Question

A simple supported steel I beam is replaced by a C-channel made with aluminum. Both sections have similar moment of inertia and are subjected to same loading. The following will remain true,
1. The maximum bending stress and deflection will remain unaltered
2. Only the maximum bending stress will remain unaltered
3. Only the maximum deflection will remain unaltered 
4. None of the above

Answer 1

Correct Answer - Option 2 : Only the maximum bending stress will remain unaltered

Explanation

For any cross section we have Bending equation 

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

where,

σ = Bending stress, y = Distance from neutral axis

M = Bending moment, I = Area moment of inertia

E = Modulus of elasticity, R = Radius of curvature

Section Modulus (Z) = I/y

Here,

It is given

• A simple supported steel I beam is replaced by a C-channel made with aluminum.
• Both sections have similar moment of inertia and are subjected to same loading.

So as the loading is same, so bending moment will be same. It is also given that Moment of inertia is same. So the section modulus will remains same.

Bending stress (σ) = M/Z 

From the bending equation it can be concluded that maximum bending stress depends upon bending moment and section modulus, as it is same for both the cases so maximum bending stress will remain unaltered.

So here only bending stress will remain unaltered.

• But modulus of elasticity for steel and aluminum is different, so radius of curvature will be different.
• As radius of curvature is different, the deflection will also be different.