The assumption in the theory of simple bending that a plane section before bending remains plane after bending leads to:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 11/12/2020 (Evening)
Detailed Explanation
Bernoulli's hypothesis — plane sections stay plane — is a purely geometric statement. It tells us how the fibres deform, not how stress relates to that deformation.
A fibre at distance y from the neutral surface, bent to radius R: \[ \varepsilon = \frac{(R+y)\,d\theta - R\,d\theta}{R\,d\theta} = \frac{y}{R} \]
Why “the strain diagram being linear” Is Correct
Since ε = y/R, the strain is directly proportional to y: the strain diagram is linear. The stress diagram is linear only if Hooke's law also holds (σ = Eε); in plastic or concrete design, strain stays linear but stress does not.
Why the Other Options Are Wrong
- A. occurrence of maximum stress at the extreme fibres: Maximum stress at the extreme fibres is a consequence, but it also needs the stress–strain law.
- B. bending stress becoming zero at the neutral axis: Zero stress at the N.A. follows, but the direct result of the assumption is linear strain.
- C. the stress diagram being linear: A linear stress diagram needs Hooke's law in addition; in limit state design of RCC, strain is linear but stress is not.
Key Point
Plane sections remain plane ⇒ ε = y/R (linear strain). Plus Hooke's law ⇒ σ = Ey/R (linear stress).
Key Concepts for Students
- The neutral surface has zero strain.
- Deep beams violate the plane-section assumption.
- IS 456 limit state design keeps the linear strain assumption.
Practice more: this is question 9 in Bending and Shear Stress MCQs – Part 1. Try the whole set and check every answer instantly.