Topic: Strength of Materials
A beam is subjected to the uniform load Wc per unit length and MA, VA & VB are the reactions as shown in the figure. The expression for shear force V(x) and Bending moment M(x) is given by
- A. V(x) = VA + Wc x, M(x) = MA + VA x - Wc x² / 2
- B. V(x) = VA - Wc x, M(x) = MA - VA x - Wc x² / 2
- C. V(x) = VA + Wc x, M(x) = MA - VA x - Wc x² / 2
- D. V(x) = VA - Wc x, M(x) = MA + VA x - Wc x² / 2
Answer: D. V(x) = VA - Wc x, M(x) = MA + VA x - Wc x² / 2
Explanation: Taking the left end A as the origin and rightward as the positive x-direction, the upward shear force is VA and downward distributed load is Wc. The shear force at distance x is V(x) = VA - Wc*x. The bending moment at distance x, considering counter-clockwise MA as positive, is M(x) = MA + VA*x - Wc*x² / 2.