EIT Statics, Dynamics & Mechanics of Materials 3 — Questions and Answers
Question 1: A simply supported beam with span L carries a uniformly distributed load w. What is the maximum bending moment?
- wL²/4
- wL²/8 (Correct answer)
- wL/2
- wL²/2
Correct answer: wL²/8
For a UDL on a simply supported beam, the maximum moment occurs at midspan and equals wL²/8.
Question 2: 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:
- aₜ = r²α
- aₜ = rα (Correct answer)
- aₜ = α/r
- aₜ = rω²
Correct answer: aₜ = rα
Tangential acceleration aₜ = rα, while the normal (centripetal) acceleration is rω².
Question 3: Which type of support provides both a horizontal reaction and a vertical reaction but no moment reaction?
- Fixed support
- Pin support (Correct answer)
- Roller support
- Link support
Correct 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.
Question 4: The section modulus S for a rectangular cross-section (width b, height h) is:
- bh²/6 (Correct answer)
- bh³/12
- bh²/12
- bh³/6
Correct answer: bh²/6
S = I/c = (bh³/12)/(h/2) = bh²/6, used to compute bending stress σ = M/S.
Question 5: Work-energy theorem states that the net work done on a particle equals its change in:
- Potential energy
- Momentum
- Kinetic energy (Correct answer)
- Power
Correct answer: Kinetic energy
The work-energy theorem: W_net = ΔKE = ½mv₂² – ½mv₁², directly linking net work to kinetic energy change.
Question 6: 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:
- 0.5
- 0.7
- 1.0
- 2.0 (Correct answer)
Correct 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.
Question 7: In a planar truss, which method allows solving for internal forces in non-adjacent members without analyzing every joint?
- Method of joints
- Method of sections (Correct answer)
- Castigliano's theorem
- Virtual work method
Correct 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.
EIT Statics, Dynamics & Mechanics of Materials 3
A simply supported beam with span L carries a uniformly distributed load w.
What is the maximum bending moment?