Strength Of Materials 4th Ed

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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]

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/in or pounds-force per square inch. This unit is often abbreviated as psi. One thousand psi is abbreviated ksi.

Design stresses that have been determined from the ultimate or yield point values of the materials give safe and reliable results only for the case of static loading. Many machine parts fail when subjected to a non-steady and continuously varying loads even though the developed stresses are below the yield point. Such failures are called fatigue failure. The failure is by a fracture that appears to be brittle with little or no visible evidence of yielding. However, when the stress is kept below \"fatigue stress\" or \"endurance limit stress\", the part will endure indefinitely. A purely reversing or cyclic stress is one that alternates between equal positive and negative peak stresses during each cycle of operation. In a purely cyclic stress, the average stress is zero. When a part is subjected to a cyclic stress, also known as stress range (Sr), it has been observed that the failure of the part occurs after a number of stress reversals (N) even if the magnitude of the stress range is below the material's yield strength. Generally, higher the range stress, the fewer the number of reversals needed for failure.

There are four failure theories: maximum shear stress theory, maximum normal stress theory, maximum strain energy theory, and maximum distortion energy theory. Out of these four theories of failure, the maximum normal stress theory is only applicable for brittle materials, and the remaining three theories are applicable for ductile materials.Of the latter three, the distortion energy theory provides most accurate results in a majority of the stress conditions. The strain energy theory needs the value of Poisson's ratio of the part material, which is often not readily available. The maximum shear stress theory is conservative. For simple unidirectional normal stresses all theories are equivalent, which means all theories will give the same result.

A material's strength is dependent on its microstructure. The engineering processes to which a material is subjected can alter this microstructure. The variety of strengthening mechanisms that alter the strength of a material includes work hardening, solid solution strengthening, precipitation hardening, and grain boundary strengthening and can be quantitatively and qualitatively explained. Strengthening mechanisms are accompanied by the caveat that some other mechanical properties of the material may degenerate in an attempt to make the material stronger. For example, in grain boundary strengthening, although yield strength is maximized with decreasing grain size, ultimately, very small grain sizes make the material brittle. In general, the yield strength of a material is an adequate indicator of the material's mechanical strength. Considered in tandem with the fact that the yield strength is the parameter that predicts plastic deformation in the material, one can make informed decisions on how to increase the strength of a material depending its microstructural properties and the desired end effect. Strength is expressed in terms of the limiting values of the compressive stress, tensile stress, and shear stresses that would cause failure. The effects of dynamic loading are probably the most important practical consideration of the strength of materials, especially the problem of fatigue. Repeated loading often initiates brittle cracks, which grow until failure occurs. The cracks always start at stress concentrations, especially changes in cross-section of the product, near holes and corners at nominal stress levels far lower than those quoted for the strength of the material.

Knowledge and understandingThe advanced mechanical design requires knowledge and understanding of the problems of deformation and strength of materials that go beyond the notion of isotropic linear elasticity, static and fatigue strength simply based on knowledge of the elastic stress state, which is the traditional mechanical design approach. And this also because the CAE (Computer Aided Engineering) softwares incorporate, in an increasing number of cases, the structural finite element simulation also in the non-linear field, making it available at reasonable prices but also requiring material behavior skills over the traditional ones in order to exploit them correctly.The student, therefore, at the end of the course will know the types of mechanical behavior and failure of materials and the related mathematical models for the design / verification of components and mechanical systems beyond the simple linear elastic behavior, i.e. based on the elastic stress state. He will also know the methods of experimental characterization and simulation of non-linear mechanical behavior by the finite element method.Applying knowledge and understandingThe student will be able to identify the most appropriate mathematical model to approximate the stress-strain relationship of the material and the mechanical strength under service conditions. He can then resolve analytically and / or by finite element simulation problems of deformation and strength of mechanical components and systems beyond simple linear elastic evaluation.

The course is about the two fundamental aspects of the mechanical behavior of materials: i) the stress-strain behavior (mechanics of materials), ii) the failure mechanism and therefore the strength of the material (structural integrity). Each of these aspects will be illustrated from the phenomenological point of view (experimental) and the mathematical description (modeling).As for the stress-strain relationship, the following behaviors will be presented:- quasi-static elasto-plasticity- cyclic elasto-plasticity- anisotropic elasticity (composite materials)- hyperelasticity (elastomeric materials)- Creep (metallic materials) and viscoelasticity (polymeric materials)Regarding failure mechanisms and strength, the following cases will be illustrated:- mechanisms and failure criteria for composite materials- fatigue strength by deformation approach- brittle fracture; effect of plasticity in the case of ductile materials- fatigue crack growth and fatigue life predictionFor each of the above topics lectures as well as classroom exercises will be given. In addition, simple applications of the finite element method with the software Abaqus (student edition) will be done in the lab. 59ce067264

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