
Mechanics Index
Machine Loading
Introduction
Many components, in use, are subject to at least one of the above loading regimes.
The stresses resulting from the loads are generally combined using the principle of superposition
All of the loads result in forces in the component material.
The result of the forces are deformations related to the type of force.
The majority of materials used in engineering are essentially elastic and conform to Hookes law
within the relevant elastic limits.
The deformations generate forces which resist the loads causing the strains.
Stress = σ = Force(N) / Area (m^{2} ) The resulting deformations are identified as strains.
Strains can linear, shear or volumetric. Linear strains are dimensioned as deflection/original
length, volumetric strains are measured as change in volume/original volume, engineering shear strains
are measured as linear movement on one plane (x,y, or z direction)relative to another plane
divided normal distance between the planes Linear Strain = ε_{x} = dx(m) / L (m) Volumetric Stain = ε _{v}= dV (m^{3} ) / V (m^{3} ) Stresses and strains can also result from other causes than external loads including
Normally a component or assembly of components is engineered to behave in a predictable way when subject to a force within the design range.
At some load a component will fail. A load causing failure in would most probably be a high load
in excess of that allowed for in the design. However failure could occur simply as a result
in a statistical abnormality in the material. The failure may be that the resulting distortion exceeds the elastic
limit and is not recoverable. This is the general case for ductile materials.
For brittle materials the failure is more likely a sudden tensile failure if the loading is tensile
or a shear failure if the loading is compression.
The performance of most materials is predictable and progressive under normal conditions of static loading. However there are a number of loading scenerios where a cliff edge condition can occur when the failure is sudden and not easily predictable.
Most engineering materials are provided with strength specifications resulting from
tests completed under strictly controlled conditions in laboratories. The most important
of these tests is the simple uniaxial tensile test. This provides information
on the proof strength, the yield stength, the ultimate strength and the elongation.
The ratio of direct stress to direct strain is called Young's Modulus Youngs Modulus = E = σ / ε_{x} The ratio of shear stress to shear strain is called the shear modulus Shear Modulus = G = τ / ε_{s} The ratio of hydrostatic pressure to volumetric strain is called the bulk modulus Bulk Modulus = K = p / ε_{v} 
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