BME Advanced Mechanics 3

Question 1

The critical buckling load for a pin-pin column of length L, modulus E, and moment of inertia I is given by Euler's formula as:

Accepted Answer

π²EI/L²

Answer

Euler's critical load for a pin-pin column is P_cr = π²EI/L², corresponding to an effective length of L.

Question 2

In a Mohr's circle construction, the center of the circle lies at:

Accepted Answer

((σ_x + σ_y)/2, 0)

Answer

The center of Mohr's circle is at the average normal stress ((σ_x + σ_y)/2, 0) on the σ–τ plane.

Question 3

Which statement correctly describes Saint-Venant's principle?

Accepted Answer

The effects of localized loads become negligible at distances large compared to the load region

Answer

Saint-Venant's principle states that the stress distribution away from the point of load application is independent of how the load is distributed, provided the resultant is the same.

Question 4

For a linearly elastic material, the relationship between shear modulus G, Young's modulus E, and Poisson's ratio ν is:

Accepted Answer

G = E/(2(1+ν))

Answer

The elastic constants are related by G = E / [2(1 + ν)], valid for isotropic materials.

Question 5

A stepped shaft transmits torque T. At a step where the radius changes sharply, the stress concentration factor K_t is used because:

Accepted Answer

Local geometry causes stress to exceed the nominal value

Answer

Geometric discontinuities like fillets and steps create local stress concentrations where actual stress = K_t × nominal stress.

BME - Bachelor of Mechanical Engineering Practice Test

BME - Bachelor of Mechanical Engineering Practice Test

BME Advanced Mechanics 3