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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: 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

- 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

Compatibility Equation

+

Note 2

Compatibility Equation

+

Note 3

Example 1

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

Solution

Compatibility Equation

Conjugate beam

method

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

Compatibility Equation

Determine the moment at fixed wall for the beam shown

Solution

Conjugate beam method