Reinforcement yield strength 1

[aladdin76]

what is the effect of having two different yield strengths of bars in the same concrete section , what to do when designing the section ... if the smallest yield strenth to be considered, what about the elastic modulus

 

[kslee1000]

Ron:

I would take your words with reserved cautious. Wish I had spent more time and paid interest in metallurgical studies. But I do agree with you without hesitation that the significance of strength deviation in structural steel and reinforcing steel is not directly comparable, because of the stiffening effect from the concrete for the latter case. You are absolutely right on this.

 

[Ron]

kslee1000...I appreciate your willingness to take my comments at "face value". If you check the respective ASTM requirements for rebar (ASTM A615) and steel shapes (ASTM A36) you will find that there are essentially no chemical restraints placed on rebar; whereas, A36 has specific chemistry requirements to control the metallurgy. Further, rebar is allowed to have less ductility, as measured by elongation, than mild steel shapes. Rebar is required to have a minimum elongation of 12 percent, while A36 steel has to have a minimum elongation of 20 percent.

What this means, at least to me, is that the controlled metallurgy of the mild steel shapes provides much greater predictability of its properties. It is weldable without significant limitation as to process, filler metals, and pre-weld/post-weld thermal conditions (except for very thick sections). Conversely, rebar has limited weldability, specifically because of its lack of controlled chemistry.

Sorry to ramble on....I just wanted to be clear about the source of my comments.

 

[kslee1000]

Ron:

Thanks. It helps to better understand the differences of these metals, and the base of your response on this matter.

 

[kslee1000]

This weekend seems not a waste. After all, been able to find two articles discussing properties of reinforcing steels. Please pay attention to Table 5, P.16 of the article from Dubai, Table 5 & Table 7, p.27 & p.28 respecticely, of the article from India. Wish we all gain better understanding after review these articles.

 

[Ron]

kslee1000...thanks for the article. Only the one from India got attached. You have to do each file separately in separate postings.

It is a good overview of the properties of rebar. In particular the summary notes the things we have discussed here. Note also the non-linearity of the stress-strain curve of cyclic loading on rebar.

 

[kslee1000]

Ron:

Thanks for your tips. Here is the one from Dubai.

 

[graybeach]

To calculate the ultimate moment, I think you can just assume strain compatibility with each bar at its own yield strength. You run into a similar situation when you calculate the ultimate strength of a prestressed beam that also has mild steel.

 

[kslee1000]

The trouble he has is the slab has already casted. I don't think there is a record, other than the lab test, to shown where the bars were used - in seperated area, or mixed in the same area; how many were this, or that...

 

[civilperson]

Ron,
The strains will be identical and the % of elongation will be identical for all stresses less than the lower yield stress.

 

[Ron]

civilperson...I agree, but the strain will be different at the yield points, which is really the only point we're concerned with...the failure.

 

[graybeach]

Ron, Assuming perfect elastic - plastic behavior, after the highest yield strengh bars and/or the bars closest to the neutral axis have yielded, all bars will be at their individual yield stress. Strains will still be compatible.

 

[kslee1000]

graybeach:

I guess "compatble" means difference is small, but not equal.

My confusion is when E is holding constant, how could the strains be the same for bars with different yield points, albeit the difference COULD be small.

 

[Ron]

Agree that the strain difference might be small, but what we could be concerned about, if there were are larger difference in the yield strength (please note that I've already stated a couple of times that I didn't think the yield difference in this case was significant), is that you would develop a strain incompatibility after the first yielding. That could lead, again if the difference were greater, to a non-ductile failure by quickly overloading the other bar.

If that were not the case, we wouldn't be concerned about mixing Grade 40 and Grade 60 bars in the same section.

 

[civilperson]

No beam in use with service loads achieves yield unless a mistaken design was used or overloaded. The steel is suppose to yield prior to concrete failure for a ductile failure. The strains of the steel will be exactly the same as the concrete surrounding them.

 

[graybeach]

civilperson has it right. The strains in the bars will be the same as the surrounding concrete. Say the strain at a particular level in a beam that has grade 40 and grade 60 bars has reached 0.003. The grade 40 bars would have yielded at 0.0014, and the grade 60 bars would have yielded at 0.002. Because both bars are now in the plastic zone, the stress in each bar when the strain in 0.003 would be 40 ksi and 60 ksi respectively.

If the OP knew the locations and yield stress of each bar, the ultimate moment could be calculated. Alternatively, he or she could calculate the service load stress and decide if the factor of safety is acceptable for the lower yield bars.

 

[kslee1000]

I don't think the above statement is correct. Let's go back to basics:

E=29000 ksi, Sy=0.003=l/L
fy = E*Sy = E(l/L)
At fy = 40 kai, the elongation l is:
l = fy*L/E = 40 ksi*L/29000 ksi = 0.00138L
At this stage with increase load, the elongation l is:
l = 0.00138L + (60-40)*L/29000 = 0.00138L + 0.00069L
= 0.00207 L = 60*L/29000 = 0.00207L, check.

Note, after yield at 40 ksi, the lower grade bars will continue to lengthen until the higer yield point is reached, but the stress in the lower grade bars would not change. The final elongation of all bars are identical, however, the stresses in bars and the concrete wrapped around the bars are different, they depend on the yield strengths of the bars.

 

[kslee1000]

Note: Sy=0.003=l/L shall be revised as "Sy = l/L". The numerical value 0.003 has no bearing on this relationship.

 

[graybeach]

Kslee1000, Theoretically, after yield, the bar will elongate without any increase in stress. The 29000 has no effect on the stress after yield.

 

[kslee1000]

graybeach:

Yes, you are right. I also noted it in my response - no stress changes for grade 40 bars after reaching yield. However, it elongates with the grade 60 bars (at the same rate) after that point (40 kai) until the stress 60 ksi is reached.