Civil Engineering Reference
In-Depth Information
Use the stiffness method to find the displacements at nodes 1 and 3 and hence solve
for all the internal member forces and support reactions.
PL
/
√
2
AE
v
3
=−
Ans
.v
1
=−
0
.
293
PL
/
AE F
12
=
P
/2
=
F
14
F
23
=−
0
.
207
P
=
F
43
F
13
=
0
.
293
PF
x
,2
=−
F
x
,4
=
0
.
207
P
F
y
,2
=
F
y
,4
=
P
/2
.
P.17.2
Use the stiffness method to find the ratio
H
/
P
for which the displacement of
node 4 of the plane pin-jointed frame shown loaded in Fig. P.17.2 is zero, and for that
case give the displacements of nodes 2 and 3.
All members have equal axial rigidity
EA
.
2
√
3)
AE
v
3
=−
2
√
3)
AE
.
Ans. H
/
P
=
0
.
449
v
2
=−
4
Pl
/
(9
+
6
Pl
/
(9
+
P
3
30
°
30
°
2
30
°
30
°
4
1
H
l
F
IGURE
P.17.2
P.17.3
Form the matrices required to solve completely the plane truss shown in Fig.
P.17.3 and determine the force in member 24. All members have equal axial rigidity.
3
1
5
60
°
60
°
60
°
60
°
2
4
l
P
F
IGURE
P.17.3
Ans. F
24
=
0.
