Compression members with moment to BS 5950-1:2000

[zytsang]

The same question has been posted on Stack Exchange, where the equations are written in Latex and maybe better presented.

According to clause 4.8.3.2 the cross-section capacity for non-slender section is:
Fc/(Ag py) + Mx/Mcx + My/Mcy <= 1 eqn(1)

According to clause 4.8.3.3.1 simplified method of member buckling resistance, the following relationship should be satisfied:
Fc/Pc + mx Mx/(py Zx) + my My/(py Zy) <= 1 eqn(2)

Let's consider a beam-column with class 1 section (doubly-symmetric) under uniform moment (so that the equivalent moment factor mx = my =1 according to Table 26) and axial compression, and ignore lateral-torsional buckling. In this case, equation (2) is always critical than equation (1), because Pc <= Ag py and py Zx <= Mcx, py Zy <= Mcy.

My questions are:

1. What is the use of equation (1), or clause 4.8.3.2, if buckling resistance is always more critical? Is there any case that equation (1) is more critical?
2. If the member is under biaxial bending but without axial force, i.e. Fc=0, Mx>0, My>0, is checking equation (2), or clause 4.8.3.3 still required?

I understand that the simplified method is at the cost of conservatism, but making one criterion obsolete seems too much to me.

Thank you for your time.

 

[BAretired]

I am not familiar with BS 5950, but buckling resistance is not always more critical. For slender members, it is more critical but for short members it is not as critical.

BA

 

[Agent666]

1) for stocky members the buckling won't be critical.

2) yes it should still be checked, often codes have another specific biaxial moment check that involves the sum of the two moment ratios raised to some exponent that might typically vary between 1.4 and 2,but with no axial load.

 

[zytsang]

1) for stocky members the buckling won't be critical.

I agree that, base on common engineering principle, for stocky / bulky members the buckling won't be critical.

However, from the equations of BS5950, the buckling check (simplified method) should be at least as critical as cross-sectional check. This is where I get confused.

 

[Settingsun]

Only a quick look, but isn't your assumption of uniform moment the reason the cross section check becomes non-critical? What happens if the m-factor is 0.4 instead of 1.0?

 

[zytsang]

Only a quick look, but isn't your assumption of uniform moment the reason the cross section check becomes non-critical? What happens if the m-factor is 0.4 instead of 1.0?

Yes, you are right. For double curvature member, the m-factor of 0.4 can make the buckling check less critical.

However in this case, I just wonder about a stocky member with class 1 section under uniform moment and small compression. According to the buckling check, the elastic section bending capacity pyZ governs the strength checking, instead of the plastic section bending capacity Mc = pyS. This is what intrigues me.

 

[Settingsun]

Don't you then go to the "more exact method" in 4.8.3.3.2 if the simplified method is too conservative? I think you answered yourself in the original post: simplified methods are conservative.