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Presentation on theme: "CIVL3310 STRUCTURAL ANALYSIS"— Presentation transcript:

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?


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