Stress & Strain
This is defined as force per unit area.
What is stress?
This law relates stress and strain linearly in elastic materials.
What is Hooke's law?
This is the twisting moment applied to a shaft.
What is torque?
This is the point where permanent deformation begins.
What is yield strength?
This is the ratio of deformation to original length.
What is Strain?
A rod with area 0.01 m² carries 10,000 N. Find stress.
1 MPa
The torsion formula relates shear stress to torque:
tau = Tr/J
Brittle materials fail with very little of this.
What is strain? (deformation)
A bar has length 2 m and elongates 4 mm. Find the strain.
0.002 m/m
A steel rod (E = 200 GPa) is 1 m long and carries 20,000 N. Area = 0.005 m². Find elongation.
0.02 mm
A solid shaft has radius 0.02 m and torque 100 Nm. Find max shear stress.
This failure theory is commonly used for ductile materials.
What is von Mises (distortion energy theory)?
A material has stress = 200 MPa and strain = 0.001. Find Young’s modulus.
200 GPa
wo rods in series carry the same load. Which experiences more elongation?
The one with lower stiffness (lower AE or E).
If shaft diameter doubles, what happens to torsional stiffness?
It increases by 16× (since J is proportional to r4).
Why do stress concentrations occur around holes?
Because load paths are disrupted, causing stress to redistribute and intensify locally.
beach marks