Advanced Methods of Structural Analysis

7.6 Temperature Changes 255

ı 11 D

666:67

EI

;ı 12 Dı 21 D

275

EI

;ı 22 D

170:67

EI

: (b)

h = 0.6m

b

= 0.2m

t 1 =− 10 °C

10

m

5m

3m

C

B

1 2

A

h

h t 3 =+20°C

t 2 =0

h

= 0.6m

b = 0.4m

h

tin= +20°

tout= − 10 ° tav=+5°

Dt=30°

Design diagram Primary system

X 1

X 2

1

5

4

3

6 8

tav=+10°

Δt=+ 20 °

tav=+5°

Δt= 30 °

tav= –5°

Δt= 10 °

ab

d 21

d 11

d 22

d 12

X 1 =1

10

10

M 1

X 2 =1

3

8

N 1 M 2

+

1.0

X 1 =1

c

82.99

14.628

Mt kNm 68.37

(factor aEI)

82.99

68.37

14.628

43.99

d X

2 =1

(^6) X 1 =1
18
3
13
10
MΣ
e
Fig. 7.20(a)Design diagram and temperature distribution; (b) Primary system. (c) Bending
moment and axial force diagrams in unit states. (d) Final bending moment diagram and static
verification. (e) Summary unit bending moment diagram
For calculation of free terms we will use expressions (7.18a). These expressions
contain the average temperaturetavand temperature gradienttfor each member;
they are
For portion 1-3
tavD
20 C.10/
2
D 5 ıI tDj 10 .C20/jD 30 ı;
for portion 4-5
tavD
0 C.10/
2
D 5 ı tDj 10  0 jD 10 ı; (c)