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Mechanics Index

Machine Loading

The primary loading regimes include
  • Direct (tensile/compression)
  • Shear
  • Bending
  • Torsion

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

The effect of the loading on the component is significantly affected by the mode of application of the loading e.g.

  • Static -slowly applied and removed
  • Static continuous load
  • Suddenly applied load
  • Repeated Load
  • Repeated reversing load

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.  

The internal forces within materials are generally averaged as stresses which are dimensioned as Force /unit area.

Stress = σ = Force(N) / Area (m2 )

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 = εx = dx(m) / L (m)

Volumetric Stain = ε v= dV (m3 ) / V (m3 )

Shear strain = ε s= dx (m ) / h (m )

Stresses and strains can also result from other causes than external loads including

  • Thermal expansion/contraction
  • Sudden accelaration/decelaration
  • Prestressing
  • Chemical Action/Corrosion
Component performance in withstanding Force

Normally a component or assembly of components is engineered to behave in a predictable way when subject to a force within the design range.       

  • The component may distort a minimum amount to support the load e.g.Crane hook, stairs, car seat.
  • It will extend a significant amount in proportion to the load e.g a spring.
  • The component may fail e.g. a shear pin
  • Often the component will transmit the force, causing movement

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.  

It is important to note that components normally fail to operate normally because the strength of the component has been reduced as a result of one of the following

  • Chemical deterioration e.g Corrosion
  • Progressive wear or erosion
  • Internal damage to material structure as a result of fatigue
  • Damage as a result of unforseen loading e.g. vandalism

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.

  • Fatigue loading
  • Whirling of Shafts
  • Axial compressive loading of long thin shafts
  • Vibratory loading at or near harmonic frequency
Material Strength measurement

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.  

Penetration hardness tests ( Brinnel, Vickers, Rockwell ) provide information on the surface hardness and also provide indirect indications of the material strength properties.

Strain gauges are used for determining the strains of components under load.

Stress / Strain Relationship

The ratio of direct stress to direct strain is called Young's Modulus

Youngs Modulus = E = σ / εx

The ratio of shear stress to shear strain is called the shear modulus

Shear Modulus = G = τ / εs

The ratio of hydrostatic pressure to volumetric strain is called the bulk modulus

Bulk Modulus = K = p / εv

Links to Machine Loading

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Mechanics Index

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Last Updated 10/09/2011