Stiffness of Steel Portal v's Concrete Frame 1

[enginspace]

I have a four storey attached building (common or party walls on both longitudinal sides), 5.5 x 26 meters (16.5 x 78') with no shear walls in the transverse direction. Steel portal frames (pinned column bases) are being utilized at fairly regular spacings at all floors which support a concrete slab on metal composite decking (with shear studs to the UB's) - providing a rigid horizontal diaphragm at each level. Due to buildability issues one (maybe more) of the frames needs to be concrete on the bottom level.

Lateral force distribution is dependent on the relative stiffness of each frame. How do I determine how much lateral force is distributed to the single R.C frame v's the other 5 steel portals. Could I transform the concrete frame to an equivalent steel section, but the frame stiffness is a combination of the column and the beam - fundamentally speaking, how do I consider both of these elements to determine the overall stiffness of the frame.

I don't reside in the US and don't have access to US standards/building codes.

Many thanks in advance.

 

[csd72]

You need to calculate the Icr to compare the stiffness:

http://www.cement.ca/cement.nsf/376...6d9dc67ef7f0c78185256d4e00656a8d?OpenDocument

Then either multiply the deflection based on gross area or set up a new frame with equivalent steel sections.

There may also be a clause in your code regarding tension stiffening.

 

[enginspace]

Thanks csd72 for your reply!

Yes, didn't mention previously, but for RC columns and RC beams our code allows 0.4Ig and 0.8Ig respectively for the stiffness of a RC frame when considering laterally stability, accounting for Icr - I believe this is based on Branson's equation (which doesn't accurately account for tensioning stiffening when compared with Bishop's equation - Eurocode).

If I did find the equivalent steel areas based on the Icr sections, how do I consider the Column stiffnes and the Beam stiffness in unison. Hypothetically, if I had 2 frames resisting lateral forces for a particular storey, same height and length, and 1 of the frames had 310UC columns and 530UB beams and the other frame had 150UC columns and 180UB beams, with no torsional moment, how do I distribute the laterally forces from the rigid diaphragm.

The lateral force is earthquake loading, which is relative small for intra-plate earthquakes, so serviceability criteria (deflection) is not may major concern (commercial usage not post-disaster usage) but strength i.e. yielding of the steel members is.

Thanks for your help.

 

[csd72]

Why didnt you mention you were using the Australian code, I havent used it for 2 years but I still remember most of it.

Are you using the static or dynamic method?

We never considered Serviceability for earthquakes, only limit states. We always based serviceability on wind loading.

Anyway back to your question, the simplest way is to do a frame analysis using the equivalent steel I values and apply a 1kN lateral load, also apply a 1kN load to the steel frames. The resultant diplacement will give you the ratio of the stiffnesses.

 

[enginspace]

Cheers csd72 that makes sense,

BTW the new AS1170.4 came out in late 2007, it's more onerous. For non-residential structures over 8.5m high, regardless of the building's location and thus acceleration coeffient, at the very least a 'simple static check' is required with a lateral force of 0.1Wi for each floor. Wi being G + 0.3Q. So for a RC slab supporting double brick this produces an equivalent wind speed of 1.7 kPa in my case!

Thanks.

 

[csd72]

That is a bit OTT considering that we have only had one major earthquake and that most of the failures in that didnt meet the wind code.

Anyway good luck with it. You will eventually geta feel for when the earthquake load may dictate and when it is less critical than the wind load. You find ways to avoid analysing every building for both loads.