Advanced Methods of Structural Analysis

410 11 Matrix Stiffness Method

Vector of internal unknowns bending moments isESfinDSE 1 CSE 2 ,where

SE 2 DkAQ TZEDEI

5

2

6

6

4

4200

2400

0030

0005

3

7

7

5 

2

6

6

4

0 0:2

1 0:2

10

1 0:333

3

7

7

5

1

EI

3:7944

22:452



D

2 6 6 6 6 6

3:8707

2:3529

2:2766

11:2709

3 7 7 7 7 7

Control:ASDEP. In our case



0111

0:20:2 0 0:333



2 6 6 6 6 6

3:8707

2:3529

2:2766

11:2709

3 7 7 7 7 7

D

11:1946

4:9979



Final bending moments at specified sections 1–4 are

SEfinDES 1 CSE 2 D

2 6 6 6 6 6

4:1667

4:1667

15:36

0

3 7 7 7 7 7

C

2 6 6 6 6 6

3:8707

2:3529

2:2766

11:2709

3 7 7 7 7 7

D

2 6 6 6 6 6

8:0374

1:8138

13:0834

11:2709

3 7 7 7 7 7

This vector allows us to construct the bending moment diagram. All ordi-
nates should be plotted according S-e diagram (Fig.11.27d). For example,
M 1 D8:037kNm should be plotted at the supportAleft at neutral line. Final
bending moment diagram is presented in Fig. 8.2g. Note that stiffness matrix method
is precise and some disagreement with data obtained previously is a result of the
rounding off.

11.8 Analysis of Statically Indeterminate Trusses.........................

Figure11.28a presents the statically indeterminate truss; the stiffnessEAfor all
members is equal. We need to compute the displacements of the all joints, and cal-
culate the internal forces.
First let us construct theZ-Pdiagram (Fig.11.28b). This diagram shows possible
joint displacements and corresponding possible loads. After that we can construct
the vector of external forces

PED^0  4  200 ̆T: