Civil Engineering Reference
In-Depth Information
2
EI
L
4
EI
L
6
EI
L
M
=
FEM
+
f
+
f
−
b
(4.13)
j
ji
i
j
In these two equations,
f
is the rotation at the joint and
b
is the lateral
translation between the ends divided by the length of the member. It will
be seen later that the values 4
EI/L
, 2
EI/L
, and 6
EI/L
are flexural stiffness
terms. The
FEM
terms are the fixed-end moments due to the loads on the
member. A special case may be used if one end of the member is pinned.
Equation 4.14 is for the
i
end of a member when the
j
end is pinned.
FEM
3
fb
EI
L
(
)
ji
M FEM
=
+
+
−
(4.14)
i
ij
i
2
Example 4.12 Slope-deflection.
Determine the moments at the ends of the members of the continuous
beam in Figure 4.24 using the slope-deflection equations.
Z
8 kips
1.2 kips/ft
X
8 kips
A
B
C
20ft
5ft
5ft
Figure 4.24.
Example 4.12 Slope-deflection.
The fixed-end moments due to the loads on each span are computed
and can be found in most elementary structural analysis textbooks.
(
)
=− −
2
wL
2
12
.
kft
/
20
12
ft
FEM
=−
=−
40
kft
AB
12
(
)
=−
2
wL
2
12
.
kft
/
2
0
ft
FEM
=
=
40
kft
BA
12
12
=−
(
) (
)
2
Pb a
L
2
85 5
10
ft
ft
FEM
=−
=− −
10
kft
BC
(
)
2
2
ft
(
) (
)
2
2
85 5
10
ft
ft
Pa b
L
FEM
CB
=
=
)
=−
10
kft
(
2
2
ft
