MODULE 1 - WSD Flexure - Organized PDF
MODULE 1 - WSD Flexure - Organized PDF
MODULE 1 - WSD Flexure - Organized PDF
Working Stress
Design - Flexure
Module 1 – Reinforced Concrete Design
Objective Upon completing this section, students should be able to know the
concept of Working Stress Design and apply the theories in investigating
and designing a singly reinforced beam
Content
Cracking Moment
Flexural Investigation of Beams
Uncracked Beam
Cracked Beam : Classical Flexural Formula
Cracked Beam : Transformed Area Method
Flexural Design of Beams
Transformed Area Method
Activities During the module, students will perform graded activities to measure
their progress during the course; Quiz, class discussion, practice
problems.
Example 3
A rectangular concrete beam, 350-mm x 500-mm simply
supported with a span length of 8 meters, is to carry a
uniform load of 25 kN/m, including its own weight.
Assuming concrete cover is 50 mm, design the beam.
𝑓𝑠(𝑎𝑙𝑙𝑜𝑤) = 120.00 Mpa
𝑓𝑐(𝑎𝑙𝑙𝑜𝑤) = 10.00 Mpa
𝑛 = 8
The maximum compressive strain occurs at the top surface of the beam, and the maximum tensile
strain occurs at the bottom surface.
The assumption of a linear strain distribution is fundamental in analysing the behaviour of a reinforced
concrete beam as the bending moment is increased up to the ultimate strength of the beam.
In Design, it is often assumed that concrete fails in compression when it reaches a compressive strain
of 0.003.
With the above assumptions, it is now possible to follow the progression of flexural cracking as the
bending moment on a RC beam is increased.
Uncracked Section
Cracked Section
3.) Determine the value of 𝑓𝑠 ′ (see if it will exceed the value of the given 𝑓𝑠 )
The tensile strength of concrete is assumed in structural design as almost nil, it necessary to strengthen
or reinforce concrete members where they are subjected to tensile stresses.
This reinforcement is usually accomplished by the embedment of steel bars or rods which must then
resist almost 100% of the tensile forces
Obviously, when the concrete is cracked, it is no longer capable in resisting tensile forces.
The tensile forces in the bottom is resisted by the reinforcement and the compression forces at the top
are resisted by the concrete.
Example 2
Calculate the strength moment capacity of the doubly
reinforced section shown. Assume that the concrete
covering is 50 𝑚𝑚.
𝑓𝑠(𝑎𝑙𝑙𝑜𝑤) = 130.00 Mpa
𝑓𝑐(𝑎𝑙𝑙𝑜𝑤) = 10.00 Mpa
𝑛 = 9
The cracking moment is the moment required to first cause the beam to crack.
this is the point at which the steel reinforcement in the beam is exposed to the environment, a possible
cause of corrosion in the steel.
any further increase in the moment in the beam causes drastically increases the curvature of the beam,
and may not be completely reversible when the load is removed.
(NSCP, 424.2.3.5b)
(NSCP, 419.2.3.1)
𝝀 = 𝑚𝑜𝑑𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟
𝒘𝒉𝒆𝒓𝒆:
𝝀 = 1.00 − 𝑛𝑜𝑟𝑚𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒
𝝀 = 0.85 − 𝑠𝑎𝑛𝑑 𝑙𝑖𝑔ℎ𝑡𝑤𝑒𝑖𝑔ℎ𝑡 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒
𝝀 = 0.75 − 𝑎𝑙𝑙 𝑙𝑖𝑔ℎ𝑡𝑤𝑒𝑖𝑔ℎ𝑡 𝑐𝑜𝑐𝑟𝑒𝑡𝑒