Strength Of Materials Summary Pdf

[Nicol Allphin]

Inmaterials science, the strength of a material is its ability to withstand an applied load without failure. 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 manner. Deformation of the material is called strain when those deformations too are placed on a unit basis. The applied loads may be axial (tensile or compressive), or shear . 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 of 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. 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.

Proportional limit is the point on a stress-strain curve at which it begins to deviate from the straight-line relationship between stress and strain. See accompanying figure at (1 & 2).

Elastic limit is the maximum stress to which a specimen may be subjected and still return to its original length upon release of the load. A material is said to be stressed within the elastic region when the working stress does not exceed the elastic limit, and to be stressed in the plastic region when the working stress does exceed the elastic limit. The elastic limit for steel is for all practical purposes the same as its proportional limit. See accompanying figure at (1, 2).

Yield point is a point on the stress-strain curve at which there is a sudden increase in strain without a corresponding increase in stress. Not all materials have a yield point. See accompanying figure at (1).

Yield strength, Sy, is the maximum stress that can be applied without permanent deformation of the test specimen. This is the value of the stress at the elastic limit for materials for which there is an elastic limit. Because of the difficulty in determining the elastic limit, and because many materials do not have an elastic region, yield strength is often determined by the offset method as illustrated by the accompanying figure at (3). Yield strength in such a case is the stress value on the stress-strain curve corresponding to a definite amount of permanent set or strain, usually 0.1 or 0.2 per cent of the original dimension.

Metal deformation is proportional to the imposed loads over a range of loads. Since stress is proportional to load and strain is proportional to deformation, this implies that stress is proportional to strain. Hooke's Law is the statement of that proportionality. Stress σ = = E Strain ε The constant, E, is the modulus of elasticity, Young's modulus or the tensile modulus and is the material's stiffness. Young's modulus is in terms of 106 psi or 103 kg/mm2. If a material obeys Hooke's Law it is elastic. The modulus is insensitive to a material's temper. Normal force is directly dependent upon the elastic modulus.

The greatest stress at which a material is capable of sustaining the applied load without deviating from the proportionality of stress to strain. Expressed in psi (kg/mm2). Ultimate strength (tensile) The maximum stress a material withstands when subjected to an applied load. Dividing the load at failure by the original cross sectional area determines the value. Elastic limit The point on the stress-strain curve beyond which the material permanently deforms after removing the load .

Point at which material exceeds the elastic limit and will not return to its origin shape or length if the stress is removed. This value is determined by evaluating a stress-strain diagram produced during a tensile test.

The ratio of the lateral to longitudinal strain is Poisson's ratio for a given material. lateral strain = longitudinal strain Poisson's ratio is a dimensionless constant used for stress and deflection analysis of structures such as beams, plates, shells and rotating discs.

When bending a piece of metal, one surface of the material stretches in tension while the opposite surface compresses. It follows that there is a line or region of zero stress between the two surfaces, called the neutral axis. Make the following assumptions in simple bending theory: The beam is initially straight, unstressed and symmetric The material of the beam is linearly elastic, homogeneous and isotropic. The proportional limit is not exceeded. Young's modulus for the material is the same in tension and compression All deflections are small, so that planar cross-sections remain planar before and after bending. Using classical beam formulas and section properties, the following relationship can be derived:

The field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio. In addition, the mechanical element's macroscopic properties (geometric properties) such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.

The 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. An important founding pioneer in mechanics of materials was Stephen Timoshenko.

In the mechanics of materials, the strength of a material is its ability to withstand an applied load without failure or plastic deformation. 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. The applied loads may be axial (tensile or compressive), or rotational (strength shear). 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. The calculated deflection of the member may be compared to deflection criteria that are 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.

Material resistance can be expressed in several mechanical stress parameters. The term material strength is used when referring to mechanical stress parameters. These are physical quantities with dimension homogeneous to pressure and force per unit surface. The traditional measure unit for strength are therefore MPa in the International System of Units, and the psi between the United States customary units. Strength parameters include: yield strength, tensile strength, fatigue strength, crack resistance, and other parameters.[citation needed]

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.

Ultimate strength is an attribute related to a material, rather than just a specific specimen made of the material, and as such it is quoted as the force per unit of cross section area (N/m2). The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens.[12] For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MPa. In Imperial units, the unit of stress is given as lbf/in2 or pounds-force per square inch. This unit is often abbreviated as psi. One thousand psi is abbreviated ksi.

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