Engineering Sciences Flashcards

What is the shear stress distribution in a circular shaft under torsion?

Answer: Linear, zero at center and maximum at the surface

In a circular shaft under torsion, shear stress varies linearly from zero at the neutral axis (center) to maximum at the outer surface: τ = Tr/J, where r is the radial distance.

Euler's buckling load for a pin-ended column is:

Answer: π²EI/L²

For a pin-ended (simply supported) column, Pcr = π²EI/L², where E is Young's modulus, I is moment of inertia, and L is the column length. This is the critical load causing elastic instability.

The Navier-Stokes equations describe:

Answer: The motion of viscous fluid substances

The Navier-Stokes equations are the fundamental PDEs governing viscous fluid motion, expressing Newton's second law for fluids with pressure, viscous, and body forces.

In a simple supported beam with a uniformly distributed load, the maximum bending moment occurs at:

Answer: The midspan

For a simply supported beam with UDL, the maximum bending moment M_max = wL²/8 occurs at midspan, where the shear force is zero.

The second law of thermodynamics states that:

Answer: Entropy of an isolated system never decreases

The second law states that in any natural process, the total entropy of an isolated system can only increase or remain constant. This limits the efficiency of all real engines and processes.

What is the relationship between shear modulus (G), Young's modulus (E), and Poisson's ratio (ν)?

Answer: G = E / 2(1+ν)

For isotropic materials, G = E/[2(1+ν)]. With E = 200 GPa and ν = 0.3 for steel, G ≈ 77 GPa. This links the three elastic constants.