Advanced Methods of Structural Analysis

7.3 Analysis of Statically Indeterminate Structures 229

q Primary system

P

X 1

X 2

1

5

4

3

2

8

7

6 6

3

4

4m 6m

5m

P 3m

q

C

B

A

1

2

1

D

Design diagram

ab

cd e

M 1

X 1 =1

d 11

d 21

10 6

10 Δ 1 P

Δ 2 P

32

2532

6.25

P=8

q=2

d 12

d (^22) X 2 =1
3
5.5
8
M 2 M^0 P
13
3
10
D
X 2 =1
(^6) X 1 =1
18
3
13
10
MΣ
D
f
D B
P
q
C
A
M kNm EC
13.085
1.817 11.349
11.268
1.324
8.036
13.085
11.268
1.817
a
g

∑

∑

H 3 → MA = 0: H 3 = 3.756kN → Q 3 = −3.756kN

HA → M 3 = 0:HA = 6.2438kN → QA = +6.2438kN

A

3

q

1.817

H 3

HA

8.036

h

QkN

1.892

3.756

3.756

6.108

6.244

+

+

6.108

N6-7

3.756

N3-A

3

6

3.756^4

D

i

Reaction of

supports

6.108

8.036 6.244

1.892

3.756 P

q^7

6.108 NkN

−

A

B

C

D

jk

Fig. 7.11(a,b) Design diagram of a frame and primary system. (c–e) Bending moment diagrams
in primary system caused by unit primary unknowns and the given load (f) Summary unit bending
moment diagram. (g) Final bending moment diagram, elastic curve (EC) and static control. (h)
Calculation of shear for member 1-3. (i) Shear force and free body diagram for jointD.(j,k)
Axial force diagram and reactions of supports