/////////////////////////////////////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\


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

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

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

where:
{P} = Joint forces
{P_f}= 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)

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

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

Figure 2 : MDM method example 2 (Axial)

StructuralAnalysisAxialEx2solution.pdf

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

Figure 3 : MDM method example 3 (Axial)

StructuralAnalysisAxialEx3solution.pdf

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

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

Finding displacement, reaction and member forces using MDM method example 1 (Truss)
Find the displacements, member forces and reactions for this truss.
Truss Example 1
Figure 5: MDM method example 1 (Truss)

StructuralAnalysisTrussEx1solution.pdf

Finding displacement, reaction and member forces using MDM method example 2 (Truss)
Find the displacements, member forces and reactions for this truss.
Truss Example 2
Figure 6 : MDM method example 2 (Truss)

StructuralAnalysisTrussEx2solution.pdf

Finding displacement, reaction and member forces using MDM method example 3 (Truss)
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)

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

Finding displacement, reaction and member forces using MDM method example 1(Beam)
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

Finding displacement, reaction and member forces using MDM method example 2(Beam)
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)

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

Finding displacement, reaction and member forces using MDM method example (Frames)
Find the displacements, member forces and reactions for this frame shown below.
Frame Ex1
Figure 13: MDM method example 1 (Frame)

StructuralAnalysisFrameEx1solution.pdf

Finding displacement, reaction and member forces using MDM method example (Frames)
Find the displacements, member forces and reactions for this frame shown below.
Frame Ex2
Figure 14 : MDM method example 2 (Frame)

StructuralAnalysisFrameEx2solution.pdf

Qualitative shear and moment diagrams

Fixed end forces derivation

Videos