Question

The bolt is made of 2014-T6 aluminum alloy and is tightened so it compresses a cylindrical tube made of Am 1004-T61 magnesium alloy. The tube has an outer radius of 10 mm, and both the inner radius of the tube and the radius of the bolt are 5 mm. The washers at the top and bottom of the tube are considered to be rigid and have a negligible thickness. Once snug against the washers, the nut is tightened a full turn. If the bolt has 10 threads per centimeter, determine the stress in the bolt.

Answer 1

Equilibrium requires

The problem is statically indeterminate since there are two unknowns in this equation.

Compatibility:- When the nut is tightened on the bolt, the tube will shorten and the bolt will elongate. Since the nut undergoes one full turn, it advances a distance of 1*(10mm/10mm)=1 mm along the bolt. Thus, the compatibility of these displacements requires

Taking the modulus of elasticity for both alloys, EAm = 45 GPa, Eal = 75 GPa, and applying the equation   we get,

Here, length not mentioned in the question Hence, Assuming the length of the assembly as 60 mm, The validity of the elastic analysis may be dependent on the length. So we need to choose the length carefully.

Solving i and ii equations simultaneously, we get

The stress in the bolt is therefore,