Q. A cantilever beam of span 3 m carries a two point loads of 20 kN and 30 kN at free end and centre respectively. In addition there will be a udl of 12 kN/m over the span of 1.5 m from the free end. Draw the SFD and BMD.

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Q. A cantilever beam of span 3 m carries a two point loads of 20 kN and 30 kN at free end and centre respectively. In addition there will be a udl of 12 kN/m over the span of 1.5 m from the free end. Draw the SFD and BMD.

SOLUTION:
Total load = 30+20 + 12×1.5 = 68 kN

SFD ( SHEAR FORCE DIAGRAM)
FA =68 kN(same inAC )
FC=(just left of c) = 68 kN
FC (just right of c) = 38 kN
FB (just left of B) = 20 kN
FB(just right of B) = 0 kN
Max SF occurs at A = 68kN (same in AC)

BMD ( BENDING MOMENT DIAGRAM)
M{B} = 0
M{C} = – (12 × 1.5) 1.5/2 – 20 × 1.5 = – 43.5kNm
M{A} = – (12 × 1.5) (1.5/2 +1.5) – 30 * 1.5 – 20 × 3
= – 40.5 – 45 – 60 = – 145.5kNm

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