Advanced Methods of Structural Analysis

284 8 The Displacement Method

ab

1

2

l=6m

h=5m

6m

P

Design diagram

1 P^12

Primary system

i=0.2EI

i=0.333EI

Z 1 Z^2

1 2

M 1

Z 1 =1

r 11

r 21

3 i=1EI

3 i=1EI

1

r 11

1 EI 3 i=1EI

(^12) r 21
c
0.12EI
Z 2 =1
(^12)
3 i
h
= 0.12EI
r 22
M 2
r 12
0.12EI
Z 2 =1
M
0.024EI
0.024EI
M
0.024EI
0.024EI
M= 0.12EI
Q=0.024EI
(^12)
r 22
r 12
0.024EI
d
e
f
(^12) R
2 P
R 1 P
P ∑X = 0 :R^2 P^ = −P
P
3 1.667P
MP
1.667P
P
1.667P
P
3
P
3
g
Fig. 8.7 (a,b) Design diagram of the frame and primary system. (c) Unit bending moment di-
agram due toZ 1 D 1 and calculation ofr 11 andr 21 .(d,e) Unit bending moment diagram due
toZ 2 D^1 and calculation ofr 12 andr 22 .(f) Free-body diagram of the crossbar in the loaded
condition. (g) Final bending moment diagram and reactions of supports