Topic: Strength of Materials
Maximum deflection in cantilever due to pure bending moment M at its ends is-
- A. $\frac{ML^{2}}{2EI}$
- B. $\frac{ML^{2}}{3EI}$
- C. $\frac{ML^{2}}{4EI}$
- D. $\frac{ML^{2}}{6EI}$
Answer: A. $\frac{ML^{2}}{2EI}$
Explanation: Using double integration method, at any distance x from A, we have $EI\frac{d^{2}y}{dx^{2}}=-M$. Integrating, $EI\frac{dy}{dx}=-Mx+C_{1}$. Integrating again, $EI(y)=-M\frac{x^{2}}{2}+C_{1}x+C_{2}$. At fixed end $x=0$, $\frac{dy}{dx}=0 \Rightarrow C_{1}=0$. At $x=0$, $y=0 \Rightarrow C_{2}=0$. The magnitude of deflection at free end ($x=L$) will be $y=\frac{ML^{2}}{2EI}$.