Shear
Stress in Beams
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Example: * (continued) So the maximum shear
force, Vmax, has a value of 5400 lb and
occurs at each end of the beam. The maximum bending
moment, Mmax, has a value of 8100 ft lb
and occurs at midspan of the beam. Start with the min/max
bending stress. They occur on the top
and bottom fibers at midspan. σ
= Mc/I where
M = 8100 ft lb, c = h/2 = 5
in, and
I = (1/12)bh3 =
(1/12)(8)(10)3 = 666.6 in4 Therefore σ =
(8100)(12)(5) / (666.6) = 729
psi Consequently at midspan of the beam σmax
= + 729 psi (on bottom fibers), σmin
= − 729 psi (on top
fibers) |
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The shear
force is given by τ =
VQ/It where V
= 5400 lb, I =
666.6 in4, t = 8 in Here you need to calculate
the value of Q. So the area involved
is from the neutral axis to the top of the beam as
shown in the figure below. Q =
(A’)(ybar) A’
= (h/2) b = (5)(8) =
40 in2 ybar = h/4 = 2.5
in So Q =
(A’) h/4 = 100 in3 So τmax =
VQ/It = (5400)(100)/(666.6)(8) =
101 psi (result) Click here to continue
with this example. |
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