Initial Cracking in Reinforced Concrete Elements 1

[Signious]

Hello,

I'm doing some refresher reading on reinforced concrete design, and an interesting question popped up.

When an uncracked concrete beam reaches the concrete tensile strength in a tension zone the concrete cracks - leaving your reinforcing steel to handle the tensile stresses.

Now, when this occurs is there any appreciable 'shock loading' on the steel.

I figure there won't be any noticeable effect for a run-of-the-mill design, but if you were to have a hybrid system with fibre in the concrete as well as rebar, if the concrete were to let go it could yield the bar well below a constant 400Mpa stress.

Thoughts?

 

[rapt]

Reinforcing steel does not have a purely elastic/plastic stress/strain relationship. As long as the reinforcement is sufficiently ductile, there is sufficient ability to absorb this. If very low ductility reinforcement is used (e.g. some welded wire mesh), then this could be a problem.

Also, good minimum reinforcement rules will normally limit the strain in the reinforcement at the time of cracking to allow this to happen (this does not apply to the BS8110 min reinforcement rules, and some codes prestressed concrete minimum rules which are inadequate for normal concrete strengths used these days!).

 

[KootK]

Interesting question. I'm not so sure that the shock is all that sudden. Consider:

1) Most civil engineering structure design is predicated upon a loading that is brought on gradually enough to be considered psuedo-static.

2) It is not the case that the rebar is unstressed when the concrete is uncracked. In fact, the rebar should be about 9X as stressed as the surrounding concrete up until cracking is initiated.

3) It's not as though rebar stress would go from near zero to Fy in an instant. Rather, the stress would jump a bit at first crack and then climb gradually as additional moment was applied.

I think that the rebar stress would develop something like this:

1) 0-->10% Fy as a gradual climb before concrete cracks.
2) 10%-->30% Fy in a shock like step.
3) 30%-->Fy in a gradual climb.

I have no idea about the actual percentages. I just grabbed some numbers for illustration purposes. This is all made substantially more complicated by the fact that flexural behaviour is not characterized by a single crack but a field of cracks. Rebar forces are only at their M/kd -- or M/jd -- values at the cracks. In between, where the concrete shares in the tension resistance, bar stresses are quite a bit lower.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[wijgeng]

Great response KootK. As if this thread hasn't already been beat to death, I will put in my $0.02.

Assuming we are talking about a beam in bending: I would expect you could find the increase (jump) in stress by comparing an uncracked section to a cracked one. In an uncracked section, the concrete and steel would both be carrying tensile stress and, as KootK mentioned, the steel would be carrying more stress than the concrete because the modulus of steel is much higher than that of concrete. Following concrete cracking, (assuming the applied load does not change) the tensile stresses which were being carried by the concrete will now have to be added to the tension in the steel. (Simply adding the stresses from the concrete to the steel isn't exactly correct, but for simplicity it is probably close enough. The actual rebar tensile stress increase would be dependent on many other things such as a change in moment arm as well.) This transfer of stress during cracking would pose a negligable threat to the steel or the bond between steel and concrete because the amount of tension being carried by the concrete itself is much much less than can be handled by steel.

Damage to steel due to rapid stress transfer might be more of something to consider if it was embedded in a material with higher tensile strength than concrete, I am not sure.

Additionally, I would expect rebar embedded in concrete to have a higher tolerance to a brief jolt of load rather than a slowly applied load. Think of trying to snap a piece of Silly Puddy. If you try to tear it quickly it will be able to resist more force than if you pulled it apart slowly. I realize Silly Puddy is more of a viscous material, but the strengths of solid materials such as steel and concrete are also dependent on dynamic loading, correct? Which is why there are specified load rates in ASTM for determining concrete cylinder strengths, etc.