Advanced Methods of Structural Analysis

Problems 307

l

1

0.5l

P

0.5l

Fig. P8.5

Ans.M 1 D

Pl

16

.

8.6.A two-span nonuniform beam with fixed ends is loaded as shown in Fig.P8.6.
Parameternis any positive number. Construct the bending moment and shear force
diagrams. Show the elastic curve. Prove thatM 0 DM 1 =2.

0

l l

(^12)
EI nEI
Fig. P8.6
Ans.M 1 D
ql^2
12 .1Cn/
;M 2 D
ql^2
24

2 C3n
1 Cn
.
8.7.A design diagram of a two-span uniform beam is shown in Fig.P8.7. Calculate
the slope at the support 1 and compute the bending moments at the supports.
0
q =2kN/m
1 2
P =12kN
a = 6m b = 4m
l 1 = 8m l 2 = 10m
F =1kN
c = 2m
EI = const
Fig. P8.7
Ans.Z 1 D
10:616
EI
rad;M 0 D8:013kN m;M 1 D15:975kN m.
8.8.A two-span uniform beam with fixed and pinned end supports is subjected to
vertical settlements of support, as shown in Fig.P8.8. Provide complete analysis for
both design diagrams.