Question

 A mild steel flat of width 120 mm and thickness 10 mm is bent into an arc of a circle of radius 10 m, by applying a moment ‘M’. If ‘E’ is 2 × 10⁵ N/mm², the magnitude of ‘M’ will be:-
1. 0.2 × 10⁵ N.mm
2. 2 × 105 N.mm
3. 2 × 10⁶ N.mm
4. 0.2 × 10⁴ N.mm

Answer 1

Correct Answer - Option 2 : 2 × 105 N.mm

Concept:

Bending equation:

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

Where,

M = Bending moment

I = Moment of inertia

E = Modulous of elasticity

R = Radius of the circular arc

Calculation:

Given,

b = 120 mm

t = 10 mm

E = 2 ×10⁵ N/mm²

R = 10 m = 10000 mm

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

\(I = \frac{{120 × {{10}^3}}}{{12}}\)

I = 10⁴ mm²

From the above equation;

\(\frac{M}{{{{10}^4}}} = \frac{{2 × {{10}^5}}}{{10000}}\)

M = 2× 10⁵ N.mm