Strength of Materials

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Strength of Materials

Strength of Materials

The field of materials strength, also known as material mechanics, generally refers to various methods of calculating stress and strain in structural members (such as beams, columns, and shafts).

The method used to predict the response of a structure under load and its susceptibility to various failure modes takes into account the characteristics of the material, such as its elastic limit, ultimate strength, Young’s modulus, and Poisson’s ratio. In addition, the macroscopic properties (geometric properties) of mechanical components, such as their length, width, thickness, boundary constraints, and sudden changes in geometric shapes, such as holes, are also considered.

This theory first considers the behavior of the one-dimensional and two-dimensional members of the structure. The state of stress can be approximated as two-dimensional, and then extended to three-dimensional to develop a more comprehensive elastoplastic behavior theory material. . The important founder of materials mechanics is Stephen Tymoshenko.

Definition

In the mechanics of materials, the strength of a material is its ability to withstand an applied load without failure or plastic deformation.  A load applied to a mechanical member will induce internal forces within the member called stresses when those forces are expressed on a unit basis.

With a complete description of the loading and the geometry of the member, the state of stress and state of strain at any point within the member can be calculated.  Once the state of stress and strain within the member is known, the strength (load carrying capacity) of that member, its deformations (stiffness qualities), and its stability (ability to maintain its original configuration) can be calculated.

The calculated stresses may then be compared to some measure of the strength of the member such as its material yield or ultimate strength.   Material strength refers to the point on the engineering stress-strain curve (yield stress) beyond which the material experiences deformations that will not be completely reversed upon removal of the loading and as a result, the member will have a permanent deflection.

Types of loadings

  • Transverse loadings – Forces applied perpendicular to the longitudinal axis of a member. Transverse loading causes the member to bend and deflect from its original position, with internal tensile and compressive strains accompanying the change in curvature of the member. Transverse loading also induces shear forces that cause shear deformation of the material and increase the transverse deflection of the member.
  • Axial loading – The applied forces are collinear with the longitudinal axis of the member. The forces cause the member to either stretch or shorten.
  • Torsional loading – Twisting action caused by a pair of externally applied equal and oppositely directed force couples acting on parallel planes or by a single external couple applied to a member that has one end fixed against rotation.

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