PE Exam Prep / Bolt Stiffness

[Laserxenon]

Hello,

I am preparing for the PE exam in 2 weeks and have some fundamental questions I would like to ask, starting with bolt stiffness. Many of these questions I know how to calculate, but I have been putting off understanding the "deeper" logic until now. Thanks in advance for your responses.

Question 1) In all of my PE references and problems, when calculating bolt stiffness, you use the nominal area instead of the tensile area. Why is this? It would seem that the thread area doesn't greatly contribute to the overall stiffness as if it did, we would use the nominal area in tensile stress calculations. We have the charts with tensile areas available, so this seems strange to me.

A few more questions forthcoming and thanks again.

 

[Pete_K]

The Lindeburg book say "it's common to use the nominal diameter" as opposed to accounting for the threaded section, so when it comes to problems on the test I would go with that. Because the test is multiple choice, it's unlikely that the difference due to including/excluding the threaded section would effect choosing the wrong answer. In reality and in other books, like "Mark's calculations for machine design", the threaded length is considered for determining the stiffness. Good luck.

 

[Laserxenon]

Hi Pete, thanks for your comment and good clarification. I was actually referring to the calculation for stiffness k= (A*E)/L where you are using the cross sectional area. Lindberg and others seem to use the nominal area, however, for example, for a 1" nominal fastener, the tensile area is ~0.60, which is 40% less than using the area based on the nominal diameter!! Seems like the tensile area would be the smarter one in real life to use for calculating bolt stiffness, the PE exam, maybe not.

Question 2:

Consider a round shaft that is welded perpendicularly to a flat plate. The shaft has a load, P, acting perpendicular to the shaft axis and located at the end of the shaft. There is also a torque, T, acting through the axis of the shaft. We are trying to find the stress at a circumferential weld due to this combined stress. Ignore direct shear for now.

One method of calculating this is to consider the bending stress acting in one plane, and the torsional stress acting in a perpendicular plane. Then, using the combined stress theory, you determine your maximum torsional shear and normal stresses. This approach makes sense to me.

The other method I have seen is to determine the same bending and torsional stresses, except you now use the square root of the sum of the squares to determine the resultant stress's magnitude. This does not make sense to me as the bending stress and torsion stress vectors are not in the same plane.

It would seem that the combined stress theory is perfect for this application. Can anyone explain what I am missing? Thanks.

 

[BridgeSmith]

"...for a 1" nominal fastener, the tensile area is ~0.60, which is 40% less than using the area based on the nominal diameter!!"

That's just the kind of thing that will trip you up on the exam - the nominal area of a 1" bolt is .785 in^2.

For Question 2, if the stresses are in orthogonal directions, the resultant stress is the 'vector sum' of the stresses (A^2 + B^2 = C^2), so the second method would make sense to me as a simplified. I'm not familiar with combined stress theory, so I'm sure how it differs, if it actually does in any substantial way. It's very possible it accounts for some internal stress interactions that are too complicated and not substantial enough to consider for typical design.

 

[Laserxenon]

Hot Rod,

Oops! Luckily I do tend to calculate out even the obvious (or not) numbers so I don't make a stupid mistake just like that! Either way, it is about 77% of the area, so I still don't understand why we just call it good using the nominal diameter unless the threads do contribute to the stiffness.

For #2) The combined stress theory allows you to find your principal normal & principal shear stresses given normal stresses in the X, Y directions and shear stress in the XY plane. Because you are finding principal (maximum) stresses due to the combined effect / influence of normal and shear stresses, in my mind, it makes a fuller picture of what the stresses actually are then finding the resultant vector sum. As the combined stress method is a simple calculation (as simple as the vector sum IMHO), I would think we would do this always. To then see it done different ways just confuses me! Thanks for your insight.

 

[BridgeSmith]

I'm not sure I grasp the combined stress theory, but it sounds as if it's basically doing the same thing in a different way. I would be curious if the two methods actually resulted in different answers, or if it's one of those (A + B) + C = A + (B + C) scenarios.

 

[canwesteng]

Q1: I think using nominal area is justified if the thread does not really enter the joint, in which case the shank diameter will dominate the deflection response. If you have an all thread bolt, the net area would control deflection. Using the thread for capacity must always be done as it is the weakest link in the system. One caveat here, if you are looking at plastic deformations (i.e. failure of the bolt), you should use net area as this will yield before the shank does.

Q2: Loads on welds are resolved into shear on the throat (assuming these are fillet welds). Principal stresses are the correct combined stress to use for a brittle element but sum of shears is used to determine the shear on the throat to be consistent with capacity equations.

 

[Laserxenon]

Hot Rod,

Agreed. After the exam I will do the calcs both ways and post to see what we find.

Canwesteng,

Firstly, thank you.

1) I actually was meaning when a bolt was loaded axially, not transversely. What you are saying makes sense for a shear / transverse situation, but imagine a flat plate bolted to a vessel under pressure. When determining the fraction of the load the bolts take (their stiffness vs. the total joint stiffness), it seems that most use the nominal area, hence my question. Now that I think about it, perhaps this is because if the bolt threaded length is minimized, not much of that reduced area will be present in the joint thickness, so the nominal area ends up being mostly accurate.

2) Can you elaborate on the brittle element that you mention? I understood that principal stresses are used regardless when you have x and y normal stresses and shearing. What I am still hung up on is that in my example (combined bending and torsion, assume the round shaft's length is in the positive Z direction), the stress vectors (bending/tension/compression & torsion)are not in the same planes. They are in the xy (shear) and yz (torsion) planes, which would be setting you up well for using combined stress theory to find principal stresses (which would then allow use of say distortion energy failure criteria).

In a different example, imagine you had a non-symmetrical weld geometry (ie not circular) that experiences torsion and direct shear. The direct shear would be in the y direction, and the shear at the extreme fiber would be in the xy plane at some angle. I could then see using the sum of the squares method to determine their vector addition.

Sorry if I am confusing the issue more / over-complicating things, I guess I just don't understand why we wouldn't be using combined stress theory. I do appreciate your comments however on capacity equations, and perhaps practicality dictates.

 

[canwesteng]

1. No, I understood it as axially. There is only max tension in the bolt between the nut and the head, ie in the joint. If this is all shank use nominal, if this is all thread use net.

2. The way fillet welds are designed all load is considered as shear regardless of direction. Fillet welds should never see flexure or torsion, only loads normal and perpendicular to the axis of the weld. By sum of squares they are both resolved into a shear on the throat. That is simply the way welds are designed, and while using principal stresses is correct from a material mechanics perspective, I'm not sure how you are determining the principal stress on the weld throat.