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

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

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Structural Analogy 20 kN 20 kN 20 kN 20 kN 20 kN 12 m m= 54 m 50 kN Shear (kN) moment (kN∙m) 12 m M=810 kN∙m C=T=67.5 kN V=30 kN F y =30 kN F BK =37.5 kN

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Structural Analogy 3 degrees of indeterminacy P1P1 P2P2 R1R1 R2R2 Stiff diagonal members assume F a =F b Weak diagonal members assume F b =0 (no compression)

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

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

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Inflection Points Clamped BC Under UDL

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Inflection Points Assumed clamped Location: 0.2L

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Inflection Points L 0.2L

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Frames under Vertical Loads

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

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Frames under Horizontal Loads hinge 1 degree indeterminacy Inflection point

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Frames under Horizontal Loads

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

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Frames under Horizontal Loads Portal method Inflection points Shear forces

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Frames under Horizontal Loads Cantilever method Inflection points Axial forces

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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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