Evaluate bending moment for overhanging beam, Mechanical Engineering

Evaluate Bending moment for overhanging beam:

Draw the shear force & bending moment diagrams for 15 m span overhanging beam, that overhangs on both sides. This is subjected to a u.d.l. of 5 kN/m on left side overhanging portion of length 5 m and a u.d.l. of 4 kN/m on right side overhanging portion of length 4 m. Mention the numerical values at all of salient points.

Solution

To determine Reaction at B

letting right side, the moments around A,

MA       =+ R B × 6 - 4 × 4 × ( 6 + (4/2))

MA = 6 RB - 128

Letting left side, take moments around A,

M A = ( 5 × 5 × (5/2))  = - 62.5

Equating these two values, we obtain

6 RB - 128 = - 62.5

6 RB = 65.5

RB = 10.92 kN

RA =  (5 × 5) + (4 × 4) - RB

RA = 41 - 10.92 = 30.08 kN

Shear Force (Starting from the left end C)

 SF at C, FC = 0

SF just left of A, FA = 0 - 5 × 5 = - 25 kN

SF just right of A, FA = - 25 + 30.08 = + 5.08 kN

SF just left of B, FB = + 5.08 kN

SF just right of B, FB = + 5.08 + 10.92 = + 16 kN

SF at D, FD = + 16 -  (4 × 4) = 0

1494_Evaluate Bending moment for overhanging beam.png

Figure

Bending Moment

BM at C and D, MC  = MD = 0

BM at A, MA = - 5 × 5 ×(5/2) = - 62.5 kN m

BM at B, MB = - 4 × 4 ×(4/2) = - 32 kN m

Posted Date: 1/22/2013 12:58:55 AM | Location : United States







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