Joint Stiffness in Bolted Assembly

[jimbod20]

Hello,

I'm trying to estimate bolt loads in a bolted assembly via hand calculations. I'm struggling with the joint stiffness. I get a wide range of answers using different estimate methods. The joint is a stack of aluminum plates. I provide the attached picture to illustrate the bolted assembly.

Can I get some guidance on ways to estimate the joint stiffness.

 

[desertfox]

Hi

Have a look at this site:-

http://www.roymech.co.uk/Useful_Tables/Screws/Preloading.html

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[Jamesg83]

Unfortunately, there is no "easy" solution as the plate resilience or stiffness depends on many influencing factors. The criticality of the joint will determine how far you go in terms of analysis and if critical I would suggest an FE analysis and/or testing of a prototype making use of strain gauging.

In general, the clamped zone of compressive stress under the bolt head widens from the bolt head or nut towards the joint interface and has the shape of a paraboloid of revolution. It is common for this to be approximated to two frusta positioned back to back and depending on hole edge distance and/or centre distance this geometry may need to be truncated in a transverse direction as to take account of these influences. The angle of said frustra is assumed to be in the region of 30 degrees (not included angle).

If you are really interested in estimating the plate resilience to a reasonable degree of accuracy I suggest reading section 5.1.2, "Resilience of superimposed clamped parts", of the German standard VDI2230 which has become industry standard for analysing critical joints.

Alternatively, for a simplified and more straightforward approach look at Shigley's Mechanical Engineering Design, section 8-5 Joints - Member Stiffness.

There is also an online bolted joint calculator that will perform the calculation for you. However, the assumptions here are that adjacent bolts and edge distances do not affect the compression zone. This is a conservative approach because of the dependence of the load experienced by the bolt on the relative stiffness’s of the bolt and plates.