Civil Engineering Reference
In-Depth Information
The fixed-end moments are calculated for each member load.
(
)
=− −
2
2
12
.
kft
/
20
12
ft
wL
FEM
=−
=−
40
kft
AB
12
(
)
=−
2
2
12
.
kft
/
2
0
ft
wL
FEM
=
=
40
kft
BA
12
12
=−
(
) (
2
)
85 5
10
ft
ft
Pb a
L
2
FEM
=−
=− −
10
kft
BC
(
)
2
2
ft
(
) (
2
)
2
85 5
10
ft
ft
Pa b
L
FEM
CB
=
=
)
=−
10
kft
(
2
2
ft
The moment-distribution is shown in Table 4.1. In the first line, the fixed-
end moments are recorded. In the second line, the distribution factor is
multiplied times the negative sum of the fixed-end moments. This is a dis-
tribution. In each subsequent one-half, the end moment is carried over the
opposite end of the members. This is a carry-over. Then, the unbalanced
moments at the joint are distributed again and carried over again.
Table 4.1.
Example 4.13 Moment-distribution
0.00
0.333
0.667
1.00
Distribution
Factor
40.00
10.00
Fixed-end
Moment
−40.00
−10.00
0.00
Distribution
1
−10.00
−20.00
−10.00
0.00
Carry-over
1
−5.00
−5.00
−10.00
0.00
1.67
3.33
10.00
Distribution
2
0.83
0.00
5.00
1.67
Carry-over
2
0.00
Distribution
3
−1.67
−3.33
−1.67
0.00
Carry-over
3
−0.83
−0.83
−1.67
0.00
0.28
0.56
1.67
Distribution
4
0.14
0.00
0.83
0.28
Carry-over
4
0.00
Distribution
5
−0.28
−0.56
−0.28
0.14
0.00
Carry-over
5
−0.14
−0.28
0.00
0.05
0.09
0.28
Distribution
6
0.02
0.00
0.14
0.05
Carry-over
6
0.00
−0.05
−0.09
−0.05
Distribution
7
−0.02
0.00
−0.02
−0.05
Carry-over
7
−45.00
30.00
−30.02
−0.05
Final Moments
