A steel plate of width 80 mm and of thickness 15 mm is bent into a circular arc of radius 8 m, what will be the maximum stress induced in plate? 

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 = 8 m = 8 × 103 mm, A = 80 mm × 15 mm, y = 15/2 mm

As we know,

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

\(\frac{\sigma }{{15/2}} = \frac{{2\; ×\; {{10}^5}}}{{8\; × \;{{10}^3}}} \Rightarrow \sigma = 187.5\;N/{mm^2}\)