Ductile Tensile Strength Moment Push

[hocho]

What formulas do you use to see how the moment at zero axial load (or even non-zero) in the Interaction Diagram can be pushed until the rebars reaching tensile strength (until it breaks)?

 

[BAretired]

What do you mean by "pushed"?. At zero axial load, the member is a beam, so use beam formulas.

BA

 

[KootK]

The rebar doesn't "break". Rather, if detailed properly, it yields and strains plastically. Rebar yielding will only occur prior to concrete crushing for axial loads below the balanced point on the interaction diagram. For such axial loads, the level of moment attainable prior to rebar yielding is given by the equations used to develop the interaction diagram or, graphically, by the interaction diagram itself. At zero axial load, the member becomes a beam rather than a beam-column and the traditional beam flexural equations can be used.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[hocho]

The rebar doesn't "break". Rather, if detailed properly, it yields and strains plastically. Rebar yielding will only occur prior to concrete crushing for axial loads below the balanced point on the interaction diagram. For such axial loads, the level of moment attainable prior to rebar yielding is given by the equations used to develop the interaction diagram or, graphically, by the interaction diagram itself. At zero axial load, the member becomes a beam rather than a beam-column and the traditional beam flexural equations can be used.

Tensile strength is when the rebar literally breaks after yielding.

BA, by pushed I was inquiring how much further moments can be increased before the rebars reach tensile strength and breaks at any moment below the balanced point for a particular eccentricity. Would you know the formulas to determine how much further moments can be attained?

 

[mike20793]

Your beam/column with no axial load has failed long before the reinforcement will break. But if you want to do the calculations, you will use the flexural equations, as others have said, and adjust your steel strain accordingly.

 

[KootK]

Tensile strength is when the rebar literally breaks after yielding.

I understand. The point that I was making is that the rupture (breaking) strain in normal reinforcing is many multiples of the yield strain. To rupture the rebar, you'd pretty much need to tie up your member like a pretzel. And, even at that, all kinds of other terrible things would likely happen first such as lap splice failures, concrete crushing etc.

If you're truly interested in behavior up to rupture, that is your prerogative of course. I just have a hard time imagining what one would want with that information outside of a research environment which is why I questioned your request for it.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

In high seismic design, we generally consider the maximum, post yield moment strength to be that calculated using the usual equations but without material safety factors and with 1.25fy used in place of fy to represent strain hardening.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[hocho]

I understand. The point that I was making is that the rupture (breaking) strain in normal reinforcing is many multiples of the yield strain. To rupture the rebar, you'd pretty much need to tie up your member like a pretzel. And, even at that, all kinds of other terrible things would likely happen first such as lap splice failures, concrete crushing etc.

If you're truly interested in behavior up to rupture, that is your prerogative of course. I just have a hard time imagining what one would want with that information outside of a research environment which is why I questioned your request for it.

Your curve seems to show grade 40 rebar where the yield plateau is longer compared to grade 60 where it rarely show yield plateau and enter strain-hardening immediately upon beginning to yield. I'd like to compute which of these bars can have more moment capacity for their respective axial and moments in the interaction diagram before the tension bars rupture.

In your opinion. Using grade 40 shows more ductility? So for a given section and moment requirements.. would it be better to put more grade 40 instead of fewer grade 60 both computed for certain fs?

 

[KootK]

Your curve seems to show grade 40 rebar where the yield plateau is longer compared to grade 60 where it rarely show yield plateau and enter strain-hardening immediately upon beginning to yield.

Who knows if it was accurate. It was an internet grab. See below for another version indicating even more strain capacity. Whatever steel grade is used, the fact remains that the strain required for rupture is substantial.

in your opinion. Using grade 40 shows more ductility?

In general, lower fy = more ductile.

would it be better to put more grade 40 instead of fewer grade 60 both computed for certain fs?

Yes, if improved ductility is the goal.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.