Question

A steel plate of width 120 mm and f thickness 20 mm is bent into a circular arc of radius 10 m. If Elastic modulus of the section is 200 GPa, ten the maximum stress induced in the beam is
1. 200 MPa
2. 30 GPa
3. 20 GPa
4. 180 MPa
5. 110 MPa

Answer 1

Correct Answer - Option 1 : 200 MPa

Concept:

Equation of pure Bending, \(\frac{M}{I} = \frac{σ }{y} = \frac{E}{R}\) where,

M = Bending moment

σ = Bending stress at a distance y from NA

I = MOI or cross-section about NA

E = Young's modulus

1/R = Curvature

Bending stress, \(\sigma = \frac{E}{R}y\)  

Calculation:

Given,

E = 200 GPa = 200000 MPa

B = 120 mm and D = 20 mm

y = D/2 = 10 mm

R = 10 m = 10000 mm

 \(\sigma = \frac{E}{R}y = \frac{{200000 \times 10}}{{10000}} = 200MPa\)

The maximum stress induced in the beam is 200 MPa.