Question

What is the critical load for a strut of length 4.0 m and flexural rigidity 28 MPa if
both ends are fixed?
A. 80.80 MN B. 79 14 MN C. 69.10 MN D. 88.90 MN E. None of the above

Answer 1

Answer on Question #54204-Engineering-Mechanical Engineering

What is the critical load for a strut of length $4.0\mathrm{m}$ and flexural rigidity $28\mathrm{MPa}$ if both ends are fixed?

A. 80.80 MN B. 79 14 MN C. 69.10 MN D. 88.90 MN E. None of the above

Solution

The critical load is, in general,

$$F_{c} = \frac{\pi^{2} E I}{L_{e}^{2}},$$

where $E$ is the modulus of elasticity, $I$ is the moment of inertia, $L_{e}$ is the effective length.

Both ends are fixed, so the effective length is $\frac{L}{2} = 2.0 \, \text{m}$.

The critical load is

$$F_{c} = \frac{\pi^{2} \cdot 28 \cdot 10^{6} \mathrm{Pa}}{(2.0 \, \text{m})^{2}} = 69.10 \, \text{MN}.$$

Answer: C. 69.10 MN.

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