A steel wire of 8 mm diameter is bent in to a circular arc of 16 m radius. The maximum stress induced in it will be ________. Given E = 2 x 10⁵ N/mm²

Question

Question

This question was previously asked in

JKSSB JE CE 2021 Official Paper Shift 1 (Held on 30 Oct 2021)

Answer 1

Concept:

As per bending formula:

\(\frac{\sigma }{y} = \frac{M}{I} = \frac{E}{R}\)

Where

M = bending moment due to load, σ = bending stress, E = Modulus of Elasticity,

R = radius of Curvature, y = distance of outer fibre from the neutral axis

I is the MOI about a neutral axis and it is given as:

\(I = \frac{{b{d^3}}}{{12}}\)

Calculation:

Given:

E = 2 × 105 N/mm2, R = 16 m = 16 × 103 mm, y = 8/2 = 4 mm

As we know,

\(\frac{\sigma }{y} = \frac{E}{R}\)

\(\frac{\sigma }{{4}} = \frac{{2\; ×\; {{10}^5}}}{{16\; × \;{{10}^3}}} \Rightarrow \sigma = 50\;N/{mm^2}\)

∴ The maximum stress induced = 50 N/mm²

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