This document discusses the working stress method for designing reinforced concrete structures. It defines key terms like neutral axis, lever arm, and moment of resistance. It describes the assumptions and steps of the working stress method, including designing for under-reinforced, balanced, and over-reinforced beam sections. The document also discusses limitations of the working stress method and introduces the limit state method as a more modern approach.

1. RCC DESIGN BY
WORKING STRESS
METHOD
By-
•Jyoti ranjan nayak

3. Introduction
• The design of a structure may be regarded as the
process of selecting proper materials and
proportioned elements of the structure, according to
the art, engineering science and technology. In order
to fulfill its purpose, the structure must meet its
conditions of safety, serviceability, economy and
functionality.

4. Terms of RCC design
• Neutral Axis (n)
• Neutral axis lies at the centre of gravity of the section. It is defined as that
axis at which the stresses are zero. It divides the section into tension and
compression zone. The position of the neutral axis depends upon the
shape (dimensions) of the section and the amount of steel provided.

5. Lever arm-
• Lever arm is the distance between the resultant compressive force and
the resultant tensile force.
Moment of resistance is the resistance offered by the beam against external loads. As there
is no resultant force acting on the beam and the section is in equilibrium, the
total compressive force is equal to the total tensile force. These two forces (equal
and opposite separated by a distance) will form a couple (and the moment of this
couple is equal to the resisting moment or moment of resistance of the section.
Moment of Resistance (Mr)

6. WORKING STRESS METHOD
• Working Stress Method is the traditional method of design not only for Reinforced Concrete but
also for structural steel and timber design. The conceptual basis of the WSM assumes that the
structural material behaves in a linear elastic manner and that appropriate safety can be ensured
by suitably limiting the stresses in the material due to the presumed working loads (service
loads) on the structure.
• WSM also assumes that both the steel reinforcement and concrete act together and are perfectly
elastic at all stages, and hence the modular ratio can be used to determine the stresses in steel
and concrete.
• The stresses under the working loads are obtained by applying the methods of ‘strength of
materials’ like the simple bending theory. The limitations due to non-linearity and buckling are
neglected.
• The stresses caused by the ‘characteristic’ or service loads are checked against the permissible
(allowable) stress, which is a fraction of the ultimate or yield stress. The permissible stress may
be defined in terms of a factor of safety, which takes care of the overload or other unknown
factors.

8. Assumptions of elastic theory
• Plane Section before bending will remain plane after bending
• Bond between steel and concrete is perfect with in elastic limit of steel
• The steel and concrete behaves as
linear elastic material
• All tensile stresses are taken by
reinforcement and none by
concrete
• The stresses in steel
and concrete are related by a
factor known as “modular ratio
• The Stress-strain relationship of steel and
concrete is a Straight line under working load

9. • Steps to design beam section by WSM
• Step 1- calculation of design constants.
• Step 2- calculation of bending moment.
• Step 3- design of section.
• Step 4- reinforcement
• Step 5- check for shear and design of shear reinforcement.
• Step 6- details of reinforcement.

10. Balanced Beam Section
• Reinforced concrete beam sections in which the tension steel also reaches
yield strain simultaneously as the concrete reaches the failure strain in
bending are called balanced sections.

11. Under-Reinforced Beam Section
• Reinforced concrete beam sections in which the steel reaches yield strain at
loads lower than the load at which the concrete reaches failure strain are
called under-reinforced sections.
• Every singly reinforced beam should be designed as under-reinforced
sections because this section gives enough warning before failure.
• Yielding of steel in under-reinforced beam section does not mean the
structure has failed, as when steel
yields, excessive deflection and
cracking in beam will occur before
failure which gives enough time to
occupants to escape before the section
fails.
• The failure in under-reinforced beam
section is due to the concrete reaching
its ultimate failure strain of 0.0035 before
the steel reaches its failure strain which
Is much higher 0.20 to 0.25.

12. Over-Reinforced Beam Section
• Reinforced concrete beam sections in which the failure strain in concrete
is reached earlier than the yield strain of steel is reached, are called over-
reinforced beam sections.
• If over-reinforced beam is designed and loaded to full capacity then the
steel in tension zone will not yield much before the concrete reaches its
ultimate strain of 0.0035. This due to little yielding of steel the deflection
and cracking of beam does not occur and does not give enough warning
prior to failure.
• Failures in over-reinforced sections are all of a sudden. This type of
design is not recommended in practice of beam design.

13. CONCEPT OF TRANSFORMED OR
EQUIVALENT SECTION
The bond between steel and concrete is assumed to be perfect so the strains in steel and the surrounding
concrete will be equal
It means that stress in steel is m times the stress in concrete or load carried by steel is m times the load carried by
concrete of equal area. Using Eqns. (i) and (ii)
(ii)
(i)

14. Limitations of working stress method
• The assumptions of linear elastic behaviour and control of stresses
within specially defined permissible stresses are unrealistic due to
several reasons viz., creep, shrinkage and other long term effects, stress
concentration and other secondary effects
• Different types of load acting simultaneously have different degrees of
uncertainties. This cannot be taken into account in the working stress
method
• The actual factor of safety is not known in this method of design. The
partial safety factors in the limit state method is more realistic than the
concept of permissible stresses in the working stress method to have
factor of safety in the design.

15. Shrinkage
Creep

16. Limit State Method
• The stresses are obtained from design
loads and compared with design
strength.
• In this method, it follows linear strain
relationship but not linear stress
relationship (one of the major
difference between the two methods
of design).
• The ultimate stresses of materials itself
are used as allowable stresses.
• The material capabilities are not under
estimated as much as they are in
working stress method. Partial safety
factors are used in limit state method.

17. • Accordingly, the working stress method is gradually replaced by the limit state method. The
Indian code IS 456 has given working stress method in Annex B to give greater emphasis to
limit state design. Moreover, cl. 18.2.1 of IS 456 specifically mentions of using limit state
method normally for structures and structural elements. However, cl.18.2.2 recommends the
use of working stress method where the limit state method cannot be conveniently adopted.
Due to its simplicity in the concept and applications, better structural performance in service
state and conservative design, working stress method is still being used for the design of
reinforced concrete bridges, water tanks and chimneys. In fact, design of tension structures and
liquid retaining structures are not included in IS 456 for the design guidelines in the limit state
method of design
• Calculation alone do not produce safe, serviceable and durable structures. Suitable material
quality control adequate detailing and good supervision are equally important.