EIT Mechanics of Materials 5

Question 1

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

Accepted Answer

9 MPa

Answer

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?

Accepted Answer

Far from the point of load application, stress distribution becomes uniform

Answer

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:

Accepted Answer

dy/dx at that point

Answer

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°?

Accepted Answer

50 MPa

Answer

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:

Accepted Answer

Geometric discontinuities cause localized stress higher than the nominal stress

Answer

Stress concentrations arise at holes, notches, and fillets where actual peak stress = K_t × nominal stress.

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EIT Mechanics of Materials 5