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E Mech 316Name: Lauren Wagner Section: 09 Date: 3/17/22 Instructor: Lodhi E Mech 316 LAB #4 Prediction of Yielding For General States of Stress OBJECTIVE • To be able to predict the yielding of general states of stress from the max shear stress theory (MSST) and the distortion energy theory (DET) of a thin-walled specimen. PROCEDURE • First measure and record the outer diameter and then the wall thickness of the aluminum 6061-T6. • Then insert the longer section of the end plug into each end of the tube. Next place the specimen with plugs into the torsion machine and bring the grips together. Lastly tighten the grips until the specimen is engaged. • Then measure and record the gauge length of the specimen defined in this situation as the distance between the machine’s grips. • Next we rotate the hand crank until a small initial torque is then indicated on the gauge. The corresponding angular displacement will be set equal to zero. • Then while continuing to twist the specimen by 4 degree increments until the relative angular displacement is equal to 40 degrees. We can record the angle and torque values. • Lastly we unload the specimen and remove it from the machine. DATA AND RESULTS Table 1. Specimen Dimensions Outer Diameter, O.D. 25.08 (mm) Wall Thickness, t 3.16 (mm) Gauge length, L0 508 (mm)Torque (in-lbs) Torque (N m) Angle of Twist (rads) 0 0 0 230 25.9863844 0.06981317 550 62.141354 0.13962634 1000 112.98428 0.20943951 1420 160.4376776 0.27925268 1900 214.670132 0.34906585 2230 251.9549444 0.41887902 2400 271.162272 0.488692191 2520 284.7203856 0.558505361 2545 287.5449926 0.628318531 2610 294.8889708 0.698131701 ANALYSIS OF DATA • Plot torque versus angle of twist. • Determine the offset angle of twist corresponding to the 0.2% offset shear strain from: roθ = γL0 where θ is in radians. • Draw the 0.2% line and graphically determine the offset yield torque. Convert this torque to a shear yield strength using equation 4-5.• Redraw the MSST and DET yield envelopes. Be sure they are properly scaled and labeled. Also indicate the two possible loading paths. Tabulate the two theoretical and one experimental measures of yield strength in shear determined in this lab. Method Shear Yield Strength (MPA) DET 159.35 MSST 138 Experimental 120.55DISCUSSION 1. Based on this experiment, explain which theoretical shear yield strength seems to be more accurate for your results. MSST is more accurate to our results. This is because looking at the data the MSST is very closely related to the experimental and the DET is not. This means that the MSST is more restricted so it has less allowable yield strength than the DET would which is more accurate with our experimental yield strength. 2. Postulate why a thin-walled tube was used in this experiment as opposed to a solid bar. Use illustrations of the shear stress distribution to support your argument. With the thin-walled tube the shear stress force is more uniformly distributed rather than if a solid bar was used it would not be uniformly distributed. CONCLUSION We can see that the MSST is more restricted and have less allowable yield strength than the DET theoretical shear yield strength, both are close to the experimental

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