Topic: Strength of Materials
When a column is fixed at both ends, corresponding Euler's critical load is
- A. $\pi^{2}EI/L^{2}$
- B. $2\pi^{2}EI/L^{2}$
- C. $3\pi^{2}EI/L^{2}$
- D. $4\pi^{2}EI/L^{2}$
Answer: D. $4\pi^{2}EI/L^{2}$
Explanation: When a column is fixed at both ends, the equivalent effective length is $L_{e}=\frac{L}{2}$. Euler's Critical Load is $P_{c}=\frac{\pi^{2}EI}{(L_{e})^{2}}$. Substituting $L_{e}$, we get $P_{c}=\frac{\pi^{2}EI}{(\frac{L}{2})^{2}} = \frac{4\pi^{2}EI}{L^{2}}$.