Question

A simply supported wood beam of rectangular cross section and span length 1.2 m carries a concentrated load P at midspan in addition to its own weight (see Fig. Q13). The cross
section has width 140 mm and height 240 mm. The weight density of the wood is 5.4 kN/m3
. Calculate the maximum permissible value of the load P, if (a) the allowable bending stress is 8.5 MPa, and (b) the allowable shear stress is 0.8 MPa.

Answer 1

Answer:

= 250mm, L = 1.3m ,

Central point load = 'W' N

σb=7N/mm2andqmax=1N/mm2

Solution:

M = Max. B.M. = WL4=w×1.34=0.325W−N.m

S = Max S.F =. Reaction = W2N=0.5WN

For rectangular section,

A = b x d = 150 x 250 = 37500 mm2

I = bd312=150×250312=195.31×106mm4

ymax=d/2=2502=125mm

Value of 'W' for bending stress criteria

MI=σy∴M=σy×y

∴325W=7×195.31×106125

∴W=33653.41N=33.65kN

Value of 'W' for shear stress criteria

qmax=1.55A

∴1=1.5×0w37500=33.65kN

∴W=50000N−50kN

Safe Value of W = min, of A & B = 33.65 kN