BCE Mechanics of Materials 2 — Questions and Answers
Question 1: In the flexure formula σ = My/I, what does the variable 'y' represent?
- The span length of the beam
- The distance from the neutral axis to the point of interest (Correct answer)
- The depth of the beam section
- The distance from the support to the load
Correct answer: The distance from the neutral axis to the point of interest
In the bending stress formula, y is the perpendicular distance from the neutral axis to the fiber where stress is being calculated.
Question 2: For a simply supported beam of span L carrying a central point load W, the maximum bending moment is:
- WL/4 (Correct answer)
- WL/2
- WL/8
- WL
Correct answer: WL/4
Each reaction is W/2; the maximum moment at midspan = (W/2)(L/2) = WL/4.
Question 3: The section modulus Z of a solid rectangular section (width b, height h) is:
- bh²/6 (Correct answer)
- bh³/12
- bh²/4
- bh³/6
Correct answer: bh²/6
Z = I / y_max = (bh³/12) / (h/2) = bh²/6; it directly gives maximum bending stress as σ = M/Z.
Question 4: For a rectangular beam cross-section, where does the maximum shear stress due to transverse loading occur?
- At the top and bottom extreme fibers
- At the neutral axis (Correct answer)
- At the quarter-depth points
- Uniformly throughout the section
Correct answer: At the neutral axis
Shear stress is zero at the free (extreme) surfaces and reaches its maximum at the neutral axis for a rectangular section.
Question 5: The second moment of area (moment of inertia) of a solid circular cross-section with diameter D about a centroidal axis is:
- πD⁴/64 (Correct answer)
- πD⁴/32
- πD³/32
- πD⁴/16
Correct answer: πD⁴/64
I = πD⁴/64 for a solid circle about a diameter; the polar moment of inertia J = 2I = πD⁴/32.
Question 6: For a simply supported beam carrying a uniformly distributed load w (per unit length) over its full span L, the maximum bending moment is:
- wL²/4
- wL²/8 (Correct answer)
- wL²/2
- wL/4
Correct answer: wL²/8
Maximum bending moment at midspan = wL²/8 for a UDL on a simply supported beam; the reactions are each wL/2.
Question 7: The neutral axis of a beam cross-section under pure bending is the locus of points where:
- Shear stress is maximum
- Bending (normal) stress is zero (Correct answer)
- Deflection is maximum
- The section modulus equals zero
Correct answer: Bending (normal) stress is zero
The neutral axis experiences neither tension nor compression during bending; normal stress is zero there and transitions from tensile to compressive across it.
BCE Mechanics of Materials 2
In the flexure formula σ = My/I, what does the variable 'y' represent?