Q. A cantilever beam of span 3 m. carrier a udl of 400 N/m over its entire span. Sketch the B.M.D and state the position and magnitud, of maximum bending moment.

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SOLUTION:

S.F.D: SHEAR FORCE DIAGRAM

FB = 0
FA = 400×3 = 1200 N

max S.F. occurs at A = 1200 N

BMD ( BENDING MOMENT DIAGRAM)

MB = 0 ( why because It’s free End )
MA = -(400×3) × 3/2 = -1800 Nm

Max. B.M occurs at fixed end = 1800 Nm (or)

max BM= – wl²/ 2 = – [(400×3×3)/2] = -1800Nm

 

 

Q. A cantilever beam of span 4 m carries an uniformly distributed load of 3 kN/m on whole span. Determine the maximum shear force and maximum bending moment.

SOLUTION:

Total load 3×4 = 12 kN

SFD( SHEAR FORCE DIAGRAM )

S.F at B = FB = 0
SF at A = FA = 12 kN

Max. S.F occurs at support A = 12kN
or
FA = wl = 3×4 = 12 kN

BMD ( BENDING MOMENT DIAGRAM )

MB = 0
MA = -(3×4)×4/2 = -24 kNm
Max B.M occurs at support A and its value = 24 kNm = 24 kNm (hogging)
or Max. B.M = -wl²/ 2 = -[(3×4×4)/2]= – 24 kNm

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