Torsion in Prestressed Concrete 1

[bvbuf]

I want to determine if torison can be neglected in a prestressed concrete beam. It is an externally applied torsional force. Say I'm putting a flagpole on a roof edge beam.

ACI318-11 11.5.1 says Tu can be neglected if it is less than

φλ√f’c(Acp2/Pcp)(√1+(fpc/4λ√f’c)).

The term fpc is defined as - compressive stress in concrete (after losses) at centriod of cross section resisting externally applied loads or at a junction of web and flange when the centriod lies within the flange. I'm not sure how to calculate it.

Is that compressive stress only based on the moment induced in the beam by the prestressing tendons. Shall I also include the dead load in this?
Is that compressive stress calculated at the face of the support?
I'm assuming the centriod of the cross section is the centriod of the area including the concrete beam and the section of slab from ACI318 13.2.4. Right?
What is meant by the phrase "resisting externally applied loads". Why is that phrase included?

Thank You

 

[cooperDBM]

Assuming that you're performing this torsion check on the complete structure the cross-section resisting external loads would be the composite section (precast and slab). fpc would then be the stress at the centroid of the composite section (ignoring the flange/web junction for the moment). Since the centroid of the composite section isn't coincident with the centroid of the precast section the stress, fpc at the composite section would be due to prestress, axial and eccentric components, and gravity loads carried by the non-composite section, including the weight of the slab if not shored. Loads carried by the composite section would not add to the stress at the composite centroid since it's also the uncracked neutral axis of the composite section.

therefore ... fpc = Pe / A + Pe * e * (yc - y) / I + Mg * (yc - y) / I

where A, e, y, and I are properties of the non-composite section and yc is the location of the composite centroid. Mg is the moment carried by the non-composite section.

If fpc is tensile then take it as zero.

If the composite centroid is in the flange then fpc is taken at the nearest web/flange junction because the long. shear will be higher at that point. If the location of fpc is shifted then external moments applied to the composite section will also come into play.

See clause 11.5.2.5 about the location of the critical section.

 

[bvbuf]

Thanks for your help cooper. I have a few more questions.

My section is a post tensioned beam cast in place with the slab. It is not precast. I'm looking at it as an inverted "L" beam with the rectangular beam and the portion of slab extending on one side (equal to hb < 4 hf) considered together.

Would I still look at A, e, y, and I as the properties of the rectangular portion of the beam and yc the centriod of the "L" beam?

Or would I look only at the "L" beam and since the stress at the centriod of the "L" beam is zero due to moment, the compressive force will only be Pe/A?

 

[cooperDBM]

Since the entire section carries all of the load, including the prestress, then you would just be left with P/A at the centroid (neutral axis) if the centroid is not in the slab. If the centroid is in the slab then fpc would be the stress at the bottom of the slab where bending will also play a part in the long. stress. The intention of this check is to consider the torsion shear stress where the bending shear stress is the highest (i.e. where the shear width is the least).