Advanced Methods of Structural Analysis

8.5 Special Types of Exposures 297

ab

a

b

A

2

b

1

2

a

A

φ

1

i1-3=0.2EI

i4-5= 0.333EI i

6-8=0.2EI

1

5

8

6

3

4

φ

10m

5m

3m

c

a

R 1 a

R 2 a

Ma

3 i 6 − 8 3 ⋅0.2EI

6 ⋅0.2EI

l 6 − 8 a=⋅ 10 0.02= 0.0012EI

A

b

×

R 1 b

0.0024EI

R 2 b

Mb

b= 5

A

×

R 1 j 2 i

1-3⋅j=2⋅0.2EI⋅0.01=0.004EI

4 i1-3⋅j=0.008EI

R 2 j

Mj

j

A

R1s

0.0012EI

(0.0024+0.004)EI =0.0064EI

(0.0024+0.008)EI=0.0104EI

R2s

a Ma+Mb+Mj

b

j

A

6 i 1 − 3

l 1 − 3 ⋅0.01= 0.0024EI

0.00336EI

R2s

M1-3 = 0.0104EI

M3-1 = 0.0064EI 0.00336EI

0.00336EI

6 8

R1s

0.0064EI

0.0012EI

de

MkNm

(factor 10–2EI)

0.112 0.212

0.100

0.454

f

Fig. 8.11 Settlements of support: (a) Design diagram; (b) Primary system; (c) Bending moment
diagram in primary system caused by settlements of supportA;(d,e) Free-body diagrams for rigid
joint and crossbar; (f) Final bending moment diagram