Statics, Dynamics & Mechanics of Materials Flashcards

A uniform beam of weight W is supported by a pin at A and a roller at B. If a concentrated load P acts at the midspan, what is the vertical reaction at B?

Answer: All of the above are equivalent

All three expressions are mathematically identical, equaling (W+P)/2 by symmetry of a simply supported beam with midspan load.

Which condition must be satisfied for a body to be in static equilibrium in 2D?

Answer: ΣFx=0, ΣFy=0, and ΣM=0

2D static equilibrium requires three independent equations: sum of forces in x, sum of forces in y, and sum of moments about any point all equal zero.

A particle moves along a straight line with acceleration a = 4t m/s². If the initial velocity is 2 m/s, what is the velocity at t = 3 s?

Answer: 20 m/s

Integrating a=4t gives v = 2t² + C; with v₀=2 m/s, v = 2(9)+2 = 20 m/s at t=3 s.

The modulus of resilience is defined as the strain energy per unit volume up to the:

Answer: Yield point

Modulus of resilience is the area under the stress-strain curve up to the yield point, representing elastic energy storage capacity.

For a hollow circular shaft in torsion, which parameter most directly increases torsional stiffness?

Answer: Increasing polar moment of inertia J

Torsional stiffness = GJ/L; increasing the polar moment of inertia J directly increases stiffness.

A 500 N force acts at 30° above the horizontal. What is its horizontal component?

Answer: 433 N

Fx = 500 cos(30°) = 500 × 0.866 = 433 N.

Poisson's ratio is the ratio of:

Answer: Lateral strain to axial strain

Poisson's ratio ν = –(lateral strain)/(axial strain), measuring how much a material contracts transversely when stretched axially.