Question

A plate of 100 mm wide and 10 mm thick is bent into an arc of a circle of radius 10 m. If the modulus of elasticity of the material is 200 GPa, then the maximum bending stress induced in the plate is

• A. 100 kN/m$^2$
• B. 100 N/mm$^2$
• C. 200 kN/m$^2$
• D. 200 N/mm$^2$

Hint:

The bending equation $\frac{\sigma}{y} = \frac{E}{R}$ is very useful when the radius of curvature is known.
It directly relates stress to the geometry of the bent shape and the material's elasticity, without needing to know the applied moment ($M$) or moment of inertia ($I$).
Again, ensure all units are consistent before calculating.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Plate 10mm thick bent to R=10m. E=200GPa. Find max bending stress.

Step 2: Key Formula (Alternate):
σ_max = Ey_max/R. y_max = t/2 = 5mm. R=10000mm. E=2×10⁵ N/mm².

Step 3: Detailed Explanation:
σ_max = (2×10⁵)×5/10000 = 10⁶/10⁴ = 100 N/mm² = 100 MPa. Width doesn't affect stress.

Step 4: Final Answer:
Maximum bending stress is 100 N/mm².