat plates can be constructed quickly
due to their simple formwork and reinforcing bar arrangements.
They need the smallest overall story heights to provide specified
headroom requirements, and they give the most flexibility in the
arrangement of columns and partitions. They also provide little
obstruction to light and have high fire resistance because there
are few sharp corners where spalling of the concrete might occur.
Flat plates are probably the most commonly used slab system
today for multistory reinforced concrete hotels, motels,
apartment houses, hospitals, and dormitories.
15
TYPES OF SLABS
Flat plates present a possible problem in transferring the shear at
the perimeter of the columns. In other words, there is a danger
that the columns may punch through the slabs. As a result, it is
frequently necessary to increase column sizes or slab thicknesses
or to use shear heads. Shear heads consist of steel I or channel
shapes placed in the slab over the columns. Although such
procedures may seem expensive, it is noted that the simple
formwork required for flat plates will usually result in such
economical construction that the extra costs required for shear
heads are more than canceled. For heavy industrial loads or long
spans, however, some other type of floor system may be required.
16
TYPES OF SLABS
17
TYPES OF SLABS
Flat slabs include two-way reinforced concrete slabs with capitals, drop
panels, or both. These slabs are very satisfactory for heavy loads and
long spans. Although the formwork is more expensive than for flat
plates, flat slabs will require less concrete and reinforcing than would be
required for flat plates with the same loads and spans. They are
particularly economical for warehouses, parking and industrial buildings,
and similar structures where exposed drop panels or capitals are
acceptable.
18
TYPES OF SLABS
In Figure above a two-way slab with beams is shown. This type of floor
system is obviously used where its cost is less than the cost of flat plates
or flat slabs. In other words, when the loads or spans or both become
quite large, the slab thickness and column sizes required for flat plates
or flat slabs are of such magnitude that it is more economical to use
two-way slabs with beams, despite the higher formwork costs.
19
TYPES OF SLABS
Another type of floor system is the waffle slab, an example of
which is shown in the next slide. The floor is constructed by
arranging square fiberglass or metal pans with tapered sides with
spaces between them as shown. When the concrete is placed
over and between the pans, the waffle shape is obtained. The
intervals or gaps between the pans form the beam webs. These
webs are rather deep and provide large moment arms for the
reinforcing bars. With waffle slabs, the weight of the concrete is
greatly reduced without significantly changing the moment
resistance of the floor system. As in flat plates, shear can be a
problem near columns. Consequently, waffle floors are usually
made solid in those areas to increase shear resistance.
Many slabs are continuously sp on the gr, as for highways,
airports, warehouse floors. In such cases, a well compacted layer
of crushed stone or gravel is provided to ensure uniform support
and to allow for sub grade drainage.
20
TYPES OF SLABS
21
TYPES OF SLABS
• Reinforced concrete slabs being discussed are
usually designed for loads assumed to be
uniformly distributed over the entire slab
panel, bounded by beams or supporting
columns centerlines. Minor concentrated
loads can be accommodated through two-way
action of the reinforcement. Heavy
concentrated
loads
generally
require
supporting beams.
• The one way and two structural action can be
visualized as shown in next two slides.
22
ONE-WAY SLAB ACTION
23
TWO-WAY SLAB ACTION
24
BEHAVIOR OF TWO-WAY EDGE-SUPPORTED SLAB
25
CORNER REINFORCEMENT
26
27
TEMPERATURE AND SHRINKAGE REINFORCEMENT
28
TEMPERATURE AND SHRINKAGE REINFORCEMENT
29
TEMPERATURE AND SHRINKAGE REINFORCEMENT
30
ANALYSIS OF TWO-WAY SLABS
31
ANALYSIS OF TWO-WAY SLABS
Two-way slabs bend under load into dish-shaped surfaces, so there is
bending in both principal directions. As a result, they must be reinforced
in both directions by layers of bars that are perpendicular to each other.
A theoretical elastic analysis for such slabs is a very complex problem
due to their highly indeterminate nature. Numerical techniques such as
finite difference and finite elements are required, but such methods are
not really practical for routine design.
Actually, the fact that a great deal of stress redistribution can occur in
such slabs at high loads makes it unnecessary to make designs based on
theoretical analyses. Therefore the design of two-way slabs is generally
based on empirical moment coefficients, which, though they might not
accurately predict stress variations, result in slabs with satisfactory
overall safety factors. In other words, if too much reinforcing is placed in
one part of a slab and too little somewhere else, the resulting slab
behavior will probably still be satisfactory. The total amount of
reinforcement in a slab seems more important than its exact placement.
32
ANALYSIS OF TWO-WAY SLABS
You should clearly understand that next three lectures are devoted to
two-way slab design based on approximate methods of analysis, there is
no intent to prevent from using more exact methods. You may design
slabs on the basis of numerical solutions, yield-line analysis, or other
theoretical methods, provided that it can be clearly demonstrated that
they have met all the necessary safety and service ability criteria
required by the ACI Code.
Although it has been the practice of designers for many years to use
approximate analyses for design and to use average moments rather
than maximum ones, two-way slabs so designed have proved to be very
satisfactory under service loads. Furthermore, they have been proved to
have appreciable overload capacity.
33
DESIGN OF TWO-WAY SLABS
THE ACI CODE
34
DESIGN OF TWO-WAY SLABS BY THE ACI CODE
The ACI Code (13.5.1.1) specifies two approximate methods
for designing two-way slabs for gravity loads. These are the
equivalent frame method and the direct design method.
Equivalent Frame Method
In this method a portion of a structure is taken out by itself,
as shown in the next figure. The same stiffness values are
used for the equivalent frame method as used for the direct
design method. This method, is very satisfactory for frames
with unusual dimensions or loadings.
35
DESIGN OF TWO-WAY SLABS BY THE ACI CODE
36
DESIGN OF TWO-WAY SLABS ACI 318-08
Direct Design Method
The Code (13.6) provides a procedure with which a set of moment
coefficients can be determined. The method, in effect, involves a
single-cycle moment distribution analysis of the structure based
on (a) the estimated flexural stiffness's of the slabs, beams (if
any), and columns and (b) the torsional stiffness's of the slabs and
beams (if any) transverse to the direction in which flexural
moments are being determined. These types of moment
coefficients have been used satisfactorily for many years for slab
design. They do not, however, give very satisfactory results for
slabs with unsymmetrical dimensions and loading patterns.
37