Elastostatics Problem maximum shear stress 1

[DanielNeubauer]

Hello everyone,

i'm new to this forum and seek help regarding a problem I had in my project where I cant seem to find the right method to tackle it.

I need a way to compute the following: a plate with thickness t1, width w and elastic modulus E1 is loaded in-plane with the force F. it is supported on it's side by another plate with respective thickness t2, same width w and elastic modulus E2 over the height h.
the connection of both is achieved by an adhesive with thickness tg, elastic modulus Eg and shear modulus Gg.

how to calculate maximum shear stress in the adhesive? any bending, peel stress or nonlinearities in the adhesive can be disregarded for now.
please see the attached figure for further clarification.

any advice is highly appreciated!

kind regards
Daniel

 

[Snickster]

Are the two plates fixed at the bottom to the structure and free everywhere else?

 

[Stress_Eng]

It’s a means to an end, but I suggest doing a web search for axial load distribution in a threaded joint. I’ve come across information on the web that derives the load transfer based on the shear lag method. That’s the method you can adopt for your problem. Your picture can be viewed as half of a bonded doubler plate. The shear lag method involves the axial stiffness of the two members and the shear stiffness going between the mid surfaces of the two members, which will include the bonding medium, be it glue, threads, bolts etc. Hope that helps.

 

[DanielNeubauer]

thanks for your replies.

Are the two plates fixed at the bottom to the structure and free everywhere else?

yes, can be viewed like that. it's actually a line of symmetry.

shear lag method

thanks for that Idea, it looks promising on first glance. I'll look into it and give an update if this is the right way.
My problem is a simplified case of a plate under load which is supported by a patch, I only added the symmetry for easier understanding. So it's pretty close to what you described.

Best regards
Daniel

 

[DanielNeubauer]

so, I found a formula, which is by Volkersen, who also formularized shear stress in adhesives on lap shear, which I was familiar with. It popped up when I researched doublers, so thanks again for the hint.
the formula can be found on chapter 3 of Bonded Joints and Repairs to Composite Airframe Structures, 2016, see Link
it is consistent with FEA, so I think it's good enough for my level of precision I need.

 

[Stress_Eng]

Glad to hear you’ve got a way forward with your problem. I found information on the shear lag method and adopted it to the analysis of thread joint axial load distributions, under different loading conditions. The method needed axial and shear stiffnesses, which I had calculated and applied in an alternative method called strain matching. The two methods, using the same stiffnesses, gave the same answers.