The steel bolt and anchor assembly is used to reinforce the

The steel bolt and anchor assembly is used to reinforce the roof of a passageway in an underground coal mine as shown in figure. In installation, the bolt is tensioned to 50001b. Calculate the stress, strain, and extension of the bolt if it is formed from 1045 steel alloy.

Solution

Note : As the Value of diameter of bolt is not clear, so i will just take it as \'d\'

>> Now, Tension in Bolt = 5000 lb

As, Area of Cross Section of Bolt = *d²/4 = A

So, Stress Generated in Bolt (Tensile Stress) = 5000/A = 5000*4/(*d²) = 6366.198/d² lb/in²  

>> Now, For 1045 Steel Alloy,

Young\'s modulus, E = 30*10⁶ psi ( for Tension )

Now, By Hooke\'s law,

=> Stress = Strain*Young\'s modulus

>> Putting all the Values,

=> 6366.198/d² = Strain*30*10⁶

=> Strain = (0.212/d²)*10^-3

Now, as Strain =Extension/Original Length

As Original length =34 in

=> Extension = (0.212/d²)*10^-3 *34 = (7.215/d²)*10^-3

=> Extension of Bolt = (7.215/d²)*10^-3