A cantilever beam of T cross-section carries uniformly distributed load. Where does the maximum magnitude of bending stress occur?

At the top of cross-section At the junction of flange and web At the mid-depth point At the bottom of the section

Concept-

For any cross-section, we have the bending equation

$\frac{σ}{y} = \frac{M}{I} = \frac{E}{R}$

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σ = stress at a distance y from NA, M = Bending moment at that c/s

I = MOI about the neutral axis, E = Modulus of elasticity

R = Radius of curvature

Calculation

a) For any T-section:

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y₂> y₁

As neutral axis is the centroidal axis of the cross-section.

So, the neutral axis lies near the top of the T-section.

So y₂ > y₁

$σ_{b o t} = \frac{M \times y_{2}}{I} & σ_{t o p} = \frac{M \times y_{1}}{I}$

As y₂ > y₁

So σ_bot > σ_top

∴ Maximum bending stress will occur at the bottom of the section.

Hint Answer

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A cantilever beam of T cross-section carries uniformly distributed load. Where does the maximum magnitude of bending stress occur?

At the bottom of the section

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