Question

A steel plate 120 mm wide and 20 mm thick is bent into a circular are of radius 10 m. What is the maximum stress produced and the bending moment which can produce this stress respectively ? (Take E = 200 GPa)
1. 100 MPa, 32 kN-m
2. 200 MPa, 1.6 kN-m
3. 200 MPa, 1600 kN-m
4. 20 MPa, 160 kN-m

Answer 1

Correct Answer - Option 2 : 200 MPa, 1.6 kN-m

Explanation:

Given data:

R= 10 m = 10000 mm,

E = 200GPa = 200000 N/mm²,

b = 120 mm, d or t = 20mm, y = 10 mm

Now MOI

I = (bt³)/12 = (120x20³)/12 = 80000 mm⁴

Using Simple bending theory find the value of Maximum Stress

 \(\frac{σ }{y} = \frac{E}{R}\)

 \(\frac{σ }{10} = \frac{200000}{10000}\) ⇒ σ = 200 MPa

So Bending Moment for this Stress

 \(\frac{M}{I} = \frac{σ }{y}\)

 \(\frac{M}{80000} = \frac{200}{10}\)= 1600000

 = 1.6 x 10⁶ N-mm = 1.6 kN-m

 Simple Bending Theroy

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