Strength of Materials

SOLVED UNIVERSITY QUESTIONS

SOLVED PROBLEM 4.10

A cantilever beam of span 4 m carries point loads of 1 kN, 2 kN and 4 kN at 1 m, 2 m and 4 m, respectively from the fixed end. Draw the shear force and bending moment diagrams (Anna Univ., June 2005, ME).

Solution:

Given data: Span, l = 4 m, loads = 1 kN, 2 kN and 4 kN, spacing, 1 m, 2 m and 4 m.

 

1. Shear Force

Considering from the free end,

Shear force at D = + 4 kN

Shear force at C = + 4 + 2 = + 6 kN

Shear force at B = + 4 + 2 + 1 = + 7 kN

Shear force at A = + 4 + 2 + 1 = + 7 kN

 

2. Bending Moment

Bending moment at D = − 4 × 0 = 0

Bending moment at C = (−4 × 2) = −8 kN · m

Bending moment at B = (−4 × 3) + (−2 × −1) = −12−2 = −14 kN · m

Bending moment at A = (−4 × 4) + (−2 × 2) + (−1 × 1) = ...