Topic: Strength of Materials
A cantilever beam 6 meter long as shown in figure is subjected to a linearly varying loading which has a maximum ordinate of 360 N/m at the fixed end on the right. The moment as a function of x is
- A. M = -3x^3
- B. M = -6x^3
- C. M = -10x^3
- D. M = -20x^3
Answer: C. M = -10x^3
Explanation: The loading varies linearly from 0 at the free end (x=0) to w = 360 N/m at the fixed end (x=L=6 m). The load intensity at distance x is w_x = (w/L) * x. The shear force at x is the area of the load diagram up to x: SF_x = -0.5 * x * (w/L)*x = -wx² / (2L). The bending moment M at x is the integral of the shear force (or taking the moment of the triangular load block): M_x = (-wx² / 2L) * (x/3) = -wx³ / (6L). Substituting w = 360 and L = 6 gives M = -360x^3 / (6 * 6) = -10x^3.