Structural Analysis Flashcards

What is the degree of static indeterminacy of a fixed-fixed beam with no internal hinges?

Answer: 3

A fixed-fixed beam has 6 reactions (3 at each fixed end) and 3 equilibrium equations, giving a degree of static indeterminacy of 3.

The principle of superposition is valid only when:

Answer: Deflections are small and material is linearly elastic

Superposition requires that deflections be small (geometric linearity) and the material follow a linear stress-strain relationship.

In the moment distribution method, the distribution factor for a member is defined as:

Answer: Ratio of its stiffness to the sum of stiffnesses of all members meeting at the joint

The distribution factor equals the stiffness of a member divided by the total stiffness of all members framing into the joint.

Which theorem states that the partial derivative of strain energy with respect to a load equals the displacement at the point and in the direction of that load?

Answer: Castigliano's second theorem

Castigliano's second theorem relates the partial derivative of strain energy to the corresponding displacement, enabling deflection calculations.

For a propped cantilever beam carrying a uniformly distributed load w over its full span L, the prop reaction is:

Answer: 3wL/8

Compatibility analysis of the propped cantilever shows the prop reaction equals 3wL/8, with the fixed end taking the remaining 5wL/8.

The carry-over factor for a far-end fixed prismatic beam member in the moment distribution method is:

Answer: 1/2

For a prismatic member with the far end fixed, exactly half of any applied near-end moment is carried over to the far end.

An influence line for a reaction at a support represents:

Answer: Variation of that reaction as a unit load moves across the structure

An influence line plots the value of a specific response quantity (reaction, shear, moment) as a unit concentrated load traverses the structure.