Complete Question
The complete question is shown on the uploaded image
Answer:
The tension on the shank is [tex]T =8391.6 N[/tex]
Explanation:
From the question we are told that
The strain on the strain on the head is [tex]\Delta l = 0.1 mm/mm = \frac{0.1}{1000} = 0.1 *10^{-3} m/m[/tex]
The contact area is [tex]A = 2.8 mm^2 = 2.8* (\frac{1}{1000} )^2 = 2.8*10^{-6} m^2[/tex]
Looking at the first diagram
At 600 MPa of stress
The strain is [tex]0.3mm/mm[/tex]
At 450 MPa of stress
The strain is [tex]0.0015 mm/mm[/tex]
To find the stress at [tex]\Delta l[/tex] we use the interpolation method
[tex]\frac{\sigma_{\Delta l} - \sigma_{0.0015} }{ \sigma _ {0.3} - \sigma_{0.0015} } = \frac{e_{\Delta l } - e_{0.0015}}{e_{0.3} - e_{ 0.0015}}[/tex]
Substituting values
[tex]\frac{\sigma _{\Delta l} - 450}{600 - 450} = \frac{0.1 -0.0015}{0.3 - 0.0015}[/tex]
[tex]\sigma _{\Delta l} -450 = 49.50[/tex]
[tex]\sigma _{\Delta l} = 499.50 MPa[/tex]
Generally the force on each head is mathematically represented as
[tex]F = \sigma_{\Delta l} * A[/tex]
Substituting values
[tex]F = 499.50*10^{6} * 2.8*10^{-6}[/tex]
[tex]=1398.6N[/tex]
Now the tension on the bolt shank is as a result of the force on the 6 head which is mathematically evaluated as
[tex]T = 6 * F[/tex]
[tex]= 6* 1398.6[/tex]
[tex]T =8391.6 N[/tex]
