What is the Factor of Safety for Overlapping Bolted Metal Plates with 12 Bolts?

[sl8rbaby]

Homework Statement

Two overlapping metal plates are bolted together with 12 bolts. The diameter of each bolt is 8mm. If the ultimate shear stress of the bolt material is 300MPa determine what factor of safety applies if the total force to be carries by the joint is 20kN.

Homework Equations

Stress = force/area
factor of safety = ultimate stress/actual stress (I think)

The Attempt at a Solution

stress=force/area
stress=20kn/∏r^2 x 12
stress=20,000N / (∏ X 0.004)^2 X 12
= 10.55 MN/m^2

factor of safety = ultimate stress/actual stress
factor of safety = 300MPa/10.55 MN/m^2
= 300 x 10^6 / 10.55 x 10^6
= 28.42

Is this correct, cause I am not that confident? also what is the unit? is there one?

 

[PhanthomJay]

Your equations are good but you squared Pi in error. Would you expect the safety factor to have units? The stress unit N/ m^2 is called a Pascal (Pa).

 

[sl8rbaby]

Your equations are good but you squared Pi in error. Would you expect the safety factor to have units? The stress unit N/ m^2 is called a Pascal (Pa).

Thanks for the reply, I thought that to work out the area of a circle which in this case is the bolt, the equation is ∏r^2? or are you saying I only need to square the radius first then times it by pi?

and no I assume there's no units as its a ratio

 

[sl8rbaby]

ok think I've sussed it:

300,000,000 x ∏ x 0.004^2 x 12 = 180,955 = max force

max force / actual force = factor of safety

180,955 / 20000 = 9.05

I sure that's the final answer!

 

[PhanthomJay]

Thanks for the reply, I thought that to work out the area of a circle which in this case is the bolt, the equation is ∏r^2? or are you saying I only need to square the radius first then times it by pi?

Yes, you have to be careful with use (or non-use) of parentheses when writing equations. The area of a circle is ∏r^2 or ∏(r^2) or (∏)r^2 or (∏)(r^2) or ∏*r^2, but it is not (∏r)^2. Also when you wrote "stress=20kn/∏r^2 x 12" , that should have read ""stress=20kN/12∏r^2" or some correct variation thereof. The way you wrote it implies you are multiplying by 12 instead of dividing by 12.

And no I assume there's no units as its a ratio

correct

 

[PhanthomJay]

ok think I've sussed it:

300,000,000 x ∏ x 0.004^2 x 12 = 180,955 = max force

max force / actual force = factor of safety

180,955 / 20000 = 9.05

I sure that's the final answer!

Well, OK, but you should round it off to 9 (one significant figure).

 

[Simon green]

Did you ever find the correct solution to this question? I am currently stuck on the same one

 

[Nidum]

sl8rbaby never came back again so you are unlikely to get a direct answer .

You can have some help on this problem though - ask the question afresh in a new thread here on homework section .
Best to give us your own statement of the question and your own attempts at solution rather than just copy what was originally posted .