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Dedication

Time

consistencY



σy
⇀τyx


σx←τxy



Structural Analysis




Structural Analysis is the forecast of the performance of a structure under prescribed loading conditions. The results that are of interest are: the deflections, reactions and stresses.


Equations:

  • {Q} = {Qf}+ [k]{u}---->At the member level (local)

  • where:
    {Q} = Member forces
    {Qf}= Fixed-end member forces
    [k] = member stiffness matrix
    {u} = member displacements

  • {P} = {Pf}+ [S]{d}---->At the structural level (global)

  • where:
    {P} = Joint forces
    {Pf}= Fixed-end forces
    [S] = stiffness matrix
    {d} = displacements

      Worked out problems with solutions in pdf files


      Displacement, Reaction and Member Forces in an Axial Structure (Matrix Displacement Method,MDM)


    1. Degrees of Freedom (DOF) for an axial member
    2. Degrees of Freedom (DOFs) Axial
      Figure 1: Degrees of Freedom (DOF) for an axial member

    3. Finding displacement, reaction and member forces using MDM method example (Axial)
    4. Find the displacements, member forces and reactions for this axial structure. Then, draw the axial diagram.

      Axial structure
      Figure 2 : MDM method example 2 (Axial)

      StructuralAnalysisAxialEx2solution.pdf


    5. Finding displacement, reaction and member forces using MDM method example (Axial)
    6. Find the displacements, member forces and reactions for this axial structure. Then, draw the axial diagram.

      Axial structure
      Figure 3 : MDM method example 3 (Axial)

      StructuralAnalysisAxialEx3solution.pdf


      Displacement, Reaction and Member Forces in a Truss (Matrix Displacement Method,MDM)


    7. Degrees of Freedom (DOF) for a truss member
    8. Degrees of Freedom (DOFs) Truss
      Figure 4: Degrees of Freedom (DOF) for a truss member

    9. Finding displacement, reaction and member forces using MDM method example 1 (Truss)
    10. Find the displacements, member forces and reactions for this truss.

      Truss Example 1
      Figure 5: MDM method example 1 (Truss)

      StructuralAnalysisTrussEx1solution.pdf


    11. Finding displacement, reaction and member forces using MDM method example 2 (Truss)
    12. Find the displacements, member forces and reactions for this truss.

      Truss Example 2
      Figure 6 : MDM method example 2 (Truss)

      StructuralAnalysisTrussEx2solution.pdf


    13. Finding displacement, reaction and member forces using MDM method example 3 (Truss)
    14. Find the displacements, member forces and reactions for this truss.

      Truss Example 2
      Figure 7: MDM method example 3 (Truss)

      StructuralAnalysisTrussEx3solution.pdf


      Displacement, Reaction and Member Forces in a Beam (Matrix Displacement Method,MDM)


    15. Degrees of Freedom (DOF) for a beam member
    16. Degrees of Freedom (DOFs) Beam
      Figure 8: Degrees of Freedom (DOF) for a beam member

    17. Finding displacement, reaction and member forces using MDM method example 1(Beam)
    18. Find the displacements, member forces and reactions for this beam. Then, draw the shear and moment diagrams.

      Beam Ex1
      Figure 9: MDM method example 1 (Beam)

      StructuralAnalysisBeamEx1solution.pdf


    19. Finding displacement, reaction and member forces using MDM method example 2(Beam)
    20. Find the displacements, member forces and reactions for this beam. Then, draw the shear and moment diagrams.

      Beam Ex2
      Figure 10: MDM method example 1 (Beam)

      StructuralAnalysisBeamEx2solution.pdf


      Displacement, Reaction and Member Forces in a Frame (Matrix Displacement Method,MDM)


    21. Degrees of Freedom (DOF) for a frame member
    22. Degrees of Freedom (DOFs) Frame
      Figure 12: Degrees of Freedom (DOF) for a frame member

    23. Finding displacement, reaction and member forces using MDM method example (Frames)
    24. Find the displacements, member forces and reactions for this frame shown below.

      Frame Ex1
      Figure 13: MDM method example 1 (Frame)

      StructuralAnalysisFrameEx1solution.pdf


    25. Finding displacement, reaction and member forces using MDM method example (Frames)
    26. Find the displacements, member forces and reactions for this frame shown below.

      Frame Ex2
      Figure 14 : MDM method example 2 (Frame)

      StructuralAnalysisFrameEx2solution.pdf

    27. Qualitative shear and moment diagrams
    28. Fixed end forces derivation

      Videos








    ↾τxy→σx

    ↽τyx
    ↓σy



    w(x)
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