1. CIVL3310 STRUCTURAL ANALYSIS
Chapter 7:
Approximate Analysis of Statically Indeterminate Structures
CIVL3310 STRUCTURAL ANALYSIS
Professor CC Chang

2. Approximate Analysis
Preliminary analysis for complex indeterminate structures
Involve some assumptions & different answers are possible

3. Structural Analogy C=T=67.5 kN FBK=37.5 kN
20 kN 20 kN 20 kN 20 kN 20 kN
12 m
m= 54 m
50 kN
Shear
(kN)
moment
(kN∙m)
C=T=67.5 kN
V=30 kN
12 m
M=810 kN∙m
Fy=30 kN
FBK=37.5 kN

4. Structural Analogy 3 degrees of indeterminacy P1 P2 R1 R2
Stiff diagonal members
assume Fa=Fb
Weak diagonal members
assume Fb=0 (no compression)

5. Example 7.1
Determine (approximately) the forces in the members of the truss. The diagonals are designed to support both tensile and compressive forces

6. Inflection Points
Points of zero moment: internal hinges (Deflection shape: zero curvature)

7. Inflection Points
Clamped BC
Under UDL

8. Inflection Points
Assumed clamped
Location: 0.2L

9. Inflection Points
0.2L
0.2L L

10. Frames under Vertical Loads

11. Frames under Vertical Loads

12. Example 7.3
Determine (approximately) the moment at the joints E and C.

13. Frames under Horizontal Loads
Inflection
point
1 degree
indeterminacy
hinge

14. Frames under Horizontal Loads

15. Frames under Horizontal Loads

16. Example 7.4
Determine (approximately) the forces acting in the members of the Warren portal.

17. Frames under Horizontal Loads
Portal method
Inflection points
Shear forces

18. Frames under Horizontal Loads
Cantilever method
Inflection points
Axial forces

19. 7. Approximate Analysis Structural analogy What are inflection points?
How to analyze frames under vertical loads?
How can inflection points be used to simplify the analysis?
What are portal method and cantilever method?