Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

at intervals of s along each side of the built-up shape. The cross section
of the built-up shape is shown in Figure P9.32b, and the crosssectional
properties for a single hat shape are shown in Figure P9.32c.
For an applied load P = 6,800 N, determine the maximum spacing
interval s that can be used if each rivet has a shear strength of 1,700 N.
z
y
FIGURE p9.32a Riveted beam.
y
s
Rivets
y
P
x
p9.33 A steel wide-flange beam in an existing structure is to be
strengthened by adding a cover plate to its lower flange, as shown
in Figure P9.33. The wide-flange shape has dimensions b f = 7.50 in.,
t f = 0.57 in., d = 18.0 in., and t w = 0.355 in. The cover plate has a
width b = 15 in. and t = 1.0 in. The cover plate is attached to the
lower flange by pairs of 0.875 in. diameter bolts spaced at intervals
s along the beam span. Bending occurs about the z centroidal axis.
(a) If the allowable bolt shear stress is 14 ksi, determine the maximum
bolt spacing interval s required to support an internal
shear force in the beam of V = 55 kips.
(b) If the allowable bending stress is 24 ksi, determine the
allowable bending moment for the existing wide-flange shape,
the allowable bending moment for the wide-flange shape with
the added cover plate, and the percentage increase in moment
capacity that is gained by adding the cover plate.
t f
Rivet
z
FIGURE p9.32b
Cross section.
V
Rivet
z'
60 mm
A = 2,400 mm 2
Iz' = 3.76 × 10 6 mm 4
FIGURE p9.32c Crosssectional
properties for a
single hat shape.
Cover
plate
t w
z
b f
y
b
d
t
FIGURE p9.33
9.9 Shear Stress and Shear Flow in
Thin-Walled members
In the preceding discussion of built-up beams, the internal shear force F H required for
horizontal equilibrium of a specific portion and length of a flexural member was expressed
by Equation (9.11):
F
H
VQ
= Dx
I
As shown in Figure 9.14c, the force F H acts parallel to the bending stresses (i.e., in the
x direction). The shear flow q was derived in Equation (9.12),
FH
VQ
q
D x
= = I
to express the shear force per unit length of beam span required to satisfy horizontal equilibrium
for a specific portion of the cross section. In this section, these ideas will be applied
to the analysis of average shear stress and shear flow in thin-walled members such as the
flanges of wide-flange beam sections.
Shear Stress in Thin-Walled Sections
Consider the segment of length dx of the wide-flange beam shown in Figure 9.16a. The bending
moments M and M + dM produce compressive bending stresses in the upper flange of the
z
z
356