Torsional Scale
Front view of torsional scale


Say David, have you priced those heavy duty scales lately? They are extremely costly. There has to be a cheaper way to find the weight of these crates. David, you are the engineer, how about designing a simple torsional weighing system to find the weight of these heavy crates?
What is known:
 The thinwalled tube is 2 meters long.
 The torsional arm is 60 cm long.
 The tube is made from steel with a shear modulus, G, of 80 GPa.
 The shear stress limit of the steel, τ_{max}, is 350 MPa.
 The cross section of the tube is 10 cm by 5 cm as shown at the left.
 The tube wall thickness is not known but the top and bottom is twice the thickness of the sides.
 The torsional arm is stiff enough that it will not bend.
 The system should be able to weigh crates up to 12.5 kN.
 Assume the tube thickness is small when compared to the cross section dimensions and can be considered a thinwalled tube.
 Assume the applied moment due to the load is about the center of the tube and there is no outofplane twisting or deflection.
