MECHANICS OF MATERIALS EXAM SCRIPT
2026 QUESTIONS WITH SOLUTIONS
GRADED A+
◉Define normal average stress. Answer: σ=P/A
◉Define average shearing stress (tau). Answer: Equal to tau (t), P/A
(force divided by cross sectional area, parallel to plane
◉Average bearing stress σ_b. Answer: When the force is normal to
the plane, the cross-sectional area of the plane can be projected by
the formula d*t, depending on the cross-section dimensions.
(Essentially the two cross-sections have to be parallel), imagine a
link fitting perfectly onto a bolt
◉Normal stress in an oblique plane of angle theta. Answer: σ=P/A
cos^2(theta) (normal to plane)
◉Shear stress in an oblique plane of angle theta. Answer: Tau=P/A
cos(theta)*sin(theta) (parallel to plane)
,◉Define the factor of safety. Answer: The ultimate load/ allowable
load.
The ultimate load is what the beam can carry at maximum, the
allowable load is what it is designed to carry under normal
conditions.
◉What is strain. Answer: The amount a material deforms per unit
length (dimensionless) (L-L_0)/dL
◉Equation relating stress and strain. Answer: σ = E*ε (essentially
Hook's law)
◉When does a material behave elastically?. Answer: When the
stress is removed, the strain drops to zero (it reforms). When the
strain does not return to zero, plastic deformation has taken place.
◉When would a beam fail due to fatigue?. Answer: A member may
fail at stress levels significantly lower than the max stress due to
repeated loads in the proper locations, if subjected to load in
repetitive cycles.
◉What is hooke's law?. Answer: σ=E*ε, where E is the modulus of
elasticity, essentially the ratio of stress to strain, sigma is the stress,
epsilon is the strain.
, ◉Deformation equation. Answer: σ=PL/AE
◉Statically indeterminate strain equation. Answer: δ=δ_L+δ_R=0,
essentially the
◉Thermal expansion equation. Answer: σ_T=a*(dT)*L, where a is
the constant of thermal expansion. Basically the strain is equal to the
constant of thermal expansion times the change in temp times the
length of the rod.
◉What is α?. Answer: α = temperature expansion coefficient (m/mK,
in/in oF)
◉Stress related to redundant support. Answer: σ=P/A=-E*a(dT)
◉Definition of strain. Answer: ε=δ/L (strain is the ratio of the
deformation to the original length of the rod)
◉What is the deformation due to an applied load?. Answer:
δ_P=(PL)/(AE)
◉Axial strain of a slender bar. Answer: ε=σ_x/E, σ_y and σ_z are
equal to zero
2026 QUESTIONS WITH SOLUTIONS
GRADED A+
◉Define normal average stress. Answer: σ=P/A
◉Define average shearing stress (tau). Answer: Equal to tau (t), P/A
(force divided by cross sectional area, parallel to plane
◉Average bearing stress σ_b. Answer: When the force is normal to
the plane, the cross-sectional area of the plane can be projected by
the formula d*t, depending on the cross-section dimensions.
(Essentially the two cross-sections have to be parallel), imagine a
link fitting perfectly onto a bolt
◉Normal stress in an oblique plane of angle theta. Answer: σ=P/A
cos^2(theta) (normal to plane)
◉Shear stress in an oblique plane of angle theta. Answer: Tau=P/A
cos(theta)*sin(theta) (parallel to plane)
,◉Define the factor of safety. Answer: The ultimate load/ allowable
load.
The ultimate load is what the beam can carry at maximum, the
allowable load is what it is designed to carry under normal
conditions.
◉What is strain. Answer: The amount a material deforms per unit
length (dimensionless) (L-L_0)/dL
◉Equation relating stress and strain. Answer: σ = E*ε (essentially
Hook's law)
◉When does a material behave elastically?. Answer: When the
stress is removed, the strain drops to zero (it reforms). When the
strain does not return to zero, plastic deformation has taken place.
◉When would a beam fail due to fatigue?. Answer: A member may
fail at stress levels significantly lower than the max stress due to
repeated loads in the proper locations, if subjected to load in
repetitive cycles.
◉What is hooke's law?. Answer: σ=E*ε, where E is the modulus of
elasticity, essentially the ratio of stress to strain, sigma is the stress,
epsilon is the strain.
, ◉Deformation equation. Answer: σ=PL/AE
◉Statically indeterminate strain equation. Answer: δ=δ_L+δ_R=0,
essentially the
◉Thermal expansion equation. Answer: σ_T=a*(dT)*L, where a is
the constant of thermal expansion. Basically the strain is equal to the
constant of thermal expansion times the change in temp times the
length of the rod.
◉What is α?. Answer: α = temperature expansion coefficient (m/mK,
in/in oF)
◉Stress related to redundant support. Answer: σ=P/A=-E*a(dT)
◉Definition of strain. Answer: ε=δ/L (strain is the ratio of the
deformation to the original length of the rod)
◉What is the deformation due to an applied load?. Answer:
δ_P=(PL)/(AE)
◉Axial strain of a slender bar. Answer: ε=σ_x/E, σ_y and σ_z are
equal to zero
