Civil Engineering Reference
In-Depth Information
P
P
e
H
=
Pe
/
d
+
=
d
H
=
Pe
/
d
FIGURE 8.2
Equivalent static system for eccentrically applied vertical load.
Equation 8.19 and its derivatives have also been solved for other typical bound-
ary and loading conditions and are provided for design use in equations and charts
(Seaburg and Carter, 1997). However, even with such design aids, the solution of
Equations 8.12, 8.14, and 8.15 is generally too cumbersome for routine design work
and an approximate method, based on a flexure analogy, is often employed.
In this method, it is assumed that the torsional moment acts as a horizontal force
couple in the plane of the flanges. The horizontal forces create bending moments
in the flanges and the problem is solved by using a simplified analysis involving
flexure only. If the torsion is created by eccentric vertical loads, an equivalent static
system consisting of a vertical load applied at the shear center and horizontal forces
applied at each flange is appropriate (Figure 8.2). Examples 8.2 and 8.4 illustrate the
use of the flexure analogy for torsional stresses created by an eccentric vertical load.
If the torsion is created by an applied horizontal force, an equivalent static system
consisting of vertical and horizontal loads applied at the shear center (creating biaxial
bending) and horizontal forces applied at each flange is appropriate (Figure 8.3a). For
the latter case, an equivalent static system as shown in Figure 8.3b may also be used.
The method is conservative as it ignores pure torsion and assumes torsional moment
is resisted entirely by warping torsion. Therefore, normal stresses due to warping are
P
P
t
f
H
H
(
d
+
t
f
)
2
d
=
+
H
d
H
(
d
+
t
f
)
2
d
FIGURE 8.3a
Equivalent static system for applied vertical and horizontal loads.
