Strain = Change in length (dL)over original length (L)
Stress = Force (F) divided by Area withstanding Force (A)
p = F / A
Youngs Modulus E = Stress (p) / Strain(e). This is a property of a material
E = p / e
Bending
General Formula for Bending
A beam with a moment of inertia I and with Youngs modulus E will have a
bending stress f at a distance from the Neutral Axis (NA) y and the NA will bend
to a radius R ...in accordance with the following formula.
M / I = s / y = E / R
Simply Supported Beam . Concentrated Load
Simply Supported Beam . Uniformly Distributed Load
Cantilever . Concentrated Load
Cantilever . Uniformly Distributed Load
Fixed Beam . Concentrated Load
Fixed Beam . Uniformly Distributed Load
Torsion /Shear
Poisson's Ratio = v = (lateral strain / primary strain )
Shear Modulus G = Shear Stress /Shear Strain
G = q /F = E / (2 .( 1 + v ))
General Formula for Torsion
A shaft subject to a torque T having a polar moment of inertia J and a shear Modulus G will have a shear stress q at a radius r and an angular deflection Q over a length L as calculated from the following formula.
T / J = G . Q / L = q / r
Pressure Vessels - Thin Walled Cylinders
For a thin walled cylinder subject to internal pressure P the circumferential
stress = p_c.
This stress tends to stretch the cylinder along its length. This is also called the longitudinal stress.
p_c = P . d / ( 4 . t )
For a thin walled cylinder subject to internal pressure P the tangential stress = p_t
This stress tends to increase the diameter). This is also called the hoop stress.
p_t = P . d / ( 2 . t )
The above two formulae are only valid if the ratio of thickness to dia is less than 1:20
Pressure Vessels - Thick Walled Cylinders
