Simple Statics Problem? 3

[Alexey881]

Hey everyone. How structural engineers would treat this problem if they had to determine all forces on all fasteners of a column loaded in the following way on top? (ignore weight)

h=w=10 in. a=b=1 in.

I've consulted several engineers, and each had a different way of resolving a force and of selecting a point of rotation, and in the end the answers of loads on the fasteners were very different. (some ways include prying, others don't) So what would you do?

 

[BAretired]

Attached is an excerpt from the CISC Handbook regarding prying action. It appears to me that the value of Q should be approximately the same as P_f when a = b. That would suggest the value of T_f should be about 2*P_f.

BA

 

[GeoPaveTraffic]

Just had to add that the title of the post is actually incorrect. This isn't a simple statics problem because it is statically indeterminate.

Mike Lambert

 

[Alexey881]

Yes, if we only had Tension at horizontal bolt then I agree 2Q=Tension on vertical bolt. However we have both T and V at horizontal bolt. (just resolve the moment on bolt line as M=F/(h-b)) (there is an assumption that angles are rigid and hence shear is transferred equally V=F/2). Now V and T counteract each other. The way I see it, when T wins we have rotation about the angle tip and Q exists; when V wins, we have rotation about the heel and no Q [however at the heel there will be a new Qlike force directed upwards)... and that force might just be equal to 1/2 the vertical bolt tension for a=b. Hmmm, but atleast we counteract alot of moment when we cross T against V.

 

[BAretired]

Interesting analysis of the problem! You say "there is an assumption that angles are rigid and hence shear is transferred equally V=F/2"? Really? Is that a valid assumption?

You talk about "when T wins or V wins"? Why not look at the equilibrium of the rigid angle in order to determine whether or not a prying force exists?


BA

 

[Alexey881]

Cause the system is indeterminate, in fact depending on the situation you may have prying on both toes of the angle, or on edge 1 and toe, or edge 2 and toe but on perpendicular axis. In fact, in the end I did not go with the assumption to which you're responding. I'm just exploring possibilities here. The only way to surely know is to make an FEA analysis or something like that. + testing. But it still wouldn't give me a generic equation applicable to wide range of situations. Unfortunately.