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

P
A
375
SHEAR CENTERS OF
THIN-wALLEd OPEN
SECTIONS
A′
FIGURE 9.25 Rear view of cantilever beam.
cause the beam to both bend and twist, as depicted in Figure 9.24b. To better understand
what causes the channel shape to twist, it is instructive to look at the internal shear flow
produced in the beam in response to the applied load P.
The beam of Figure 9.24 is shown from the rear in Figure 9.25. The shear flow produced
at Section A–A′ in response to the external load P will be examined.
For the cantilever beam loaded as shown in Figure 9.26a, the upward internal shear
force V must equal the downward external load P. The shear force V creates a shear flow q
that acts in the web and the flanges in the directions shown in the figure.
P
P
y
y
A
A
B
x
q
z
d
2
x
F f
Fw = V
z
V
A′
d
2
A′
(a) Shear flow in the channel shape
(b) Resultant shear forces in the flanges
and the web
FIGURE 9.26 Internal shear flow and resultant forces acting on Section A–A′.
b
F f