Cm coefficient calculation for B1 multiplier

[BAGW]

Hi,

According to Appendix 8, cm = 1.0 when columns are subjected to transverse loading between supports. What is this transverse loading? What causes transverse loads? Is this from lateral loads (wind/seismic)?

 

[jayrod12]

Correct.

 

[BAGW]

When designing columns that supports the trusses, like moment frame connections, I dont need to treat the the chord compression and tension forces on the column as transverse load right? The cm for those can be calculated using the equation cm = 0.6 - 0.4(M1/M2) correct?

 

[jayrod12]

I would be inclined to use 1.0 unless the column size is becoming troublesome.

 

[BAGW]

Yup, using cm=1.0 gives B1=1.35 which is killing the column. This is under the gravity load case (1.2D + 1.6L) and not even the lateral load case. If I calculate the cm using the equation, it gives me a value of 0.76 and a B1 = 1.0. I dont want to size the column 35% more than what is required.

 

[KootK]

What causes transverse loads? Is this from lateral loads (wind/seismic)?

Gotta be careful with precise definitions. Lateral loads delivered to columns by a typical moment frame beam would not trigger Cm = 1.0. Wind loads delivered to a column by a girt on the other hand would.

Your best litmus test for Cm is as follows:

If your column shear diagram has a discrete step in it, Cm = 1.0. Otherwise, Cm is per the equation.

When designing columns that supports the trusses, like moment frame connections, I dont need to treat the the chord compression and tension forces on the column as transverse load right? The cm for those can be calculated using the equation cm = 0.6 - 0.4(M1/M2) correct?

The trick here is to recognize that there's an important difference between

a) a case where the lateral load is just a load and;
b) a case where the lateral load is both a load and a lateral restraint.

I've tried to illustrate the difference below. With your truss / moment connection situation, the lateral load is also a lateral restraint (case B). As such you, can calculate cm (and your euler buckling loads) as the worst of these two cases:

1) a column spanning from the base plate to the truss bottom chord with Cm < 1.0 per the equation and a moment at the top.
2) a column spanning from the truss bottom chord to the truss top chord with Cm < 1.0 per the equation and a moment at the bottom.

This should improve things substantially. Naturally, it's business as usual when checking the other column axis.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BAGW]

Thanks kootK. That makes perfect sense to me