Question

Find the maximum stress induced in a steel
flat 150 mm wide x 12 mm thick, if it is bent
into a circular arc of 12000 mm radius.
E=2 x 10 N/mm


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Answer 1

Answer:

Step-by-step explanation:300N/mm^2

Answer 2

The maximum stress induced on the steel is 100 N/mm²

Given

Width of steel = 150 mm

The thickness of steel = 12 mm

The radius of curvature when the steel was bent = 12000 mm

Young's modulus of Elasticity of steel = 2 × 10⁵ N/mm²

To Find

Maximum stress induced on the steel when it is bent

Solution

The formula for calculating bending stress is given by

$\frac{\sigma}{y} = \frac{E}{R}$ where

$\sigma$ = the bending stress to be calculated

$y$ = the distance of the neutral axis from the outermost surface of the steel. That is the distance from the center of the steel's thickness to the outermost surface. Since the thickness of the steel is 12 mm, $y$ is 6 mm

$E$ = the Young's modulus of elasticity of steel = 2×10⁵ N/mm²

$R$ = the radius of curvature of the steel after it was bent = 12000 mm

Substituting the above values to the equation we get

$\frac{\sigma}{6} = \frac{2\times10^5}{12000}$

$\sigma = \frac{2\times10^5 \times 6}{12\times 10^3 }$

$\sigma = \frac{2\times10^5}{2\times10^3}$

$\sigma=100 N/mm^2$

Hence, the maximum stress induced on the steel is 100 N/mm²