Structure analysis ii
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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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Structure Analysis II

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Structure analysis ii

Structure Analysis II


Analysis of statically indeterminate structures by the force method part 1

Analysis of statically Indeterminate structures by the Force Method

Part 1


Structure analysis ii

Review Conjugate beam

method


Structure analysis ii

Conjugate-Beam Supports


Structure analysis ii

Review Example 1

Find the deflection at Point B


Structure analysis ii

Review Example 2

Find the deflection at Point C


Determinacy stability

Determinacy & Stability

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: General 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


Structure analysis ii

Note 1

Compatibility Equation

+


Structure analysis ii

Note 2

Compatibility Equation

+


Structure analysis ii

Note 3


Force method of analysis beams

Force Method of Analysis: Beams

Example 1

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


Structure analysis ii

Solution

Compatibility Equation


Structure analysis ii

Conjugate beam

method


Example 2

Example 2

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


Structure analysis ii

Compatibility Equation


Example 3

Example 3

Determine the moment at fixed wall for the beam shown


Structure analysis ii

Solution

Conjugate beam method


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