# Unity check, Interaction

• posted

Pardon my lack of knowledge on this subject, but;

I have a HSS arch in axial compression as well as bending.

The moments on the arch are anywhere from +30 to -40 ksi.

Apparently a unity check has to be done.

fa/Fa + fb/Fb < 1

Is this possible with an arch or should it be a straight column?

Does this have to be done locally at the heaviest loaded member?

Or also over the whole arch, say from purlin to purlin?

Much appreciated

Peter

• posted

This is a significantly more complex problem than you seem to realize.

First, your unity check equation above is incomplete. The moment will cause a deflection of the member. The axial load acting on this deflected shape will create an additional moment. This effect, called (logically enough) moment amplification, must be taken into account in the unity check.

Second, the allowable axial stress (Fa) will be a function of the restraints at the ends of the arch and within the structure. Depending on the configuration of the structure, buckling might occur locally (i.e., between points of bracing withing the structure) or globally (buckling of the overall arch).

I think that this is a difficult enough problem that you probably need to get the assistance of a qualified structural engineer. You might try posting this question on the civil engineering group (sci.engr.civil). There are a number of building and bridge oriented consulting engineers there who may be able to help.

David Duerr, P.E. Houston, Texas

• posted

Pardon my lack of knowledge on this subject, but;

I have a HSS arch in axial compression as well as bending.

The moments on the arch are anywhere from +30 to -40 ksi.

Apparently a unity check has to be done.

fa/Fa + fb/Fb < 1

Is this possible with an arch or should it be a straight column?

Does this have to be done locally at the heaviest loaded member?

Or also over the whole arch, say from purlin to purlin?