Advanced Methods of Structural Analysis

Problems 319

primary system of the force method and corresponding unit bending moment

diagramM 1 are presented in Fig.9.2g.

Ta b l e 9. 1 Calculation of bending moments

Points M 1 M 1 Z 1 M 2 M 2 Z 2 MP^0 MP.kNm/

1 0:0 0:0 0:25 4:8 0:0 4:8

2–1 0:0 0:0 C0:5 C9:6 0:0 C9:6

2–3 0:0 0:0 1:0 19:2 C 32 C12:8

3–2 0:0 0:0 C0:5 C9:6 C 32 C41:6

2–4 C12:0 3:2 0:0 0:0 0:0 3:2

4–2 C12:0 3:2 0:0 0:0 0:0 3:2

4–5 12:0 C3:2 0:0 0:0 0:0 C3:2

5 0:0 0:0 0:0 0:0 0:0 0:0

C 0:0 0:0 0:25 4:8  16 20:8

Factor EI

The vertical displacement of pointAfor entire structure equals

AD

XZ MPM 1

EI

dsD

1

2 EI

1

2

 12  12 

2

3

3:2

1

1 EI

3:2 4  12

C

8

6  2 EI

.12:8 12 C 4 20:8 16 41:620/

D887:46C887:47Š 0

Construction of shear and axial force diagrams, computation of all reactions and
their verifications should be performed as usual.

Problems.......................................................................

9.1.Design diagram of the frame is shown in Fig.P9.1.

1.Determine the number of unknowns by the force method, displacement, and

mixed methods.

2.Show the primary system of the mixed method and set up of corresponding

canonical equations;

3.Explain the meaning of primary unknowns and canonical equations of the

mixed method.

4.Define the unit of coefficients and free term of canonical equations.

5.Describe the way of calculation of all coefficients of canonical equations and

free terms.

6.Explain the advantage of the mixed method with comparison of the force and

displacement methods.