calculating reinforcing actual stress
 

calculating reinforcing actual stress
how do you calculate the actual stress in reinforcing under a given load? i have plenty of references showing how to get the capacity, but not the actual stress.
i know stress is p/a + m/s.
but let's say we have a reinforcing bar in the middle of a 12x12 beam/column.
for sake of this example what if p is zero and m is large.
i guess i'm confusing myself on the basics here with the situation where the reinforcing is at the c.g. of the section, which i presume is not the neutral axis.
if i missed some required information feel free to state some assumption, hopefully i can figure this out with a nudge in the right direction.
i'm doing this exercise in the first place because part of the code i'm working uses the actual reinforcing stress to calculate the required lap length.
sounds like you've never quite mastered or were never shown the strain compatibility concept. check out some older concrete design books such as wang and salmon in the 80s.
otherwise check out how a moment interaction diagram is developed as it is quite similar to what you want.
regards,
qshake
eng-tips forums:real solutions for real problems really quick.
stress is proportional to strain, in the elastic range (which is the only time you would calculate an actual stress in a reinforcing bar).
for bending, the further you are from the neutral axis, the larger the strain, and therefore, the larger the stress.
for axial loads, strain in the reinforcing bar must be the same as strain in the concrete.
qshake's suggestion is good--any reinforced concrete textbook should cover this stuff.
daveatkins
thanks guys. i'll try looking again, but like you said i am missing something in the basic concept.
when you construct the interaction diagram you are dealing with strains/stresses assuming a stress/strain in either the concrete or steel (either the steel reached it's allowable limit or the concrete did). really you start (at least i did when i made the interaction diagram) with assuming various values of k (various points for the neutral axis) and then go through all the compatibility equations to come up with the axial-moment capacity.
that approach does not seem to work for what i am talking about here. the concrete or steel would not be at one of the limits. let's say i calculate the stress at the extreme fiber of the concrete using p/a + m/s to give the stress in the concrete at the face. how do i get the neutral axis corresponding to that point, so i can calculate the corresponding stress in the steel?
like you said there's a basic point that i didn't imprint here.
if you read a reinforced concrete textbook it will explain it. it's difficult to answer in forum.
mjl23,
your concept is completely right if the section is uncracked, but completely wrong if the section is cracked. the steel is about 9 times stiffer than the concrete. so the stress in steel will be about nine times than the stress in surrounding concrete.
if the section is uncracked, the stress at na due to moment is zero, so the stress in the stess at this location should be n*p/a.
this discussion should be equivalent for masonry or concrete. i'm posting my solution with some masonry symbols in case the solution is helpful to others or justifies scrutiny by others.
my solution to determine the actual stress in reinforcing steel due to an applied moment and axial force:
t = depth of masonry beam
fb = m/s - p/a = m (t/2) / i - p/a
η = es / em
ρ = as / (b d)
k = [2 (ρ η) + (ρ η)2]1/2 - (ρ η)
fs = η fb [(1-k)/k]
i believe this addresses the comment of shin25fff"> since η is in place to simulate the equivalent area of steel to masonry.
that is using service load stresses, not ultimate.
mjl23,
the equations that you are writing for k and fs are for cracked sections. where as equation for fb that you have written is for uncracked section.
to decide which equation is to use, you have to find out if the section is cracked or uncracked.
thanks for your help.
shin25
after reviewing an old wang & salmon book, i find where it is mentioned that mc/i is applicable (only?) when using a transformed section, which i guess would be equivalent to the uncracked section.
can you enlighten me and explain why the p/a + mc/i is only applicable for an uncracked section? (something to do with not knowing i?)
of the references i've been through the caveat is always mentioned "only applies to pure bending". which is i guess why the earlier post suggested looking at deconstructing the development of the p-m diagram. i presume i could start with a given p-m and work backwards in the usual construction of the pm diagram.
when you mention needing to know if the section is cracked or not, are you just talking about checking that the concrete/masonry hasn't exceeded the allowable?
structuraleit
i may be missing your point. my question is about calculating the actual stress in the reinforcing, so i don't know why you would mention 'ultimate'.
mc/i assumes the entire section is acting.
in concrete, you assume that the concrete carries no tensile stresses, only the reinforcement carries tension. this is not actually true until the concrete cracks, but the concrete will crack.