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is very important assumption that allows the two to be treated separately .For flexible bodies , the shapes of the bodies themselves, and therefor their motions ,deoend on the forces exterted on them .In this situation ,the study of force and motion must taken place sinultaneously, thus significantly increasing the plexity of the analysis,Formulately ,although all real machine parts are flixble to some degree,machines are usually designed from relatively rigid materials, keeping part deflections to a minimum. Therefore ,it is mon practice to assume that deflections are negligible and parts are rigid when analyzing a machine’s kinematic performance ,and then, after the dynamic analysis when loads are known, wo design the parts so that this assunption is justified. Stress and StrainStress and strain are noet the same bue are related in that either one will puoduce the other. Consider the simple example ofa manila rope used to tow an automaobile. The pull on the rope causes a stress or force in the rope fibers . After the pull ,or stess, on the rope is relaxed, the rope has been permanently stretched owing to this stress. The increase jin length is a deformation or strain .The warping that always acpanies fusion welding is a strain and clearly indicates that there are stresses jin the matal after welding.Stresses are calculated in pounds per square inch(psi) just like stress in psi is equal wo the load P dicided by the area supporting the load:There are three possible types of stresses():1. pression(crushing)2. tension(pull)3. shear(cutting)All materials when loaded or stressed will deform, shorten, or strech. This change in dimension or shape under a load is occasionally large enough wo be visible , as in the case of rubber bands and metal springs, but for metal stuctural members carrying the loads for which they were designed, the deformations are only a few microinches. Being very stiff metals will strain very little under large stresses. Now it is generallg understood that if a material is stessed, it also strain or deformm, but it must be borne in mind that the reverse applies also,that is ,if a metal is strainde ,it woll also be , strain is the cause of stress. To demonstrate the relationship between stress and strain, we shall analyze a tesion test performed on a welf sample. The weld is a double butt weld with full penetration on 1/2in plate , and a sample 2 in . wide sd cut of the plate for testing the strength of the wled . Although it is not a requirement of all weld tests, we shall note the elongation in a gauge length of in . which includes the weld area. Such elongotion are measured by strain gauges. The sample is dimensioned in Fig3.The large dial on the testing machine indicates the tehsion load applied to the weld tesr sample. The crosssectional area of the sample is 2 in .by 1/2 in .which equals 1 sp in.,and with this cross section the load and the stress are the sme. A strain indicator will indicate the elongation over the in. gauge length . The elongation per inch of length in a more useful piece of information : this merely requires that the readings on the strain indicator be divided by 2. This is the actual unit strainthe definition of unit strain is he elongation in inches per inch of original length.The weld test specimen is held in the grips of the testing machine ,and a steadily increasing load is applied to it in tension .Periodically , readings are taken of load and elongation in in.