Effective Moment of Inertia - Precast Stairwell

[WpgKarl]

Lets say you have a stairwell, made out of 4 precast walls. These walls are connected at the corners with welded steel connections, designed for the forces experienced at the joint interfaces.

What would the effective moment of inertia of the box be in this case? If I compare the above system to a solid cast-in-place concrete monolithic box, I would guess that the precast system would have an effective moment of inertia somewhat less than the CIP option. This is due to the fact that the connections would be designed to yield under the ultimate loads, and then they would allow relative displacements between the members.

To calculate the forces on the connections, I would assume you need to look at Vq/Ib. So then you need to know what the moment of inertia "I" is to get a force, but you don't really know what "I" is until you design a connection??

What is normally done for this type of situation?

 

[VoyageofDiscovery]

Hi WpgKarl,

The Moment of Inertia is not affected by the connections.

Design the connections for the Moment of Inertia.

Don't forget to check the bearing resistance of the concrete, as the bolts bear on the concrete, as well.

HTH

VOD

 

[shin25]

You can easily calculate the moment of inertia assuming its a box shape. Then use this moment of inertia to calculate the shear transfer.

The shear connectors need to be designed assuming that full section (all elements in the box) will contribute to moment of inertia.

 

[csd72]

v = VQ/It

 

[mrengineer]

If you have an idea who the precaster might be, you may want to see if they really want to deal with the connections that would be required if you treat the stairwell as a box. I worked on a major all precast project in the Denver area where the precaster wanted to just analyze straight shear walls without consideration for the flanges, so that they would not have do deal with the connections required for box action.