Suppose that a 4-inch-diameter round bar is extended with a 50.000-lb axial load. The bar has an initial length of 5 feet and extends 0.006 inches. What is the Youngs modulus for the material from which the bar is Solution We can obtain the Youngs modulus by using Hooke's law, and Equation (1)and Equation(2) The stress in the bar is Thus the Young's modulus for this material Stress concentration When an elastic body with a local geometrical irregularity is stressed, there usually is a localized variation in the stress state in the immediate neighborhood of the irregularity The maximum stress levels at the irregularity may be several times larger than the nominal stress levels in the bulk of the body. This increase in stress caused by the irregularity in geometry is called a stress concentration Stress Concentration Factor Where the stress concentration can not be avoided by a change in design, it is important to base the design on the local value of the stress rather than on an average value. The usual procedure in design is to obtain the local value of the stress by use of a stress concentration factor ss in the presence of a geometric irregularity or discontinuity, a nom, nominal stress which would exist at the point if the irregularity were not there Typical kt Curve 6. Fatigue Loads or deformations which will not cause fracture in a single application can result in fracture when applied repeatedly Fracture may occur after a few cycles, or after millions of cycles This process of fracture under repeated loading is called fatigue. Fatigue is one of the three common causes of mechanical failure. the others being wear and corrosion. Consider a situation in which the stress at a point in a body varies with time Experiments show that the alternating stress o a is the most important factor in determining the number of cycles of load a material can withstand before fracture, while the mean stress level a m is less important Fatigue Curve Notes It is customary to designate the stress which can be withstood for some specified number of cycles as the fatigue strength of the material Fatigue cracks are most likely to form and grow from locations where holes or sharp corners cause stress In designing parts to withstand repeated stresses, it is important to avoid stress concentrations. Keyways, oil holes, and screw threads are potential sources of trouble and require special care in design in order to prevent fatigue failures 7. Finite Element Method ( FEM) The FEM is a numerical analysis technique for obtaining approximate solutions to engineering and designSuppose that a 4-inch-diameter round bar is extended with a 50.000-lb axial load. The bar has an initial length of 5 feet and extends 0.006 inches. What is the Young’s modulus for the material from which the bar is made? . Solution We can obtain the Young’s modulus by using Hooke’s law, and Equation (1) and Equation (2). The stress in the bar is The strain is Thus, the Young’s modulus for this material is 5. Stress Concentration When an elastic body with a local geometrical irregularity is stressed, there usually is a localized variation in the stress state in the immediate neighborhood of the irregularity. The maximum stress levels at the irregularity may be several times larger than the nominal stress levels in the bulk of the body. This increase in stress caused by the irregularity in geometry is called a stress concentration. Stress Concentration Factor Where the stress concentration can not be avoided by a change in design, it is important to base the design on the local value of the stress rather than on an average value. The usual procedure in design is to obtain the local value of the stress by use of a stress concentration factor. σmax , maximum stress in the presence of a geometric irregularity or discontinuity, σnom, nominal stress which would exist at the point if the irregularity were not there. Typical Kt Curve 6. Fatigue Loads or deformations which will not cause fracture in a single application can result in fracture when applied repeatedly. Fracture may occur after a few cycles, or after millions of cycles. . This process of fracture under repeated loading is called fatigue. Fatigue is one of the three common causes of mechanical failure, the others being wear and corrosion. Consider a situation in which the stress at a point in a body varies with time. Experiments show that the alternating stress σa is the most important factor in determining the number of cycles of load a material can withstand before fracture, while the mean stress level σm is less important. Fatigue Curve Notes It is customary to designate the stress which can be withstood for some specified number of cycles as the fatigue strength of the material. . Fatigue cracks are most likely to form and grow from locations where holes or sharp corners cause stress concentrations. . In designing parts to withstand repeated stresses, it is important to avoid stress concentrations. Keyways, oil holes, and screw threads are potential sources of trouble and require special care in design in order to prevent fatigue failures. 7. Finite Element Method (FEM) The FEM is a numerical analysis technique for obtaining approximate solutions to engineering and design problems