Statics, Dynamics & Mechanics of Materials Flashcards

A simply supported beam with span L carries a uniformly distributed load w. What is the maximum bending moment?

Answer: wL²/8

For a UDL on a simply supported beam, the maximum moment occurs at midspan and equals wL²/8.

A rigid body undergoes pure rotation about a fixed axis. The relationship between tangential acceleration (aₜ) and angular acceleration (α) for a point at radius r is:

Answer: aₜ = rα

Tangential acceleration aₜ = rα, while the normal (centripetal) acceleration is rω².

Which type of support provides both a horizontal reaction and a vertical reaction but no moment reaction?

Answer: Pin support

A pin (hinge) support resists translation in all directions (provides Rx and Ry) but allows rotation, so it provides no moment reaction.

The section modulus S for a rectangular cross-section (width b, height h) is:

Answer: bh²/6

S = I/c = (bh³/12)/(h/2) = bh²/6, used to compute bending stress σ = M/S.

Work-energy theorem states that the net work done on a particle equals its change in:

Answer: Kinetic energy

The work-energy theorem: W_net = ΔKE = ½mv₂² – ½mv₁², directly linking net work to kinetic energy change.

A column with both ends pinned has an effective length factor K = 1.0. If one end is fixed and the other is free, K becomes:

Answer: 2.0

A fixed-free (flagpole) column has K = 2.0 because it buckles as if it were half of a pin-pin column of twice the length.

In a planar truss, which method allows solving for internal forces in non-adjacent members without analyzing every joint?

Answer: Method of sections

The method of sections cuts the truss through up to three members and uses equilibrium equations to find their forces directly.