Interpretation of bolt threaded and unthreaded length for Member Stiffness calculation

[Henrique Orlandini]

Hi, I'm designing a bolted joint for the first time and Shigley's fasteners chapter was recommended to me for a good starting point.

I'm not writing the entire demonstration, but in the end, we have the following formula to calculate the bolt stiffness:

kb = (Ad * At * E)/(Ad * Lt + At * Ld)

Which Ld and Ad are the bolt unthreaded length and area, Lt and At are the bolt threaded length and area and E is the Young Modulus.

But now the issue arise. To define Ld, Shigley's assumes I'm using a partially threaded bolt (such as ISO 4014), the threaded length calculation is actually an exact match of ISO 4014 dimensions. At my company though, it's very common to use fully threaded bolts (ex.: ISO 4017).

Going strictly by the definitions on the chapter, Ld would be zero, and kb would be defined as (Ad * At * E)/(Ad * Lt). But if the bolt unthreaded length is null, the area should be null (how should I have an area of a non-existent section?). If Ad is null then I have 0/0, so yeah.

The way I'm seeing is that even if Ld is zero, nominally I can calculate Ad and move on with the rest of the design, but I'm still insecure of making assumption at my stage, so any of you could give me a light about Bolt Stiffness calculation using fully threaded bolts, I would appreciate.

 

[rb1957]

reformat the expression ...
kb = E/(Lt/At +Ld/Ad)

(check the math for yourself ... never trust what you read on the interweb, particularly if it is written by me !!??)

 

[Stick.]

Shigley's treats a bolt with threaded and unthreaded portions as two springs in series. Your case of a fully threaded bolt would just be a single spring. If you look back a bit in the derivation of the equation you posted, the equation for the stiffness of the threaded portion of the bolt is given and that's all you need to use for your bolt stiffness.

 

[rb1957]

yes, and that means Ld = 0

 

[mfgenggear]

Op
Use the root dia as shoulder

 

[3DDave]

Unless the part is sliced through no area is zero. If the length of some segment is zero than any non-zero area will have zero contribution to elastic extension.

 

[Henrique Orlandini]

Thanks @rb1957 and @Stick. , upon better reading Shigley's does already answer my question just as you said, I should just consider the threaded bolt as a "single" spring for bolt stiffness calculation.