Problems 309
8.11.A frame is subjected to uniformly distributed loadq, as shown in Fig.P8.11.
The stiffness of the right elastic support isk(kN/m). The relative stiffnesses for
all members are shown in the circles. Calculate the angle of rotation of the joint 1.
Construct the bending moment diagram. Check the limiting caseskD1andkD 0.
Trace the elastic curves for both limiting cases. Is it possible to find a stiffness of
elastic support such that rigid joint 1 would not rotate under the given load?
8m 8m6mq1
1(^22) k
Fig. P8.11
Ans.Z 1 D
12q
EI
24 ̨^323
11 C9 ̨
, ̨D
1
1 C512k^6 EI
.
8.12a–d.Design diagrams for four-frames with different boundary conditions at
support 3 are shown in Fig.P8.12. All frames are subjected to uniform distributed
loadq. For all frames the span island heighthDl. The flexural rigidity isEI
for all members. Construct the internal force diagrams. Trace the elastic curves and
show the inflection points. Explain the differences in structural behavior caused by
the different types of supports 3.
2
q
l
3 1
a
2
l
(^31)
b q
3
q
l
2
1
c
l
3
2
q
1
d
h
Fig. P8.12
Ans. (a)Z 1 D
ql^3
96 EI
;(b)Z 1 D
ql^3
15 EI
;(c)Z 1 D
ql^3
56 EI
8.13.A sidesway frame is subjected to horizontal loadP along the crossbar
(Fig.P8.13). The connections of the crossbar with the left and right vertical mem-
bers are hinged while the connection with the intermediate vertical member is rigid.
The bending stiffness of all vertical members isEIand for the crossbar it is 2 EI.
Will the axial forces in the crossbar be equal to zero or not? Verify your answer