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Structure Analysis II

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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  1. Structure Analysis II

  2. Analysis of statically Indeterminate structures by the Force Method Part 1

  3. Review Conjugate beam method

  4. Conjugate-Beam Supports

  5. Review Example 1 Find the deflection at Point B

  6. Review Example 2 Find the deflection at Point C

  7. 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

  8. 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

  9. Note 1 Compatibility Equation +

  10. Note 2 Compatibility Equation +

  11. Note 3

  12. Force Method of Analysis: Beams Example 1 Determine the reaction at the roller support B of the beam shown

  13. Solution Compatibility Equation

  14. Conjugate beam method

  15. Example 2 Determine the reaction at the roller support B of the beam shown, the support B settles 1.5 in

  16. Compatibility Equation

  17. Example 3 Determine the moment at fixed wall for the beam shown

  18. Solution Conjugate beam method

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