Topic: Strength of Materials
Determine the equation of the elastic curve for the cantilever beam of uniform cross section as shown in the figure due to the applied bending moment M1 (Consider Young's modulus as E and Moment of inertia as I)
- A. y = M1*x² / 3EI
- B. y = M1*x² / EI
- C. y = M1*x² / 2EI
- D. y = M1*x² / 4EI
Answer: C. y = M1*x² / 2EI
Explanation: The differential equation for the elastic curve is EI(d^2y/dx²) = M(x). Since a constant moment M1 is applied at the free end, M(x) = M1. Integrating once gives EI(dy/dx) = M1*x + C1. At the fixed end (x=0), slope dy/dx = 0, so C1 = 0. Integrating again gives EI*y = M1*(x²/2) + C2. At x=0, deflection y = 0, so C2 = 0. The equation becomes y = M1*x² / 2EI.