Structural Analysis Flashcards

In matrix stiffness analysis, the element stiffness matrix for a truss member of length L, area A, and modulus E is of size:

Answer: 4×4

A truss member has 2 DOFs per node (x and y translation) and 2 nodes, giving a 4×4 element stiffness matrix in 2D.

The three-moment equation (Clapeyron's theorem) is used to analyze:

Answer: Continuous beams over multiple spans

Clapeyron's three-moment theorem relates the moments at three successive supports of a continuous beam, enabling indeterminate analysis span by span.

A structure is geometrically unstable if:

Answer: All reactions are parallel or concurrent even if the reaction count is sufficient

Even with the correct number of reactions, a structure is geometrically unstable if all reaction lines of action are parallel or pass through a common point.

In the stiffness method, the joint equilibrium equation is written as:

Answer: [K]{d} = {F}

The stiffness method forms [K]{d} = {F}, where [K] is the global stiffness matrix, {d} the displacement vector, and {F} the load vector.

Which of the following correctly defines the flexibility coefficient f_ij?

Answer: Displacement at i due to a unit force applied at j

The flexibility coefficient f_ij is the displacement at coordinate i caused by a unit force applied at coordinate j, with all other loads absent.

The plastic hinge in a steel beam forms at the section where:

Answer: The bending moment reaches the plastic moment capacity M_p

A plastic hinge forms when the cross-section's bending moment reaches M_p, causing unlimited rotation at constant moment.

For a simply supported beam of span L with a central point load P, the maximum bending moment is:

Answer: PL/4

Each support reaction is P/2, and taking moments to midspan gives a maximum moment of (P/2)(L/2) = PL/4.