Statement for Linked Answer Questions: 52 & 53

A massless beam has a loading pattern as shown in the figure. The beam is of rectangular cross-section with a width of 30mm and height of 100mm.

Q. The maximum bending moment occurs at
Option (A)
Location B
Option (B)
2675mm to the right of A
2500mm to the right of A
3225mm to the right of A
Correct Option:
Question Solution:
Given data

First calculate RA & Rc

Take moments about A

MA = 0 = RCx4000 = (3000/1000)x 2000x3000
Þ RC = 4.5x103N = 4500N

Form RA + RC = (3000/1000)x2000

RA = 6x103 - 4.5x103 = 1.5x103N = 1500N

Draw SFD

Maximum bonding moment occurs at which SF is zero

Therefore S.F. is zero at 2000+x from A or 2000-x from B

Form Fp=0, A=2000+x=2500mm

i.e. 1.5x103 = (3000x / 1000)

Þ x = 500mm
maximum bebding stress is given by

fmax = (Mmax / I) ymax

Mmax at point p = 4.5x103x1500-(3000/1000)x(1500/2) = 3.375x106

I = (bd3 /12) = ((30x1003)/12) = 2.5x106 mm4

ymax = 50mm

fmax = {(3.375x106x50)/(2.5x106)} = 67.5Mpa