Mechanics of Materials Flashcards

A rectangular beam (b = 50 mm, h = 100 mm) carries a shear force of 30 kN. What is the maximum shear stress?

Answer: 9 MPa

For a rectangular section, τ_max = 1.5 × V/A = 1.5 × 30,000/(0.05×0.1) = 9 MPa.

Which of the following correctly describes St. Venant's Principle?

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.

The slope of the elastic curve at a point on a beam equals:

Answer: dy/dx at that point

The slope of the deflection curve θ ≈ dy/dx (for small angles) at any cross-section.

A uniaxial stress state of σ_x = 100 MPa acts on an element. What is the shear stress on a plane inclined at 45°?

Answer: 50 MPa

On a 45° plane under uniaxial stress, τ = (σ_x/2)sin(2×45°) = 100/2 × 1 = 50 MPa.

Stress concentration factors (K_t) in design are used because:

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.

For a statically indeterminate axially loaded bar, the compatibility equation ensures that:

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.

The section modulus S of a cross-section is defined as:

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.