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# Steel stress in reinforced concrete bridge deck

## Steel stress in reinforced concrete bridge deck

(OP)
All,

I have been trying to calculate f_s, the tensile stress in the reinforcement for this concrete deck design. I am trying to determine my required crack control spacing per AASHTO LRFD codes, which requires the tensile stress in the steel at the service I limit state. I have tried doing this like in a concrete beam (which is how this slab was designed, as instructed by the local DOT) but i'm getting a stress around 766 KSI, which seems unreasonable. This method basically involves finding the strain the steel based on similar triangles, utilizing the strain in the concrete and distance to the neutral axis. Strain can then be converted to stress using the Modulus (29,000 KSI).

Are there equations anyone is aware that will calculate f_s?

### RE: Steel stress in reinforced concrete bridge deck

If it's a concrete deck on steel girders, You should be able to use Moment / Section modulus for the composite section (deck+girders) at the top of the deck, but remember to transform it back to its actual volume (divide the stress on the transformed section by the modular ratio) to get the actual stress. It should work the same for RC girders, I think. I'm not sure how to calculate it for prestressed girders.

Rod Smith, P.E., The artist formerly known as HotRod10

### RE: Steel stress in reinforced concrete bridge deck

BridgeSmith - I may be wrong but I think you are talking about stress in reinforcement in the deck parallel to the girders via composite deck-beam behavior while the OP may be talking about stress in reinforcement perpendicular to the girders (i.e. deck span direction).

Am I wrong here?

### RE: Steel stress in reinforced concrete bridge deck

(OP)
BridgeSmith and Jae,

I was in a hurry in creating this thread so I may not have been clear.

This is a doubly reinforced slab. Bottom Transverse reinforcement will carry the positive moments between girders and top transverse reinforcement will carry negative moment over girders. I need to calculate the stress in the transverse reinforcement for both positive and negative moment, aka top and bottom transverse steel. I have both positive and negative moments already calculated according to the Service I limit state

Hopefully this clears things up

### RE: Steel stress in reinforced concrete bridge deck

You may be right, JAE.

I'm not sure what the OP is referring to, really. We don't check the crack control provisions for our concrete decks. I was thinking of the stress checks for the 1% reinforcement requirement where the stress in the concrete exceeds 0.9fr (fr = rupture stress = .24 f'c1/2).

BaileyW, if you are calculating the stress based on a strip of the slab spanning between the girders, and you're getting a stress that high, I suspect you haven't applied the distribution width to the wheel load. You typically engage about 11 feet of the deck length to resist a wheel load.

If you read the commentary for the empirical deck design provisions, you'll discover that the full-scale testing concluded that concrete slabs on girders don't fail in flexure, anyway. Apparently, there's considerably more horizontal arching action than was thought, so the wheel load is distributed over a much wider area than has been assumed. The actual failure mode for these decks is punching shear, at a load around 5 times the HS-20 (HL-93) wheel load.

Rod Smith, P.E., The artist formerly known as HotRod10

### RE: Steel stress in reinforced concrete bridge deck

(OP)
BridgeSmith,

Thank you and Jae for the help.

I reached out to an old professor of mine and he pointed at my disappointing error.

By using the method I mentioned, I was essentially calculating the stress in the steel AT FAILURE. This is why my numbers were so severely skewed, because by assuming a concrete compressive strain of .003, that would create a massive load which doesn’t actually exist. By simply using the most basic of mechanics of materials equations f = my/I, I found my answers.

Thank you all for the help, I’m a new user but will frequent this forum whenever I find myself stumped.

### RE: Steel stress in reinforced concrete bridge deck

You shall check if the extreme fiber has exceeded the allowable tensile stress or not, then determine either My/I, or My/Itr is appropriate in calculating the steel stress.

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