Staggered bolts: Block shear & s^2/4g 1

[beagleboy]

Fellow Engineers,

When we calculate block shear for staggered bolt pattern, we add "s^2/4g" (x plate thickness) to the tensile area "Ant". Does anybody know where does this equation comes from or it's basis? Why not use sqrt(s^2 + g^2) (using Pythagoras's theorem) instead? AISC 360 calls for "s^2/4g" but provides no further explanation.

Any thoughts/inputs would be appreciated.

Thanks in advance!

"There is no TENSION, it's always a COMPRESSION," said a wise man

 

[E720]

This thread I believe answers your question.

https://www.eng-tips.com/viewthread.cfm?qid=308105

 

[beagleboy]

Great, thank you so much!

"There is no TENSION, it's always a COMPRESSION," said a wise man

 

[E720]

Larry Muir who works for AISC and writes a bunch of articles for them sent me this concerning the matter:

The term, s^2/4g, goes back a long way. It was developed by V.H. Cochrane and presented in Engineering New Record in 1922. The formula is a simplification of a theoretical approach he proposed in 1908. The concern was that the stress along the hypotenuse was a combination of shear and tension, so using this as the tension area would be “unconservative” since the shear strength is less than the tensile strength. It should be noted that the method has been questioned over the years. The folks at University of Illinois proposed at least a couple of different methods (Wilson’s rule, relative gage method) in the 1940s and 1950s. Despite the detractors the formulation has held on for nearly one hundred years, and seeing that the Specification will not be updated again until 2022 it will see its centennial.



If you are really interested in exploring this topic further, the 1922 Engineering News Record and a number of the University of Illinois papers can be found online.



Please let me know if you have any further questions.

 

[msquared48]

I thought the OP was swearing...

Mike McCann, PE, SE (WA)