EIT Mechanics of Materials 5 — Questions and Answers
Question 1: A rectangular beam (b = 50 mm, h = 100 mm) carries a shear force of 30 kN. What is the maximum shear stress?
- 6 MPa
- 9 MPa (Correct answer)
- 12 MPa
- 4 MPa
Correct answer: 9 MPa
For a rectangular section, τ_max = 1.5 × V/A = 1.5 × 30,000/(0.05×0.1) = 9 MPa.
Question 2: Which of the following correctly describes St. Venant's Principle?
- Stress concentrations extend throughout the entire member length
- Far from the point of load application, stress distribution becomes uniform (Correct answer)
- Shear stress always equals normal stress at a free surface
- Deformation is proportional to load for all materials
Correct answer: Far from the point of load application, stress distribution becomes uniform
St. Venant's Principle states that stress distributions become essentially uniform at distances greater than the largest dimension of the loaded area.
Question 3: The slope of the elastic curve at a point on a beam equals:
- The bending moment M at that point
- The integral of the deflection curve
- EI × d²y/dx²
- dy/dx at that point (Correct answer)
Correct answer: dy/dx at that point
The slope of the deflection curve θ ≈ dy/dx (for small angles) at any cross-section.
Question 4: A uniaxial stress state of σ_x = 100 MPa acts on an element. What is the shear stress on a plane inclined at 45°?
- 0 MPa
- 50 MPa (Correct answer)
- 100 MPa
- 70.7 MPa
Correct answer: 50 MPa
On a 45° plane under uniaxial stress, τ = (σ_x/2)sin(2×45°) = 100/2 × 1 = 50 MPa.
Question 5: Stress concentration factors (K_t) in design are used because:
- They reduce the allowable load on a member
- Geometric discontinuities cause localized stress higher than the nominal stress (Correct answer)
- They account for dynamic loading conditions
- They replace the need for a factor of safety
Correct answer: Geometric discontinuities cause localized stress higher than the nominal stress
Stress concentrations arise at holes, notches, and fillets where actual peak stress = K_t × nominal stress.
Question 6: For a statically indeterminate axially loaded bar, the compatibility equation ensures that:
- Equilibrium of forces is satisfied
- Deformations are consistent with physical constraints (Correct answer)
- Stresses do not exceed yield strength
- The reaction forces are zero
Correct answer: Deformations are consistent with physical constraints
The compatibility equation enforces geometric constraints (e.g., zero net deformation at a fixed wall) to solve indeterminate problems.
Question 7: The section modulus S of a cross-section is defined as:
- S = I × c
- S = I / c (Correct answer)
- S = I / A
- S = A × c
Correct answer: S = I / c
Section modulus S = I/c, where c is the distance from the neutral axis to the extreme fiber; σ_max = M/S.
EIT Mechanics of Materials 5
A rectangular beam (b = 50 mm, h = 100 mm) carries a shear force of 30 kN.
What is the maximum shear stress?