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Unformatted text preview: Introduction to Strength of materials: (Chapter-2) Class #3, #4 – September 20, 27 Introduction to Stress and Strain, and mechanics of deformable bodies Stress: Load/Area or Force/Area [F/L.L] [kips/square inch] Where F=Force (pound force) and L=Length (inches or feet for SI units) Strain: Change in length over original length of the member under tensile or compressive load. As we load the material, the material will extend if the extension we all delta L, L, or change in length, then the change in length divided by the original length will give us the strain in the material ∆ ε = L/L [Unit of Length/Unit of Length] and therefore it is a dimensionless quantity. ∆ To establish a relationship between stress and strain, we can perform tests on a given specimen, one such test is the tensile test, where the specimen is loaded in tension in a machine (Tensile Test Machine) and the stress and strain are recorded. The graph looks like the one in figure bellow: (Note: Tests including but not limited to tensile tests on crystals of materials have also been performed using other mechanical means which we will cover later) σ ε σ ε σ ε Figure-1: Relation between Stress and Strain The slope of the stress strain Curve is termed the Modulus of Elasticity. Or Young’s Modulus. And the relationship is called Hooke’s Law as he was the first person to observe that there is a linear relationship between stress and elongation of a bar in tension. From the graph it can be observed that the stronger the material the greater the slope, so in Figure- 1 wee see that steel is the strongest material Es, then Aluminum, (E AL ), and then Ec Concrete. Looking at a typical stress strain curve, when the specimen is loaded, it will deform and elongate as shown below in a linear fashion with a slope E up to the proportional limit. At this point the material if loaded further will start to yield. If unloaded the specimen will return to its origin O. (Approximately, with a 0.2% offset) After the yield the material is in plastic region and if unloaded the material will not return to its original length and will have what is called a permanent deformation or permanent set. Passed the elastic range in Figure-3, each time we reload then the material becomes stronger but its elastic limit/point decreases if loaded to the elastic limit and becomes less ductile. During the plastic deformation and continued loading the grains of the material rearrange...
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