Civil Engineering Reference
In-Depth Information
The slope-deflection equations are applied to each span. In this case,
the normal equations (4.12 and 4.13) are used for span
AB
and a special
case (4.14) is used for span
BC
since support
C
is a roller. It should
be noted that there are no rotations at support
A
and therefore
f
A
=
0.
Also, since there is no translational movement between the ends,
b
is zero.
4
EI
L
2
EI
L
2
20
EI
EI
M
=
FEM
+
f
+
f
=−+ =− +
40
f
40
f
AB
AB
A
B
B
B
10
2
E
I
4
EI
L
4
20
EI
EI
M
=
FEM
+
f
+
f
=
40
+
f
=
40
+
f
BA
BA
A
B
B
B
L
5
FEM
3
EI
L
10
2
3
10
EI
3
10
EI
M
=
FEM
−
CB
+
f
= −
10
−+ =− +
f
15
f
BC
BC
B
B
B
2
Equilibrium equations are written at each joint that has a real rotation. In
this case, that is only joint
B
.
EI
3
10
EI
MM
+
= =+ −+
0 0
f
15
f
BA
BC
B
B
5
50
f
=−
f
B
B
EI
Substituting the value of
f
B
back into the moment equation will result in
the final member-end moments.
EI
50
=− −
M
=− +−
40
45
kft
AB
10
EI
EI
50
=−
M
=+ −
40
30
kf
t
BA
5
EI
3
10
EI
50
=− −
M
BC
=− +
15
−
30
kft
EI
4.9
MOMEnt-DiStRibutiOn MEtHOD
The moment-distribution method is an iteration process that uses the
same basic assumptions and equations as the slope-deflection method.
Moment-distribution
was developed by Hardy Cross in 1930 (Cross
1930). The difference between the two is that at each joint the fixed-end
moments are first summed and distributed to each member in proportion to
