Designing

1. By
Dr. Salah Uddin

2.  Constituent Materials & Properties
 Basic Principles of Reinforced Concrete
 Working Stress Method of Analysis
 Ultimate Strength Method
 Shear in Beams
 Bond, Anchorages and Development Lengths
 Columns & Footing

3. • Analysis of prismatic and non-prismatic sections in flexure
• Compatibility based analysis of sections and code requirements
for flexure
• Analysis of one way solid and ribbed slabs, two way solid slabs
with general discussion on other slab systems
• Design for flexure

4. Advantages
1. High compressive Strength
2. Better resistance to fire than steel
3. Long service life with low maintenance cost
4. can be cast to take shape required
and Disadvantages
1. Low tensile strength
2. Cost of forms
3. Low compressive strength than steel resulting large sections
4. Cracks

5. Codes of Practice
Significant code for structural concrete in USA is Building Code
Requirements for Structural Concrete, ACI 318 or the ACI Code.
There are many others e.g.
• International building Code (IBC),
• The American Society of Civil Engineers standard ASCE 7,
• The American Association of State Highway and Transportation
Officials (AASHTO) specifications,
• Specifications issued by the American Society for Testing and
Materials (ASTM),
• The American Railway Engineering Association (AREA), and
• The Bureau of Reclamation, Department of the Interior.

6. Design Philosophies
The design of a structure may be regarded as the process of selecting
the proper materials and proportioning the different elements of the
structure according to state-of-the-art engineering science and
technology.
In order to fulfill its purpose, the structure must meet the conditions of
safety, serviceability, economy, and functionality.
• The unified design method (UDM) is based on the strength of
structural members.
• A second approach for the design of concrete members is called the
strut-and-tie method (STM).
• A basic method that is not commonly used is called the working
stress design or the elastic design method.
• Limit state design is a further step in the strength design method.

7. Safety Provisions
The ACI Code has separated the safety provision into an overload or
load factor and to an under capacity (or strength reduction) factor, 𝜙. A
safe design is achieved when the structure’s strength, obtained by
multiplying the nominal strength by the reduction factor, 𝜙, exceeds or
equals the strength needed to withstand the factored loadings (service
loads times their load factors).

8. STRUCTURAL CONCRETE ELEMENTS
The concrete building may contain some or all of the following main
structural elements
• Slabs are horizontal plate elements in building floors and roofs. The depth of the
slab is usually very small relative to its length or width.
• Beams are long, horizontal, or inclined members with limited width and depth.
Their main function is to support loads from slabs.
• Columns are critical members that support loads from beams or slabs. They may be
subjected to axial loads or axial loads and moments.
• Frames are structural members that consist of a combination of beams and columns
or slabs, beams, and columns.
• Footings are pads or strips that support columns and spread their loads directly to
the soil.
• Walls are vertical plate elements resisting gravity as well as lateral loads as in the
case of basement walls.
• Stairs are provided in all buildings either low or high rise.

9. Stress-Strain Curves of Concrete
• All curves consist of an initial
relatively straight elastic
portion,
• Reaching maximum stress at a
strain of about 0.002;
• Rupture occurs at a strain of
about 0.003

10. Strength of Concrete
Tensile Strength of Concrete
The tensile strength of concrete ranges from 7 to 11% of its compressive strength,
with an average of 10%.
Flexural Strength (Modulus of Rupture) of Concrete
Flexural strength is expressed in terms of the modulus of rupture of concrete (fr),
which is the maximum tensile stress in concrete in bending.
The modulus of rupture of concrete ranges between 11 and 23% of the compressive
strength.
A value of 15% can be assumed for strengths of about 4000 psi (28 N/mm2).
Shear Strength
Shear strength may be considered as 20 to 30% greater than the tensile strength of
concrete, or about 12% of its compressive strength. The ACI Code, Section 22.6.6.1,
allows a nominal shear stress of 2 𝜆√f ′c psi (0.17 𝜆√f ′c N∕mm2) on plain concrete
sections.

11. Modulus of Elasticity
The modulus of elasticity is a measure of stiffness, or the resistance of the material to
deformation. In concrete, as in any elastoplastic material, the stress is not proportional
to the strain, and the stress–strain relationship is a curved line.
1. The initial tangent modulus (Shown in fig) is represented by the slope of the
tangent to the curve at the origin under elastic deformation. This modulus is of
limited value and cannot be determined with accuracy.
2. For practical applications, the secant modulus can be used. The secant modulus is
represented by the slope of a line drawn from the origin to a specific point of
stress (B) on the stress–strain curve (Shown in Fig). Point B is normally located at
f ′c∕2.
The ACI Code allows the use of Ec = 57,000√f ′c (psi) = 4700√f ′c MPa. The modulus
of elasticity, Ec, for different values of f ′c are shown in Table A.10.

13. Assumptions
Reinforced concrete sections are heterogeneous (nonhomogeneous), because they are
made of two different materials, concrete and steel. Therefore, proportioning structural
members by strength design approach is based on the following assumptions:
1. Strain in concrete is the same as in reinforcing bars at the same level, provided that
the bond between the steel and concrete is adequate.
2. Strain in concrete is linearly proportional to the distance from the neutral axis.
3. The modulus of elasticity of all grades of steel is taken as Es = 29 × 106 lb/in.2
(200,000MPa or N/mm2). The stress in the elastic range is equal to the strain
multiplied by Es.
4. Plane cross sections continue to be plane after bending.

14. Assumptions
5. Tensile strength of concrete is neglected because (a) concrete’s tensile strength is
about 10% of its compressive strength, (b) cracked concrete is assumed to be not
effective, and (c) before cracking, the entire concrete section is effective in resisting
the external moment.
6. The method of elastic analysis, assuming an ideal behavior at all levels of stress, is
not valid. At high stresses, nonelastic behavior is assumed, which is in close
agreement with the actual behavior of concrete and steel.
7. At failure the maximum strain at the extreme compression fibers is assumed equal
to 0.003 by the ACI Code provision.
8. For design strength, the shape of the compressive concrete stress distribution may
be assumed to be rectangular, parabolic, or trapezoidal. In this text, a rectangular
shape will be assumed (ACI Code, Section 22.2).

16. Three types of flexural failure of a structural member can be expected depending on
the percentage of steel used in the section.
1. Steel may reach its yield strength before the concrete reaches its maximum strength,
Fig. 3.3a. In this case, the failure is due to the yielding of steel reaching a high strain
equal to or greater than 0.005. The section contains a relatively small amount of steel
and is called a tension-controlled section or under-reinforced section.

17. 2. Steel may reach its yield strength at the same time as concrete reaches its ultimate
strength, Fig. 3.3b. The section is called a balanced section.

18. 3. Concrete may fail before the yield of steel, Fig. 3.3c, due to the presence of a high
percentage of steel in the section. In this case, the concrete strength and its maximum
strain of 0.003 are reached, but the steel stress is less than the yield strength, that is, fs
is less than fy. The strain in the steel is equal to or less than 0.002. This section is
called a compression-controlled section or over-reinforced section.

20. Two approaches for the investigations of a reinforced concrete member will be used in
this book:
Analysis of a section implies that the dimensions and steel used in the section (in
addition to concrete strength and steel yield strength) are given, and it is required to
calculate the internal design moment capacity of the section so that it can be compared
with the applied external required moment.
Design of a section implies that the external required moment is known from
structural analysis, and it is required to compute the dimensions of an adequate
concrete section and the amount of steel reinforcement. Concrete strength and yield
strength of steel used are given.

21. For the design of structural members, the factored design load is obtained by
multiplying the dead load by a load factor and the specified live load by another load
factor.
The magnitude of the load factor must be adequate to limit the probability of sudden
failure and to permit an economical structural design.
The choice of a proper load factor or, in general, a proper factor of safety depends
mainly on
• the importance of the structure (whether a courthouse or a warehouse),
• the degree of warning needed prior to collapse,
• the importance of each structural member (whether a beam or column),
• the expectation of overload, the accuracy of artisanry, and
• the accuracy of calculations
Based on historical studies of various structures, experience, and the principles of
probability, the ACI Code adopts a load factor of 1.2 for dead loads and 1.6 for live
loads.

23. The nominal strength of a section, say Mn, for flexural members, calculated in
accordance with the requirements of the ACI Code provisions must be multiplied by
the strength reduction factor, 𝜙, which is always less than 1. The strength reduction
factor has several purposes:
1. To allow for the probability of understrength sections due to variations in
dimensions, material properties, and inaccuracies in the design equations.
2. To reflect the importance of the member in the structure.
3. To reflect the degree of ductility and required reliability under the applied loads.

25. • When a beam is about to fail, the steel will yield first if the section is
underreinforced, and in this case the steel is equal to the yield stress.
If the section is overreinforced, concrete crushes first and the strain is
assumed to be equal to 0.003.
• A compressive force, C, develops in the compression zone and a
tension force, T, develops in the tension zone at the level of the steel
bars. The position of force T is known because its line of application
coincides with the center of gravity of the steel bars.
• The position of compressive force C is not known unless the
compressive volume is known and its center of gravity is located. If
that is done, the moment arm, which is the vertical distance between
C and T, will consequently be known.

27. In Fig., if concrete fails, 𝜀c = 0.003, and if steel yields, as in the case of a
balanced section, fs = fy.
The compression force C is represented by the volume of the stress
block, which has the nonuniform shape of stress over the rectangular
hatched area of bc. This volume may be considered equal to
C = bc( 𝛼1 f′c ), where 𝛼1 f′c is an assumed average stress of the
nonuniform stress block.

28. The position of compression force C is at a distance z from the top
fibers, which can be considered as a fraction of the distance c (the
distance from the top fibers to the neutral axis), and z can be assumed to
be equal to 𝛼2c, where 𝛼2 <1. The values of 𝛼1 and 𝛼2 have been
estimated from many tests, and their values, are as follows:
𝛼1 = 0.72 for f ′c ≤ 4000 psi (27.6MPa); it decreases linearly by 0.04 for
every 1000 psi (6.9MPa) greater than 4000 psi
𝛼2 = 0.425 for f ′c < 4000 psi (27.6MPa); it decreases linearly by 0.025
for every 1000 psi greater than 4000 psi

29. • To derive a simple rational approach for calculations of the internal
forces of a section, the ACI Code adopted an equivalent rectangular
concrete stress distribution.
• A concrete stress of 0.85 f ′c is assumed to be uniformly distributed
over an equivalent compression zone bounded by the edges of the
cross section and a line parallel to the neutral axis at a distance a= 𝛽1c
from the fiber of maximum compressive strain, where c is the
distance between the top of the compressive section and the neutral
axis (Fig. 3.8).
• The fraction 𝛽1 is 0.85 for concrete strengths f′c ≤ 4000 psi (27.6MPa)
and is reduced linearly at a rate of 0.05 for each 1000 psi (6.9MPa) of
stress greater than 4000 psi, with a minimum value of 0.65.

33. A balanced condition is achieved when steel yields at the same time as
the concrete fails, and that failure usually happens suddenly. This
implies that the yield strain in the steel is reached ( 𝜀y =fy/Es) and that the
concrete has reached its maximum strain of 0.003.
The percentage of reinforcement used to produce a balanced condition
is called the balanced steel ratio, 𝜌b. This value is equal to the area of
steel, As, divided by the effective cross section, bd:

34. Two basic equations for the analysis and design of structural members
are the two equations of equilibrium that are valid for any load and any
section:
1. The compression force should be equal to the tension force;
C = T
2. The internal nominal bending moment, Mn, is equal to either the
compressive force, C, multiplied by its arm or the tension force, T,
multiplied by the same arm:
Mn = C(d − z) = T(d − z)
(Mu = 𝜙Mn after applying a reduction factor 𝜙)
The use of these equations can be explained by considering the case of
a rectangular section with tension reinforcement. The section may be
balanced, under reinforced, or over reinforced, depending on the
percentage of steel reinforcement used.

35. Let us consider the case of a balanced section, which implies that at
maximum load the strain in concrete equals 0.003 and that of steel
equals the first yield stress divided by the modulus of elasticity of steel,
fy/Es. This case is explained by the following three steps.

36. From the strain diagram of Fig. 3.11,
From triangular relationships (where cb is c for a balanced section) and
by adding the numerator to the denominator,
Substituting Es = 29 × 103 ksi,