Civil Engineering Reference
In-Depth Information
A
W
B
W
T
C
T
Wh
F
IGURE
3.4
Torques applied
to a beam
h
(a)
(b)
A
B
m
W
m
W
A
B
W
m
W
B
C
B
M
m
M
(a)
C
(b)
F
IGURE
3.5
Internal force system generated by an external shear load
in direction. The complete force systems acting on the two faces of the section mm
are shown in Fig. 3.5(b).
Systems of forces such as those at the section mm are known as
internal forces
. Gen-
erally, they vary throughout the length of a structural member as can be seen from
Fig. 3.5(b) where the internal moment,
M
, increases in magnitude as the built-in end is
approached due to the increasing rotational effect of
W
. We note that applied loads of
one type can induce internal forces of another. For example, in Fig. 3.5(b) the external
shear load,
W
, produces both shear and bending at the section mm.
Internal forces are distributed throughout beam sections in the form of stresses. It fol-
lows that the resultant of each individual stress distribution must be the corresponding
internal force; internal forces are therefore often known as
stress resultants
. However,
before an individual stress distribution can be found it is necessary to determine the
corresponding internal force. Also, in design problems, it is necessary to determine
the position and value of maximum stress and displacement. Usually, the first step
in the analysis of a structure is to calculate the distribution of each of the four basic
internal force types throughout the component structural members. We shall therefore
determine the distributions of the four internal force systems in a variety of structural
members. First, however, we shall establish a notation and sign convention for each
type of force.
