The GATE Grind

GATE 2021 CE (CE1) – Question 31

Structural Analysis · Deflections of determinate beams, frames and trusses · 1 mark · Numerical answer

A beam has deformation $y=x^2-xL$. Find its curvature at midspan (integer).

see the reproduced source diagram and its labels.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 2 to 2

Explanation

Exact curvature is $\kappa=y^{\prime\prime}/[1+(y^\prime)^2]^{3/2}$. Here $y^\prime=2x-L$ and $y^{\prime\prime}=2$. At x=L/2 the slope vanishes, so curvature is **2**, without needing a small-slope approximation.