A cantilever beam of span 6 m and is fixed at A and free at B. It carries three point loads of 10 kN, 20 kN and 30 kN at a distance of 2 m, 4 m and 6 m respectively from fixed end Draw S.FD. and B.M.D. Find the maximum shear force and maximum bending moment.

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Q.A cantilever beam of span 6 m and is fixed at A and free at B. It carries three point loads of 10 kN, 20 kN and 30 kN at a distance of 2 m, 4 m and 6 m respectively from fixed end Draw S.FD. and B.M.D. Find the maximum shear force and maximum bending moment.

SOLUTION

S.F.D

Total load 10 + 20+ 30 = 60 kN

S.F at B = FB = + 30 kN
In portion DB the S.F remains same and is equal to 30kN
In portion CD, the S.F remains same and is equal to 50 kN
S.F at C = S.F at A =FC=FA 60 kN
In portion AC, The S.F remains same and is equal to 60 kN.
Max S.F occurs at support A = 60 kN

B.M.D

M{B} = 0

M{D} = – 30 * 2 = – 60kNm

M{C} = – 30 * 4 – 20 * 2 = – 120 – 40 = – 160kNm

M{A} = – 30 * 6 – 20 * 4 – 10 * 2

=- 180 – 80 – 20 =-280 kNm

Max B.M occurs at fixed support A and its value

=280 kNm

= 280kNm (hogging)

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