1. A wheel lug nut wrench such as the one pictured below is needed. The wrench m

Question

1. A wheel lug nut wrench such as the one pictured below is needed. The wrench may be made of any of the materials listed in the table. Choose the appropriate material performance indices from Table 11.5 to select a stiff and light material for the lug nut wrench. Consider all stresses that would be applied when grabbing the handle and trying to turn the wrench attached to a lug nut. Calculate material index values for all materials in the table below and rank the best three candidates. Material Aluminum Cast iron Copper Magnesium Steel Titanium p (kg/m3) 2800 7000 8900 1800 7800 4500 E (GPa) 73 150 115 45 200 120 G (GPa) 28 60 0.33 0.30 0.34 0.35 0.29 0.33 ay (MPa) 410 275 120 200 650 850 17 78

Explanation / Answer

Solution :-

The handle and spokes should be stiff. The design is based on the stiffness and the parts are subjected to beam bending. we will compare E(1/2)/rho for various materials.

Though the index is high for magnesium, it is not used for the above application. Titanium is difficult to machine. So the best three materials are aluminum, steel, cast iron.

material E(1/2)/rho aluminum 96.49 cast iron 55.32 copper 38.1 magnesium 117.85 steel 63.89 titanium 76.98

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