Structural Analysis & Design Flashcards

A simply supported beam of length 10 ft carries a concentrated load of 500 lb at its midpoint. What is the vertical reaction at each support?

Answer: 250 lb

By symmetry, each support carries half the total load: 500/2 = 250 lb.

Which condition must be satisfied for a structure to be in static equilibrium?

Answer: Both the sum of all forces and the sum of all moments equal zero

Static equilibrium requires ΣF = 0 (in all directions) and ΣM = 0 about any point simultaneously.

For a cantilever beam of length L with a uniform distributed load w, what is the maximum bending moment?

Answer: wL²/2

The maximum moment in a cantilever with UDL occurs at the fixed support and equals wL²/2.

In the method of joints for truss analysis, which equilibrium equations are applied at each joint?

Answer: ΣFx = 0 and ΣFy = 0

At each pin joint, members are concurrent so ΣM = 0 is automatically satisfied; only ΣFx = 0 and ΣFy = 0 are needed.

Euler's critical buckling load for a column with both ends pinned and length L is given by which formula?

Answer: Pcr = π²EI / L²

For a pin-pin column, the effective length equals L and Pcr = π²EI/L², known as Euler's formula.

A steel rod with cross-sectional area of 2 in² is subjected to a tensile force of 60,000 lb. What is the axial stress?

Answer: 30,000 psi

Axial stress σ = P/A = 60,000 lb / 2 in² = 30,000 psi.

The factor of safety (FS) is defined as which of the following?

Answer: Ultimate (or yield) stress divided by allowable stress

FS = Failure stress (ultimate or yield) / Allowable stress, ensuring that the design stress remains well below the failure point.