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CHAPTER 4 Stress-Strain Relationships Introduction When an object is loaded with a force, it produces a stress, which then causes it to deform. Stress is the applied force that tends to deform a body. From the perspective of what is happening within an object, stress is the internal distribution of forces within the body that balance and react to the loads applied to it. Nominal stress, or engineering stress, is the applied load divided by the original cross-sectional area of a material. True stress is the applied load divided by the actual cross-sectional area (the instantaneous values for the area, or the changing area with respect to time) of the specimen at that load. Stress (symbol ) is defined as force per unit area, commonly in units of 1b/in. or N/m?. There are two basic types of stress: normal stress and shear stress. Normal is either tension or compression. Tension or compression stresses result from direct loading, or from bending, as well as from other loading conditions. Shear stress results from direct shear loading, or torsion, as well as from other loading conditions. Strain is the response of an object to an applied stress. Engineering strain is the amount of deformation in the direction of the applied force divided by the initial length of the material. Strain (symbol ) is a unitless number, although it is often left in the unsimplified form, such as inches per inch or meters per meter. If the stress is small, the material may only strain a small amount and the material will return to its original size after the stress is released. This is called elastic deformation, because, like elastic, it returns to its unstressed state. Elastic deformation only occurs in a material when stresses are lower than a critical stress called the yield strength. If a material is loaded beyond its elastic limit, the material will remain in a deformed condition after the load is removed. This is called plastic deformation. The engineering stress-strain (o-E) curve is a plot of the data obtained using the original cross- sectional area and the corresponding strain of the specimen under test. The true stress in either a tension or compression test is determined by dividing the applied load by the actual cross- sectional area of the specimen at that load. To obtain such o- data for plotting true stress versus strain, the actual cross-section would have to be measured for each data point. These additional cross-sectional measurements must be made with precision and make it more difficult to perform such a test. In the range of stress usually encountered in most engineering applications, there is no significant difference between true stress and engineering stress. Engineering or apparent stress is much more commonly used by the engineer since the design of any type of load-carrying member