Stress parallel to a plane is usually denoted as "shear stress" and can be expressed as
τ = Fp/ A (2)
τ = shear stress (Pa (N/m2), psi (lbf/in2))
Fp = shear force in the plane of the area (N, lbf)
A = area (m2, in2)
A shear force lies in the plane of an area and is developed when external loads tend to cause the two segments of a body to slide over one another.
Strain is defined as "deformation of a solid due to stress".
Normal strain and can be expressed as
ε = dl / lo
= σ / E (3)
dl = change of length (m, in)
lo = initial length (m, in)
ε = strain - unit-less
E = Young's modulus (Modulus of Elasticity) (Pa , (N/m2), psi (lbf/in2))
Note that strain is a dimensionless unit since it is the ratio of two lengths. But it also common practice to state it as the ratio of two length units - like m/m or in/in.
The rod in the example above is 2 m long and made of steel with Modulus of Elasticity 200 GPa (200 109 N/m2). The change of length can be calculated by transforming (3) to
dl = σ lo / E
= (127 106 Pa) (2 m) / (200 109 Pa)
= 0.00127 m
= 1.27 mm
Stressing an object stores energy in it. For an axial load the energy stored can be expressed as
U = 1/2 Fn dl
U = deformation energy (J (N m), ft lb)
Most metals deforms proportional to imposed load over a range of loads. Stress is proportional to load and strain is proportional to deformation as expressed with Hooke's Law.
E = stress / strain
= σ / ε
= (Fn / A) / (dl / lo) (4)
E = Young's Modulus (N/m2) (lb/in2, psi)
Modulus of Elasticity, or Young's Modulus, is commonly used for metals and metal alloys and expressed in terms 106 lbf/in2, N/m2 or Pa. Tensile modulus is often used for plastics and is expressed in terms 105 lbf/in2 or GPa.
G = stress / strain
= τ / γ
= (Fp / A) / (s / d) (5)
G = Shear Modulus of Elasticity - or Modulus of Rigidity (N/m2) (lb/in2, psi)
τ = shear stress ((Pa) N/m2, psi)
γ = unit less measure of shear strain
Fp = force parallel to the faces which they act
A = area (m2, in2)
s = displacement of the faces (m, in)
d = distance between the faces displaced (m, in)
The Bulk Modulus Elasticity - or Volume Modulus - is a measure of the substance's resistance to uniform compression. Bulk Modulus of Elasticity is the ratio of stress to change in volume of a material subjected to axial loading.
Elastic moduli for some common materials:
- E -
- G -
- K -
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Loads - forces and torque, beams and columns.
Some typical properties of engineering materials like steel, plastics, ceramics and composites.
Hooke's law - force, elongation and spring constant.
Plastic deformation properties.
The Bulk Modulus - resistance to uniform compression - for some common metals and alloys.
Elastic properties and Young's modulus for metals and alloys like cast iron, carbon steel and more.
Shear Modulus (Modulus of Rigidity) is the elasticity coefficient for shearing or torsion force.
When a material is stretched in one direction it tends to get thinner in the other two directions.
Some metals and their Poisson's Ratios.
Allowable wall stress in pipes according ASME M31.3.
Stress and force when thermal expansion a pipe, beam or similar is restricted.
Stress in rotating disc and ring bodies.
Calculate the stress in steam boiler shells caused by steam pressure.
Endurance limits and fatigue stress for steels.
Stress is force applied on cross-sectional area.
Radial and tangential stress in thick-walled cylinders or tubes with closed ends - with internal and external pressure.
Hoop and longitudinal stress thin-walled tubes or cylinders.
Properties of structural lumber.
Threaded bolts tensile stress area.
Weight rating of threaded hanger rods.
Young's Modulus (or Tensile Modulus alt. Modulus of Elasticity) and Ultimate Tensile Strength and Yield Strength for materials like steel, glass, wood and many more.
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