Q. Calculate the maximum shear force and bending moment for cantilever beam of span 3 m and carries an udl of 2kN / m over length of 1m from free end and a point load of 10 kN is acting at distance of 1 m from fixed end.

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Q. Calculate the maximum shear force and bending moment for cantilever beam of span 3 m and carries an udl of 2kN / m over length of 1m from free end and a point load of 10 kN is acting at distance of 1 m from fixed end.

SOLUTION:

SFD (SHEAR FORCE DIAGRAM)

Total load= 2 × 1 + 10 = 12kN
F{B} = 0
F{D} = 2kN(2 × 1 = 2kN)
F{C} = 12kN(2 × 1 + 10 = 12kN)
F{A} = 12kN(2 × 1 + 10 = 12kN)

F max =Max S.F occurs at fixed end A and its value
= 12KN

BMD (BENDING MOMENT DIAGRAM)
M{B} = 0
M{D} = – (2 × 1) 1/2 = – 1kNm
M{C} = – (2 × 1) (1/2 + 1) = – 3kNm
M{A} = – (2 × 1) (1/2 + 2) – 10 × 1 = – 5 – 10 = – 15kNm
Max B.M occurs at fixed end A
MA = Mmax= -15kNm = 15 kNm(hogging)

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