Question

The long bolt passes through the 30-mm-thick plate. If the force in the bolt shank is 8 kN, determine the average normal stress in the shank, the average shear stress along the cylindrical area of the plate defined by the section lines a–a, and the average shear stress in the bolt head along the cylindrical area defined by the section lines b–b.

Answer 1

σt=207.9 Mpa

σa=4.719 Mpa

σb=45.47 Mpa

Step-by-step explanation:

The problem doesn't have the image of the values a-a and b-b however here the image determinate tha values and how can you resolve even for a different values a-a and b-b here use industries long bolt

σt
`=(P)/(A)`

d=7mm

a-a=18mm, La=30mm

b-b=7mm, Lb=8mm

`A_(cross)=(\pi )/(4)*d^(2)`

`A_(cross)=(\pi )/(a)*0.007m^(2)\\A_(cross)=38.48x10^(-6)m^(2)`

σt
`=(8kN)/(38.48x10^(-6)m^(2))`

σt
`=207900207.9=207.9x10^(6)pa`

σt=207.9 Mpa

σa
`=(P)/(Aa)`

`A_(a-a)=\pi *d*L\\A_(a-a)=\pi *0.018m*0.030m\\A_(a-a)=1.695 x10^(-3)m^(2)`

σa
`=(8kN)/(1.695x10^(-3)m^(2))`

σa= 47197640.012

σa=4.719 Mpa

σb
`=(P)/(Ab)`

`A_(b-b)=\pi *d*L\\A_(a-a)=\pi *0.007m*0.008m\\A_(a-a)=0.175 x10^(-3)m^(2)`

σb
`=(8kN)/(0.1759^(-3)m^(2))`

σb= 4547284.088

σb=45.47 Mpa