Structural analysis

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Degrees of Indeterminacy[edit]

When analyzing structural models, the first question to ask yourself is whether the system is determinant or indeterminate. If you are looking at a truss, the first step is to count the number of unknown forces. This is the number of members (a single axial force for each member) summed with the number of unknown reaction forces. Second, count the available equations of equilibrium. This number is found by taking the number of joints and multiplying by 2 (two equations of equilibrium per joint). Finally, subtract the number of equilibrium equations from the unknown forces to find the degrees of indeterminacy.

Degrees of freedom[edit]

Degrees of freedom(DoF) In two dimension space, single part of structure have 2 displacements and 1 rotation.

In three dimension space, single part of structure have 3 displacements and 3 rotations.

In general, a rigid body in d dimensions has d(d + 1)/2 degrees of freedom (d translations and d(d −1)/2 rotations), 2 directions combine to 1 rotation, therefore use Binomial coefficient to determine number of rotations.

Energy method[edit]

w:energy method

Influence line[edit]

Influence line is defined as the function which shows the variation of a structural quantity (shear force, bending moment, deflection etc.) due to the change in the position of unit load.

Virtual work[edit]

Castigliano's method[edit]

Flexibility method[edit]

Stiffness method[edit]

Stiffness is defined as the resistance to deformation. stiffness is inversely proportion to flexibility