How to calculate the stress on a bolt?

[seungwoo Park]

Homework Statement

A hanger is fixed from the ceiling by using 4 bolts. The diameter of bolts are d=20.752mm, and load is equal to P=2kN. Determine normal stress of 4 bolts

why the Pa= +300N(upwards) is?
i think it should be -300N(downwards) like my solution(below).
and
Fa = 500 - 300 = 200N
but the solution and other problems solve like that(Fa=500+300)

Homework Equations

stress = load/area
moment = load*length

The Attempt at a Solution

 

[Dr.D]

Are you aware that this is a statically indeterminate problem? You have attempted to reduce the indeterminacy by assuming symmetry, but that may not be valid. There are basically 4 unknown bolt loads and only 3 equations available (two moment sums and one force sum).

 

[Dr.D]

With the assumptions you have previously made, the results are
Fa1 = Fa2 = 300 N down
Fb1 = Fb2 = 1300 N up
The actual stress in the bolt is another matter. These are simply the net forces transferred, but they do not account for how tightly the bolt squeezes the two parts together. With zero external load, we could still have very high stress in the bolts if they are tightened to an excessive degree.

 

[seungwoo Park]

Hi! Dr.D Thanks for response.
I asked this question to professor
He said, your solution is correct in terms of statics but we need to consider worst case when we design something(because this class is mechanical design class)
I think, He want to consider worst case...

 

[PhanthomJay]

Hi! Dr.D Thanks for response.
I asked this question to professor
He said, your solution is correct in terms of statics but we need to consider worst case when we design something(because this class is mechanical design class)
I think, He want to consider worst case...

Looks to me like both you and the text are wrong. The text messed up on the negative sign...you were OK here. But beyond that, you and the text both added the vertical load distribution of 500 to each bolt, but this is not correct. When you consider sum of forces in y direction must be 0, you get that sum as 2000, not 0.

 

[seungwoo Park]

So what's your solution about this problem?? I think it is okay...

 

[PhanthomJay]

So what's your solution about this problem?? I think it is okay...

Hi
The textbook solution is incorrect. Your solution is incorrect. Dr. D has given you the correct answer for bolt load. You should explain why, and also explain the significance of the plus and minus sign (up and down loads).

 

[Dr.D]

He said, your solution is correct in terms of statics but we need to consider worst case when we design something(because this class is mechanical design class)
I think, He want to consider worst case...

The truly worst case is simply not defined with the given information. You could torque the bolts all the way to failure before the load P is ever applied. That seems to me to be the worst case, but nothing has been given about how the bolts are tightened. It is a poorly posed problem.

 

[CWatters]

Do you even need the bolts marked A ?

 

[PhanthomJay]

The truly worst case is simply not defined with the given information. You could torque the bolts all the way to failure before the load P is ever applied. That seems to me to be the worst case, but nothing has been given about how the bolts are tightened. It is a poorly posed problem.

As long as the bolts are torqued in accordance with recommended values, the stress in the bolt can be computed by a simple P/A. Often I don't specify a torque value, instead, I specify the 'turn of the nut' method tighten snug then 1/3 or 1/2 of a turn more with a wrench.

Do you even need the bolts marked A ?

In theory, no, but in practice, yes. Worst case does not depend on bearing pressure against the ceiling; rather, bolts are assumed to take the loads.

 

[Dr.D]

Often I don't specify a torque value, instead, I specify the 'turn of the nut' method tighten snug then 1/3 or 1/2 of a turn more with a wrench.

I think we are discussing an academic problem here, one for which a student is expected to be able to determine an answer. The method described by Phanthomjay is fine in practice (although it does not address the question of actual bolt stress), but it is not really a suitable answer for an academic problem.