2. Stress and strain Normal Stress, often symbolized by the greek letter sigma, is defined as the force perpendicular to the cross ectional area divided by the cross sectional area. (axial Axial Strain, a non-dimensional parameter, is defined as the ratio of the deformation in length to the original length Strain is often represented by the Greek symbol epsilon( Application Suppose the force is perpendicular to the longitudinal axis. The stress will be a Shear Stress, defined as force parallel to an area divided by the area. Just as an axial stress results in an axial strain, so does shear stress produce a Shear Strain(n) Application 2----Shearing Force Let's consider a shaft, to which an external torgue is applied(such as in power transmission). The shaft is said to be in torsion. The effect of torsion is to create an angular displacement of one end of the shaft with respect to the other. For a shaft of circular cross section, the relationship between the shear stress and torque is where J is the polar moment of inertia Application 3----Transmission Shaft Notes In general, more than one type of stress may be active in a solid body, due to combined loading conditions. (tension, compression, shear, torsion, etc. )When faced with an engineering problem, an engineer must recognize if more than state of stress exists. Because stresses are vector quantities, care must be taken when adding the terms together Application Transmission system of machine tools Notes The simple loading cases considered in this chapter form the basics of the study of strength of material Method is often used to solve problems involving complicated geometries or loading conditions for structural ar 3. Poisson Effect When a tensile load is applied to a uniform beam the increase in the length of the beam is accompanied by decrease in the lateral dimension of the beam The decrease or the increase in the lateral dimension is due to a lateral strain, which is proportional to the strain along the axial direction The ratio of the lateral strain to the axial strain is related to the poisson ratio named after the mathematician who calculated the ratio by molecular theory The minus sign in Equation is needed in order to keep track of the sign in the strain. For example, because tension corresponds to a decrease in the lateral direction, the lateral strain is negative 4 Hookes law Hooke's Law says that the stretch of a spring is directly proportional to the applied force. Engineers say "Stress is proportional to stra This law is formulated in terms of the stress and strain and may be written as where E is a material constant known as Young's modulus Example 12. Stress and Strain . Normal Stress, often symbolized by the Greek letter sigma, is defined as the force perpendicular to the cross sectional area divided by the cross sectional area. (axial stress) . . Axial Strain, a non-dimensional parameter, is defined as the ratio of the deformation in length to the original length. Strain is often represented by the Greek symbol epsilon( ). Application 1——（Tension & Compression） Suppose the force is perpendicular to the longitudinal axis. The stress will be a Shear Stress, defined as force parallel to an area divided by the area..Just as an axial stress results in an axial strain, so does shear stress produce a Shear Strain (γ). Application 2——Shearing Force Let’s consider a shaft, to which an external torque is applied (such as in power transmission). The shaft is said to be in torsion. The effect of torsion is to create an angular displacement of one end of the shaft with respect to the other. For a shaft of circular cross section, the relationship between the shear stress and torque is where J is the polar moment of inertia. Application 3——Transmission Shaft Notes In general, more than one type of stress may be active in a solid body, due to combined loading conditions.(tension, compression, shear, torsion, etc.) When faced with an engineering problem, an engineer must recognize if more than state of stress exists.. Because stresses are vector quantities, care must be taken when adding the terms together. Application 4——Transmission system of machine tools Notes The simple loading cases considered in this chapter form the basics of the study of strength of materials. .. The Finite Element Method is often used to solve problems involving complicated geometries or loading conditions for structural analysis. 3. Poisson Effect When a tensile load is applied to a uniform beam, the increase in the length of the beam is accompanied by a decrease in the lateral dimension of the beam. . The decrease or the increase in the lateral dimension is due to a lateral strain, which is proportional to the strain along the axial direction. The ratio of the lateral strain to the axial strain is related to the Poisson ratio, named after the mathematician who calculated the ratio by molecular theory. The minus sign in Equation is needed in order to keep track of the sign in the strain. For example, because tension corresponds to a decrease in the lateral direction, the lateral strain is negative. 4. Hooke’s Law Hooke's Law says that the stretch of a spring is directly proportional to the applied force. Engineers say "Stress is proportional to strain". This law is formulated in terms of the stress and strain and may be written as : where E is a material constant known as Young’s modulus. Example 1