Advanced Methods of Structural Analysis

308 8 The Displacement Method

Δ

1

l l

Fig. P8.8

Ans.M 1 D

12

7

EI

l^2

:

8.9.A two-span uniform beam with fixed ends is subjected to uniformly distributed
loadqand vertical settlements of the intermediate support, as shown in Fig.P8.9.
Define the value of the settlement in order that: (a) the bending moment at the in-
termediate support equals zero; (b) the bending moment at the fixed supports equals
zero; (c) the bending moment at the midpoint of the span equals zero.

q

1

ll

Δ

Fig. P8.9

Ans. (a)D

ql^4

72 EI

.#/:

8.10.A design diagram of a frame is presented in Fig.P8.10. Supports 2, 3, and 4
are fixed, sliding, and rolled, respectively. Bending stiffnesses areEIand 2EIfor
vertical and horizontal members, respectively; their relative stiffnesses are shown
in circles. Compute the angle of rotation of the joint 1. Construct the internal force
diagrams.

8m 8m

6m

q

3 4

2

1

1

(^22)
Fig. P8.10
Ans.Z 1 D
8q
EI
.rad/; M 13 D
58q
3
;M 31 D
38q
3
;M 14 D14q