Question

The span and the material of the two beams A and B are the same. The area of cross section of the two beams are equal. The cross section is square. In the case of beam A, the plane of moment is parallel to the sides of the square and in the case of beam B, the plane of moment coincides with the diagonal as shown in the given figure.

Consider the following inferences from the above data:

1. For the same loading, the deflection of the beam B is smaller than that of beam A.
2. If the load on the two beams is the same, then the maximum stress in beam B is greater than that in beam A.
3. Beam A can resist smaller load than beam B.
4. Flexural rigidity of both the beams is equal.

Which of these inferences are incorrect?

• A. 2 and 4
• B. 1 and 3
• C. 1 and 4
• D. 2, 3 and 4

Answer 1

The correct option is A 2 and 4

The moment of inertia of both beams about their horizontal axis will be same.

$i.e.I_A=I_B=\left(\frac{h^4}{12}\right)$

Deflection $\Delta \propto \frac{1}{EI}$ and since EI of beam A and B is same so deflection will be same. Therefore
(1) is incorrect.
Maximum stress in beam having more section modulus will be less.

$Z_A=\frac{I_A}{h/2}=\frac{2I_A}{h}$

$Z_B=\frac{I_B}{h/\sqrt{2}}=\left(\frac{\sqrt{2}{I}_B}{h}\right)$

as $Z_A>Z_B,so,f_A<f_B$

The maximum stress in beam B is more than that in A, so (2) is correct.
The beam having higher section modulus will resist more load. So (3) is incorrect.
EI is called the flexural rigidity of the beam and it is same both beams. Therefore (4) is correct.