As per IS 456:2000, which one of the following statements is not correct ?
- AThe strain diagram across the depth of the cross-section is linear.
- BThe tensile strength of concrete is ignored.
- CThe stress in steel shall correspond to strain in steel.
- DIf a partial safety factor of 1·15 is used for design purpose, then the maximum stress in steel is limited to 0·45 fy. (where fy = characteristic strength of steel)Correct
Solution
Concept
Assumptions in flexure design (limit state)
Formula
Design stress in steel = fy / 1.15 = 0.87 fy
Step-by-step solution
1. Plane sections remain plane: the strain diagram is linear (a). 2. Tensile strength of concrete is ignored (b). 3. Steel stress corresponds to steel strain from the stress–strain curve (c). 4. With γms = 1.15 the design stress in steel is fy/1.15 = 0.87 fy, not 0.45 fy. (0.45 fck is the concrete design stress.)
Explanation
The maximum design stress in steel at the limit state is 0.87 fy. The value 0.45 f applies to concrete (0.45 fck), and 0.5–0.6 fy is the working-stress permissible value for steel.
Why the other options are wrong
Statements (a), (b) and (c) are among the design assumptions of IS 456 Annex G.
Shortcut
Steel: 0.87 fy. Concrete: 0.45 fck.
Common mistake
Mixing up steel and concrete factors.
Correct answer: D) If a partial safety factor of 1·15 is used for design purpose, then the maximum stress in steel is limited to 0·45 fy. (where fy = characteristic strength of steel)