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What could possible sources of error be when trying to calculate the torsion (torsional stiffness ) of a long hollow circular aluminum bar which is

What could possible sources of error be when trying to calculate the torsion (torsional stiffness ) of a long hollow circular aluminum bar which is carrying a load. A rigid supporting frame is holding the aluminum bar in place using fixtures. The values were measured using weights and dial gauges. A clamp bracket was mounted adjacent to the torque arm near the tip end of the aluminum bar. What would be the difference between theoretical values from formulas and experimental values. Experimental shear stress: ???? = ???? ∙ ???? = ???? ∙ (2 × ???????????????????? 2 ????????????????????????????) Theoretical Shear stress is known to be: ???? = ???? ∙ ????/J

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