## Biaxial Bending in Column for Response Spectrum case

## Biaxial Bending in Column for Response Spectrum case

(OP)

I have carried out a response spectrum analysis for a reinforced concrete moment frame building and have the following questions:

a) Do you combine U1 and U2 acceleration in a single RS case?

b) My columns experience biaxial bending. With the response spectrum I have min and max values for bending moments. Should I take max values in both directions when designing my column? It makes more sense for me to take max in one direction and min in the other as this is the case when carrying out equivalent static analysis. With equivalent static we only need to apply a 30 percent load in adjacent direction of the principal axis which means I have much lower moment in secondary axis.

Thanks

a) Do you combine U1 and U2 acceleration in a single RS case?

b) My columns experience biaxial bending. With the response spectrum I have min and max values for bending moments. Should I take max values in both directions when designing my column? It makes more sense for me to take max in one direction and min in the other as this is the case when carrying out equivalent static analysis. With equivalent static we only need to apply a 30 percent load in adjacent direction of the principal axis which means I have much lower moment in secondary axis.

Thanks

## RE: Biaxial Bending in Column for Response Spectrum case

You want to capture all combinations of load actions in your analysis and design. I am not sure what the "U1" and "U2" refer to but I can certainly help with point b).

You can take envelope actions - that is take the maximum moments in both major and minor axis and apply them simultaneously with appropriate combinations of axial actions (minimum and maximum axial actions - this yields a total of two combinations); this sort of approach can be quite inefficient as you effectively perform design checks for everything in one go and if lateral combinations drive the design then you enter trouble town (in terms of material efficiency).

A more thorough way to go is to check your column against design actions on combination-by-combination basis. That is you make a list of all load combinations (as directed by your design code) and derive sets of design actions (axial, major moment, minor moment) for each combination. You then check columns for all individual combinations to verify that you have enough member capacity.

## RE: Biaxial Bending in Column for Response Spectrum case

1) Use 100% of the response spectra results in one direction and 30% of the response spectra results in the other direction.

2) Use an SRSS (Square Root Sum of the Squares) of the results from both directions.

Note: these are both "statistical" methods of combining the results from those two independent directions.

3) Alternatively, you could rotate your structural model and apply the response spectra in axes that are 30 and / or 45 degrees from the main direction. Then take the worst case scenario. This isn't statistical at all, but it's trying to capture the worst case non-orthogonal earthquake. Very few people do it this way though as I think it's a lot more work.

## RE: Biaxial Bending in Column for Response Spectrum case

You are expected to analyze for the loading applied independently in two orthogonal directions. Regarding the design of elements, the combination of effects ,for 100% of the forces for one direction plus 30% of the forces for the other direction.

Each member shall be designed considering the effects of worst combination applicable for that member. The design effect shall be the envelop of the combinations.

What is the code that you are following ? You may look to ASCE 7-16 12.5 DIRECTION OF LOADING .

## RE: Biaxial Bending in Column for Response Spectrum case

b) When combining cases you do either SRSS again or the 100% - 30% rule.

Look at the other thread from yesterday, there's an example that might help you understand.

In addition to what was previously said, be sure to calculate the bending resistances as accurately as you can, because of capacity design (if you calculate the bending capacity as for example 100 kNm and it's actually 120 kNm you're not actually safer because shear depends on the bending CAPACITY and you'll underestimate it).

## RE: Biaxial Bending in Column for Response Spectrum case

b)

-Min Mx & Max My

Min Mx & Max My

-Max Mx & Max My

Max Mx & Max My

-Min Mx & Min My

Min Mx & Min My

-Max Mx & Min My

Max Mx & Min My