aci 3-18, flexure

huangyhg

aci 3-18, flexure
i am trying to assess an existing beam in flexure using aci 3-18, section 10.2. what surprised me is that there seems to be no limit on how small a distance from the compression fiber to the neutral axis is (parameter c). i am aware that the beam was not designed to modern standards.
am i missing something, or is it prescribed somwhere else?
i'm not sure i totally understand your question.  distance c is simply the distance from the compression fiber to the neutral axis.  it is simply a "fact" of the section - a property that is just there...not something that you need to place a minimum limit on.
jae is right.  it wouldn't make sense to put a limit on c.  keep in mind that c is not constant for a given section, it changes with load and concrete strength.  the typical c we use corresponds to the nominal moment capacity.  if you are looking at evaluating deflections, rotation, or post-yielding strength you probably won't have the same value for the distance from the extreme compression fiber to the neutral axis.  re  
jae, ucfse,
thanks for your replies. please bear in mind that i am talking about assessing an existing beam, not designing a new one.
the issue is that i end up with the depth of compression zone being small (10-20mm, theoretically), and would this not lead to spalling of the concrete. bs8110 indirectly limits compression zone depth by limiting lever arm to 0.95*d (d being a distance from the extreme compression fibre to the centoriod of tensile steel).
i am not saying that the beam i am assessing is well deigned, but i have to deal with is there.
i've never heard of spalling of concrete because of a small compression zone depth. after tensile cracking, for a lot of beams the compression zone may be small at times because of a small amount of load that is on the beam compared to the design load.
does the reinforcing meet the minimum ratio required?
bkal,
you are correct that bs8110 does limit x to .95*d. this rule is not in many other codes such as aci318.
there are good reasons to limit x in this way. if you actually do the design properly from first principles rather than using rectangular stress blocks and black-box formulae as many designers do, you will find that for very small values of x, the strain in the reinforcement is very high (much higher than the breaking strain of the reinforcement). one way to limit this strain is to place a minimum limit on x.
this is then a defacto minimum reinforcement rule ensuring that the reinforcement strain is limited.
this limit should actually depend on the peak strain for the reinforcement being used. for lower ductility reinforcement the .95 factor should actually be less still.
unfortunately too many designers have never done the real calculations to see the effect of the assumptions made in the approximations built into the codes to make design easy. unfortunately all of these assumptions are not always conservative and can have adverse consequences when a design is outside the bounds of the approximation.
i think what you are asking is actually "what haapens if my beam crushes?"  when you are performing the calculations, you are seeing a beam that is over reinforced and therefore is subject to a brittle conpression failure rather than a ductile response to the plasticity of the reinforcing steel.  try running your calcs with the maximum steel ratio based on 0.75* the balanced steel ratio and see what that does to the compression zone.  my guess is you are taking into account more steel than is allowed for a ductile failure.
what i understand if u got a small value of c= 0.85fc'ab under a stress block diagram and equating it to t=asfy, u will notice that the maximum moment is lesser amount since your beam maybe of big section..but you got a an underreinforced beam. is your calculation of steel ratio is lower than the minimum? then the tendency of your beam will crack. or maybe your shear reinforcement is not enough and maybe you might not considered some torsion that affect the beam..
bkal,
the limit is there but not in straight words and normally used, so used by any of us
for maximun stresses on concrete and steel
the codes gives
- concrete maximum compresion strain  (side compresion)
- steel maximum traction strain       (side in traction)
- the strain in concrete and reinforcement shall be directly proportional (except for deep beam behavior)
that is meaning there is a straight line defining a fixed "c"
so there is a limit.
when there is only traction rebar up to the yield strain the "c" is bigger than the minimun from the code.
adding traction rebar has to be done fullfiting the straight line strain, that's meant when the traction steel has reached the yield strain and the moment it is not balanced. the steel is added based on the strain of the compresión and traction rebar.
for revision a similar aproach has to be taken.
that's meant
direct proportional strain
force equilibrium (sure forces and moments)
well known it is the method for trial and error, guess a "c", calculate the strain, stresses, forces, check the equilibrium. the output a maximun moment and "c"
ajose
ajose,
where does aci 318 define a maximum design steel strain?
also, the maximum compression strain is just that, a maximum. sometimes it is necessary to limit the compression strain to less than this maximum if the strain in the tension steel is too high (even though aci does not define the limit for this). in this case it is not possible to use the rectangular stress block for concrete or standard ultimate strength formulae. the real stress/strain diagram for the concrete must be used. this happens when the area of reinforcement is small and the value of c is small or when the reinforcement is not very ductile.
so a minimum value of c is not defined by the code. the only way the code limits this is by requiring a minimum area of reinforcement. even then aci has a 133% strength limit on this value. when this 133% limit is applied, the designer should investigate the real strength depending on the ductility of the reinforcement.
dear rapt,
strain is not just strain,
strain*elasticity moduli= stresses,
and allways will be.
the other question, well ....
it is hard answer the question without qoute the code, then reading on aci 318-99:
chapter 10 flexure and axial loads
section 10.2 assumptions
article 10.2.2 state the proporcionality
article 10.2.3 state the maximun strain in concrete
article 10.2.4 state that if steel is not yielding the steel stress is strain*elasticity moduli
article 10.2.6 state the stress distribution, let the designer choose between rectangular, trapezoidal parabolic or any other shape that fit
so i was not so wrong.