Railways NTPC (Technical Ability) Engineering Mechanics and Strength of Materials Strength of Materials

Strength of Materials

Category : Railways

Strength of Materials


  • Strength of materials, is a subject which deals with the behavior of solid objects subject to stresses and strains.
  • 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.
  • An important founding pioneer in mechanics of materials was Stephen Timoshenko.
  • The study of strength of materials often 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 it length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.
  • In materials science, the strength of a material is its ability to withstand an applied load without failure. 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 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 member, its deformations (stiffness qualities), and 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.                                
  • Material strength refers to the point on the engineering stress-strain curve (yield stress) beyond witch 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.                                
  • The ultimate strength refers to the point on the engineering stress-strain curve corresponding to the stress that produces fracture.               
  • Transverse loading - Forces applied perpendicular the longitudinal axis of a member. Transverse loading causes the member to bend and deflect from its original position, with internal tensile and compressive 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 the longitudinal axis of the member. The forces cause the member to either stretch or shorten.
  • Torsional loading - Twisting action caused by a part of externally applied equal and oppositely directed couples acting on parallel planes or by a single external couple applied to a member that has one end fixed against rotation.
  • Compressive stress is the stress state caused by applied load that acts to reduce the length of the material along the axis of the applied load, it is in other words a stress state that causes a squeezing of the material simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces.
  • Compressive strength for materials is generally than their tensile strength. However, structures in compression are subject to additional failure modes, such as buckling, that are dependent on the member's geometry.
  • Tensile stress is the stress state caused by an applied load that tends to elongate the material along the axis of the applied load, in other words the stress caused by pulling the material. The strength of structures of equal cross sectional area loaded in tension is independent of shape of the cross section. Materials loaded in tension are susceptible to stress concentrations such as material defects or abrupt changes in geometry.
  • Shear stress is the stress state caused by the combined energy of a pair of opposing forces acting along parallel lines of action through the material, in other words the stress caused by faces of the material sliding relative to one another.
  • Yield strength its the lowest stress that produces a permanent deformation in a material. In some materials, like aluminum alloys, the point of yielding is difficult 'o identify, thus it is usually defined as the stress required to cause 0.2% plastic strain. This is called a 0.2% proof stress.
  • Compressive strength is a limit state of compressive tress that leads to failure in a material in the manner of ductile failure (infinite theoretical yield) or brittle failure (rupture as the result of crack propagation, or sliding along a weak plane - see shear strength).
  • Tensile strength or ultimate tensile strength is a limit state of tensile stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of that Failure, some hardening in the second stage and breakage after a possible "neck" formation) or brittle failure (sudden breaking in two or more pieces at a low stress state). Tensile strength can be quoted as either true stress or engineering stress, but engineering stress is the most commonly used.
  • Fatigue strength is a measure of the strength of a material or a component under cyclic loading, and is usually more difficult to assess than the static strength measures. Fatigue strength is quoted as stress amplitude stress range \[(\Delta \sigma ={{\sigma }_{\max }}-{{\sigma }_{\min }}),\] usually at zero mean stress, along with the number of cycles to failure under that condition of stress.
  • Impact strength, is the capability of the material to withstand a suddenly applied load and is expressed in terms of energy. Often measured with the Izod impact strength test or charpy impact test, both of which measure the impact energy required to fracture a sample.
  • Deformation of the material is the change in geometry created when stress is applied Deformation is expressed by the displacement field of the material.
  • Strain or reduced deformation is a mathematical term that expresses the trend of the deformation change among the material field. Strain is the deformation per unit length. Deflection is a term to describe the magnitude to which a structural element is displaced when subject to an applied load.
  • Elasticity is the ability of a material to return to its previous shape after stress is released. In many materials, the relation between applied stress is directly proportional to the resulting strain (up to a certain limit), and a graph representing those two quantities is a straight line.
  • The slope of this line is known as Young's modulus, or the "modulus of elasticity." The modulus of elasticity can be used to determine the stress-strain relationship in the linear-elastic portion of the stress-strain curve.
  • The linear-elastic region is either below the yield point, or if a yield point is not easily identified on the stress- strain plot it is defined to be between 0 and 0.2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs.
  • Plasticity or plastic deformation is the opposite of elastic deformation and is defined as unrecoverable strain. 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 stress. Materials such as metals usually experience a small amount of plastic deformation before failure while ductile metals such as copper and lead or polymers will plasticly deform much more.
  • 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.
  • A Factor of safety is a design criteria that an engineered component or structure must achieve. FS = UTS/R, where FS: the factor of safety, R: The applied stress, and UTS: ultimate stress (psi or N/m2)
  • Margin of Safety is also sometimes used to as design criteria. It is defined MS = Failure Load/(Factor of Safety * Predicted Load) - 1
  • 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.

Notes - Strength of Materials

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