CHAPTER 10 ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY

10. 1 STATICALLY INDETERMINATE STRUCTURES 2 10. 1 Structural Analysis Eighth Edition l ©

Statically Indeterminate Structures § 3 Advantages & Disadvantages - For a given loading, the max stress and deflection of an indeterminate structure are generally smaller than those of its statically determinate counterpart - Statically indeterminate structure has a tendency to redistribute its load to its redundant supports in cases of faulty designs or overloading Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

Statically Indeterminate Structures § 4 Advantages & Disadvantages - Although statically indeterminate structure can support loading with thinner members & with increased stability compared to their statically determinate counterpart, the cost savings in material must be compared with the added cost to fabricate the structure since often it becomes more costly to construct the supports & joints of an indeterminate structure - Careful of differential disp of the supports as well Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

Statically Indeterminate Structures Method of Analysis - To satisfy equilibrium, compatibility & force-disp requirements for the structure § Force Method § Displacement Method § 5 Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

10. 2 FORCE METHOD OF ANALYSIS GENERAL PROCEDURE 6 10. 2 Structural Analysis Eighth

Force Method of Analysis: General Procedure § § § 7 From free-body diagram, there would be 4 unknown support reactions 3 equilibrium eqn Beam is indeterminate to first degree Use principle of superposition & consider the compatibility of displacement at one of the supports Choose one of the support reactions as redundant & temporarily remove its effect on the beam Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

Force Method of Analysis: General Procedure This will allow the beam to be statically determinate & stable § Here, we will remove the rocker at B § As a result, the load P will cause B to be displaced downward § By superposition, the unknown reaction at B causes the beam at B to be displaced upward § + 8 Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

Force Method of Analysis: General Procedure § Assuming +ve disp act upward, we write the necessary compatibility eqn at the rocker as: = + 9 Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

Force Method of Analysis: General Procedure § § § Using methods in Chapter 8 or 9 to solve for B and f. BB, By can be found Reactions at wall A can then be determined from eqn of equilibrium The choice of redundant is arbitrary The moment at A can be determined directly by removing the capacity of the beam to support moment at A, replacing fixed support by pin support The rotation at A caused by P is A The rotation at A caused by the redundant MA at A is ’AA = 10 Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd +

Force Method of Analysis: General Procedure 11 Structural Analysis Eighth Edition l © 2012

10. 6 FORCE METHOD OD ANALYSIS TRUSSES 10. 3 12 Structural Analysis Eighth Edition

Force Method of Analysis: Trusses Example 10. 7 Determine the force in member AC of the truss shown. AE is the same for all the members. 13 Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

Force Method of Analysis: Trusses Example 10. 7 (Solution) Principle of superposition By inspection the truss is indeterminate to the first degree. Capability Equations Reference to member AC requires 14 Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

Force Method of Analysis: Trusses Example 10. 7 (Solution) Capability Equations For ΔAC we require application of the real load of 2 k. N and a virtual unit force acting at the cut ends of member AC 15 Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

Force Method of Analysis: Trusses Example 10. 7 (Solution) Capability Equations For f. AC AC we require application of real unit forces and virtual unit forces acting on the cut ends of member AC. Substituting the data into Eq. (1) and solving yields 16 Structural Analysis Eighth Edition l © 2012 Pearson Education South Asia Pte Ltd

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