Civil Engineering Reference
In-Depth Information
J
X
Y
C
D
A
B
F
CD
F
CE
u
h
F
GE
F
DE
G
E
X
Y
(a)
d
a
b
c
j
(b)
S
C
S
D
IL
c
1
d
1
a
1
b
1
(c)
M
E
IL
c
2
d
2
a
2
b
2
F
IGURE
20.17
Determination of
forces in the
members of a truss
(d)
M
C
IL
considering a section XX through CE, CD and GE, we have
F
CE
sin
θ
=
S
CD
so that
S
CD
sin
θ
F
CE
=
(20.25)
Similarly
S
CD
sin
θ
F
DE
=
(20.26)
From Fig. 20.17(b) we see that for a load position between A and J,
S
CD
is positive.
Therefore, referring to Fig. 20.17(a),
F
CE
is compressive while
F
DE
is tensile. For
a load position between J and B,
S
CD
is negative so that
F
CE
is tensile and
F
DE
is
compressive. Thus
F
CE
and
F
DE
will always be of opposite sign; this may also be
deduced from a consideration of the vertical equilibrium of joint E.
If we now consider the moment equilibrium of the truss at a vertical section through
joint E we have
F
CD
h
=
M
E
