Civil Engineering Reference
In-Depth Information
axis through its centroid, but not symmetry. We shall nowdevelop the theory of bending
for beams of arbitrary cross section.
F
IGURE
9.15
Unsymmetrical
beam sections
(a)
(b)
ASSUMPTIONS
We shall again assume, as in the case of symmetrical bending, that plane sections of the
beam remain plane after bending and that the material of the beam is homogeneous
and linearly elastic.
SIGN CONVENTIONS AND NOTATION
Since we are now concerned with the general case of bending we may apply loading
systems to a beam in any plane. However, no matter how complex these loading
systems are, they can always be resolved into components in planes containing the
three coordinate axes of the beam. We shall use an identical system of axes to that
shown in Fig. 3.6, but our notation for loads must be extended and modified to allow
for the general case.
As far as possible we shall adopt sign conventions and a notation which are consistent
with those shown in Fig. 3.6. Thus, in Fig. 9.16, the externally applied shear load
W
y
is
y
v
w
y
(
x
)
O
W
z
z
u
w
z
(
x
)
w
P
x
M
y
T
F
IGURE
9.16
Sign
conventions and
notation
M
z
W
y
