The complete theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. The study of strength of materials often refers to various methods of calculating the stresses and strains in structural ashby materials and the environment solution pdf, such as beams, columns, and shafts. The field of strength of materials deals with forces and deformations that result from their acting on a material. 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.
The stresses acting on the material cause deformation of the material in various manners including breaking them completely. Deformation of the material is called strain when those deformations too are placed on a unit basis. The stresses and strains that develop within a mechanical member must be calculated in order to assess the load capacity of that member. This requires a complete description of the geometry of the member, its constraints, the loads applied to the member and the properties of the material of which the member is composed.
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. The calculated stresses may then be compared to some measure of the strength of the member such as its material yield or ultimate strength. The calculated deflection of the member may be compared to a deflection criteria that is based on the member’s use. The calculated buckling load of the member may be compared to the applied load. The calculated stiffness and mass distribution of the member may be used to calculate the member’s dynamic response and then compared to the acoustic environment in which it will be used.
The ultimate strength of the material refers to the maximum value of stress reached. 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. A simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces. Compressive strength for materials is generally higher than their tensile strength. The strength of structures of equal cross sectional area loaded in tension is independent of shape of the cross section. Mechanical properties of materials include the yield strength, tensile strength, fatigue strength, crack resistance, and other characteristics.
This is called a 0. Tensile strength can be quoted as either true stress or engineering stress, but engineering stress is the most commonly used. In order for a material or object to have a high impact strength the stresses must be distributed evenly throughout the object. It also must have a large volume with a low modulus of elasticity and a high material yield strength. Deformation is expressed by the displacement field of the material. Strain is the deformation per unit length. Plastic deformation is retained after the release of the applied stress.
Most materials in the linear-elastic category are usually capable of plastic deformation. Brittle materials, like ceramics, do not experience any plastic deformation and will fracture under relatively low strain, while ductile materials such as metallics, lead, or polymers will plasticly deform much more before a fracture initiation. Consider the difference between a carrot and chewed bubble gum. The carrot will stretch very little before breaking. The chewed bubble gum, on the other hand, will plastically deform enormously before finally breaking.