NCEES #516

[Ble_PE]

I'm having a little trouble figuring out how they solved this problem in the book. I've never designed prestress, so I'm using the SERM 4th to try to figure this problem out. For those that don't have the NCEES sample questions, here is the problem:

You have a prestressed beam with the following dimensions: b=18", h=36", L=50'

There are 2 rows of prestressing tendons with 6 tendons per row. The bottom row is 3" from the bottom of the beam and the top row is 2" above this row. The strands are low relaxation 1/2" diameter, fpu = 270 ksi, As = 0.153 in^2 per strand, and stress at release = 175 ksi per strand.

They then ask if the top fiber stress at mid-span of the beam due to self-weight is 0.65 ksi, what is the total top fiber stress at release.

The steps they take in the solution are the same ones that I take, but they use S for the entire section to calculate the stress, whereas the SERM and PCI manual use St (section modulus of top section). Why is this?

Thanks.

 

[civilized_naah]

The steps they take in the solution are the same ones that I take, but they use S for the entire section to calculate the stress, whereas the SERM and PCI manual use St (section modulus of top section). Why is this?
Thanks.

The formula for the bending stress is sigma = M/S, where you use the (appropriate) section modulus. In other words, to calculate the bending stress at the TOP FIBER, you use the section modulus based on the TOP FIBER distance from the N.A. (y_top). Thus, S_top = I/y_top. I don't quite understand what you mean when you say "they use S for the entire section".

The most imprtant thing for these problems is to keep the sign convention (for the stresses) straight, i.e. properly distinguish tensile and compressive stresses. Hope this helps.