Stress = Force / Area. The area A = π(d/2)² = π(0.005)² = 7.85e-5 m². Stress = 20000 N / 7.85e-5 m² = 254647.91 Pa or 254.65 MPa.

The maximum bending moment for a simply supported beam with a point load at the center is given by M = WL/4, where W is the load and L is the length of the beam.

Strain can be calculated using the formula: Strain = Stress / Young's Modulus. Thus, Strain = 100 MPa / 200 GPa = 0.0005.

The neutral axis in a beam subjected to bending is the axis where the bending stress is zero.

The area under the shear force diagram represents the bending moment at that section of the beam.

A positive bending moment indicates that the beam is sagging, meaning the top fibers are in compression and the bottom fibers are in tension.

The maximum shear force in a cantilever beam with a uniform distributed load occurs at the fixed support.

For a simply supported beam with a point load P at the center, the maximum bending moment is given by M = PL/4.

The critical load P = (π² * E * I) / (L²). Substituting the values: P = (π² * 200e9 * 0.0001) / (3²) = 1.96 kN.

The critical load for buckling of a column fixed at both ends is given by P_cr = π²EI / L².

Yield strength is defined as the stress at which a material begins to deform plastically, meaning it will not return to its original shape.

Increasing the moment of inertia decreases the bending stress in a beam for a given bending moment.

Stress is defined as the force applied per unit area, hence the formula is Stress = Force / Area.

The bending stress in a beam is calculated using the formula σ = My/I, where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia.

The deflection (δ) of a cantilever beam with a point load (P) at the free end is given by δ = PL³ / 3EI.

The moment of inertia for a rectangular beam is given by the formula I = (b * h^3) / 12, where b is the base width and h is the height.

Stress is defined as the force applied per unit area, hence the formula is Stress = Force / Area.

The modulus of elasticity is defined as the ratio of stress to strain in the linear elastic region of a material.

Poisson's ratio is defined as the ratio of lateral strain to axial strain in a material subjected to uniaxial stress.

The shear stress (τ) in a circular shaft is related to the torque (T) and the polar moment of inertia (J) by the formula τ = T / J.

The shear force at the midpoint of a simply supported beam with a uniform load is zero.

Shear stress is defined as the internal force (shear force V) divided by the area (A) over which it acts, hence Shear Stress = V / A.

Shear stress τ = (T * r) / J, where J = (π/32) * d^4. For d = 0.05 m, J = (π/32) * (0.05)⁴ = 4.91e-9 m^4. τ = (500 * 0.025) / 4.91e-9 = 31.84 MPa.

The unit of shear force in the SI system is Newton (N).

The unit of stress in the SI system is Pascal (Pa), which is equivalent to one Newton per square meter.