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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 12 m C=T=67.5 kN 20 kN 20 kN 20 kN 20 kN 20 kN [email protected] m= 54 m M=810 kN∙m V=30 kN 12 m 20 kN 20 kN 20 kN 20 kN 20 kN Fy=30 kN F cos shear 10 50 kN 50 kN Shear (kN) moment (kN∙m) FBK=37.5 kN Structural Analogy 3 degrees of indeterminacy P1 P2 R1 Stiff diagonal members assume Fa=Fb Weak diagonal members assume Fb=0 (no compression) R2 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?