Civil Engineering Reference
In-Depth Information
Joint
D
A
B
C
E
Member
DA
AD
AB
BA
BE
BC
CB
EB
DFs
-
0.5
0.5
0.4
0.3
0.3
-
1.0
FEMs
0
0
−
32.0
+
32.0
0
−
21.3
+
21.3
0
Balance A and B
+
16.0
+
16.0
−
4.3
−
3.2
−
3.2
Carry over
+
8.0
−
2.15
+
8.0
−
1.6
Balance
+
1.08
+
1.08
−
3.2
−
2.4
−
2.4
Carry over
+
0.54
−
1.6
+
0.54
−
1.2
Balance
+
0.8
+
0.8
−
0.22
−
0.16
−
0.16
Carry over
+
0.4
−
0.11
+
0.4
−
0.08
Balance
+
0.05
+
0.06
−
0.16
−
0.12
−
0.12
Final moments
+
8.94
+
17.93
−
17.93
+
33.08
−
5.88
−
27.18
+
18.42
0
33.08
27.18
17.93
18.42
A
17.93
F
IGURE
16.45
Bending moment
diagram for the
frame of Ex. 16.21
(bending moments
(kN m) drawn on
tension side of
members)
B
C
5.88
D
8.94
E
hu
v
hu
v
B
C
B
C
P
M
CD
M
BA
u
v
u
v
h
h
u
v
u
v
M
AB
M
DC
F
IGURE
16.46
Calculation of sway
effect in a portal
frame
R
D,H
R
A,H
A
D
A
D
(a)
(b)
The bending moment diagram is shown in Fig. 16.45 and is drawn on the tension side
of each member. The bending moment distributions in the members AB and BC are
determined by superimposing the fixing moment diagramon the free bending moment
diagram, i.e. the bending moment diagram obtained by supposing that AB and BC are
simply supported.
We shall now consider frames that are subject to sway. For example, the frame shown in
Fig. 16.46(a), although symmetrical itself, is unsymmetrically loaded and will therefore
