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Structure Analysis II. Analysis of statically Indeterminate structures by the Force Method Part 1. Review Conjugate beam method. Conjugate-Beam Supports. Review Example 1. Find the deflection at Point B. Review Example 2. Find the deflection at Point C. Determinacy & Stability.

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Review MethodConjugate beam

method



Review Example 1 Method

Find the deflection at Point B


Review Example 2 Method

Find the deflection at Point C


Determinacy stability
Determinacy & Stability Method

Determinacy: when all the forces in structure can be determined from equilibrium equation , the structure is referred to as statically determinate. Structure having more unknown forces than available equilibrium equations called statically indeterminate

If n is number of structure parts & r is number of unknown forces:

r = 3n, statically determinate

r > 3n, statically indeterminate


Force method general procedure
Force Method: MethodGeneral Procedure

  • Determine the number of redundant reactions

  • Remove enough redundants to form a determinate structure

  • Calculate the displacements that the known loads cause in the determinate structure

  • Calculate displacements at the same points in the determinate structure due to the redundants

  • The sum of the displacements calculated in steps (3) and (4) must be equal to the displacements at the actual indeterminate structure

  • Use equilibrium to determine the remaining reactions


Note 1 Method

Compatibility Equation

+


Note 2 Method

Compatibility Equation

+


Note 3 Method


Force method of analysis beams
Force Method of Analysis: MethodBeams

Example 1

Determine the reaction at the roller support B of the beam shown


Solution Method

Compatibility Equation


Conjugate beam Method

method


Example 2
Example 2 Method

Determine the reaction at the roller support B of the beam shown, the support B settles 1.5 in



Example 3
Example 3 Method

Determine the moment at fixed wall for the beam shown


Solution Method

Conjugate beam method


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