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

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

Structural Analogy C=T=67.5 kN FBK=37.5 kN 20 kN 20 kN 20 kN 20 kN 20 kN 12 m 6@9 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

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

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

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

Inflection Points Clamped BC Under UDL

Inflection Points Assumed clamped Location: 0.2L

Inflection Points 0.2L 0.2L L

Frames under Vertical Loads

Frames under Vertical Loads

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

Frames under Horizontal Loads Inflection point 1 degree indeterminacy hinge

Frames under Horizontal Loads

Frames under Horizontal Loads

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

Frames under Horizontal Loads Portal method Inflection points Shear forces

Frames under Horizontal Loads Cantilever method Inflection points Axial forces

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?