EI Structural Analysis & Design 2 — Questions and Answers
Question 1: The flexure formula for bending stress in a beam is σ = Mc/I. What does 'c' represent?
- The centroidal distance from the neutral axis to the base
- The distance from the neutral axis to the outermost fiber (Correct answer)
- The total depth of the beam cross-section
- The radius of gyration of the cross-section
Correct answer: The distance from the neutral axis to the outermost fiber
In σ = Mc/I, c is the perpendicular distance from the neutral axis to the extreme fiber where stress is maximum.
Question 2: For a rectangular cross-section of width b and height h, the moment of inertia about the centroidal horizontal axis is:
- bh³/6
- bh³/12 (Correct answer)
- bh²/6
- b³h/12
Correct answer: bh³/12
The moment of inertia of a rectangle about its centroidal x-axis is I = bh³/12.
Question 3: The maximum shear stress in a solid circular shaft of radius r subjected to torque T is given by:
- τ = T/(πr³)
- τ = 2T/(πr³) (Correct answer)
- τ = T/(2πr³)
- τ = 4T/(πr³)
Correct answer: τ = 2T/(πr³)
For a solid circular shaft, τ_max = Tr/J = T·r/(πr⁴/2) = 2T/(πr³).
Question 4: Which theorem states that the deflection at point A due to a unit load at point B equals the deflection at B due to a unit load at A?
- Castigliano's Theorem
- Maxwell's Reciprocal Theorem (Correct answer)
- Betti's Law
- Virtual Work Principle
Correct answer: Maxwell's Reciprocal Theorem
Maxwell's Reciprocal Theorem states that flexibility coefficients are symmetric: δ_AB = δ_BA.
Question 5: A beam has a shear force V, first moment of area Q, moment of inertia I, and width b at a cross-section. The horizontal shear stress is:
- τ = VQ/Ib (Correct answer)
- τ = VI/Qb
- τ = VIb/Q
- τ = Vb/QI
Correct answer: τ = VQ/Ib
The shear formula τ = VQ/(Ib) gives the average horizontal shear stress at a given level in a beam.
Question 6: In Mohr's circle for plane stress, the center of the circle is located at:
- ((σx + σy)/2, 0) (Correct answer)
- ((σx - σy)/2, 0)
- (0, τxy)
- ((σx + σy)/2, τxy)
Correct answer: ((σx + σy)/2, 0)
The center of Mohr's circle lies on the σ-axis at the average normal stress (σx + σy)/2, with zero shear.
Question 7: Principal stresses are defined as the normal stresses that occur on planes where the shear stress is:
- Maximum
- Equal to the normal stress
- Zero (Correct answer)
- Minimum
Correct answer: Zero
Principal planes are oriented so that shear stress vanishes, leaving only maximum and minimum normal stresses.
EI Structural Analysis & Design 2
The flexure formula for bending stress in a beam is σ = Mc/I.
What does 'c' represent?