Unformatted text preview: 05Ch05.qxd 9/25/08 2:29 PM Page 445 445 SECTION 5.8 Shear Stresses in Rectangular Beams Problem 5.8-5 A steel beam of length L 16 in. and crosssectional dimensions b 0.6 in. and h 2 in. (see figure) supports a
uniform load of intensity q 240 lb/in., which includes the weight
of the beam.
Calculate the shear stresses in the beam (at the cross
section of maximum shear force) at points located 1/4 in., 1/2 in.,
3/4 in., and 1 in. from the top surface of the beam. From these
calculations, plot a graph showing the distribution of shear stresses
from top to bottom of the beam. q = 240 lb/in.
h = 2 in. b = 0.6 in. L = 16 in. Solution 5.8-5 Shear stresses in a simple beam
(psi) 0 1.00 0 0.25 0.75 1050 0.50 0.50 1800 0.75 0.25 2250 0 2400 Distance from the
top surface (in.) V h2
2I 4 y2 b
1 1920 lb I bh3
12 Eq. (5-39): t
2 1.00 (N.A.)
0.4 in.4 GRAPH OF SHEAR STRESS t UNITS: POUNDS AND INCHES
t 1920 (2)2
2(0.4) 4 (t psi; y1 y2
1 (2400)(1 y2) d
1 in.) Problem 5.8-6 A beam of rectangular cross section (width b and height h)
supports a uniformly distributed load along its entire length L. The
allowable stresses in bending and shear are sallow and tallow, respectively.
(a) If the beam is simply supported, what is the span length L0 below
which the shear stress governs the allowable load and above which the
bending stress governs?
(b) If the beam is supported as a cantilever, what is the length L0
below which the shear stress governs the allowable load and above which
the bending stress governs? ...
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