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# Tension Deck Steel for Negative Moment Capacity

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jachekal
Tension Deck Steel for Negative Moment Capacity

I have be doing some work in PGSuper and have come across some results that seem a bit strange. I am checking the negative moment capacity of some girders and am a bit confused about the amount of deck steel that is being calculated based on how it is defined. I have created 2 models which are identical except in the way they define the deck reinforcing. One model uses the option of defining steel as a bar size and the spacing of the bars. The other model uses the lump sum input option for the deck steel. When I compare the two models, I get much more tension force in the deck steel out of the model that uses the bar size and spacing input compared to the tension force in the negative moment capacity from the model that uses the lump sum input (the lump sum model tension force in the negative moment calculations matches what I would expect to see). Based on the inputs I gave the models I would expect to see the same steel area therefore the same tension force in the deck under negative moment for both models. I am not quite sure what is going on between the differences between the two models. Are there any known issues with the way that PGSuper calculates the deck steel areas or perhaps could you tell me if I am using the inputs for the deck steel incorrectly? I have included a pdf which has a short explanation of the problem with supporting calcs.

Additionally in the help documentation regarding this there is an example given:
"For example, in the image below you will see that for the Top Mat there are #6 bars at 18 inches and 0.18 in2/ft. The total reinforcement in the top mat is 0.68 in2/ft."
I would expect the result of this example to be 0.47 in2/ft (coming from 0.44 * 12/18 + 0.18).

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Rick Brice
Thanks for the great question

Thanks for the great question. First, the documentation you sited does contain a typo. The correct value is 0.473 in^2/ft. The same example calculation is given for input dialog help and has it correct. See https://www.wsdot.wa.gov/eesc/bridge/software/Documentation/PGSuper/6.1/.... I'll get the documentation corrected.

The deck reinforcement input for the two models you provided are very different. This is the cause of the different moment capacity results.

I'll illustrate based on the reinforcement at Pier 2.

From the Details Report, Section Properties table, the tributary width is 83"

For the "Lump Sum Steel" example the reinforcement is:
Bottom Mat = (0.233 sq in per ft)*(83/12) = 1.612 sq in
Top Mat = (0.29 sq in per ft)*(83in/12) = 2.006 sq in

For the "Spaced Reinforcing" example the reinforcement is:
Bottom Mat = #5 @16"
83"/16" = 5.2 -> 6 bars
6 bars * 0.31 sq in = 1.860 sq in

Top Mat
#5 @ 21" ->83/21 = 3.95 -> 4 bars : 4 *0.31 = 1.240 sq in
5 sets of #8 bars at 42" -> 83/42 = 2 bars : 5(2*0.79) = 7.90 sq in
1 set of #8 bars at 84" -> 83/84 = 1 bar : 1*0.79 = 0.79 sq in
(0.113 sq in per ft)(83/12) = 0.782 sq in
Total 1.240 + 7.90 + 0.79 + 0.782 = 10.712 sq in.

jachekal
Richard,

Richard,

Thank you for looking at this, however I still would like to ask about this further. The comparison I was making was actually for Girder D over Pier 3 simply to isolate the problem (which I believe I forgot to mention so apologies for causing any confusion) which has supplemental negative moment reinforcing over the pier in the lump sum model which you left out of your calculations in your email. I am going to redo the calculations you presented for Girder D over Pier 3. Note Girder D has a b_eff of 84 inches:

For the “Lump Sum Steel” example the reinforcement is:
Bottom Mat: (0.233 sq in per ft)*(84/12) = 1.631 sq in
Top Mat: (0.29 sq in per ft)*(84/12) = 2.03 sq in
Supplemental Over Pier: (1.016 sq in per ft)*(84/12) = 7.112 sq in
Total = 1.631 + 2.03 + 7.112 = 10.773 sq in

Spaced Reinforcing:
Bottom Mat: (84/16) = 5.25 bars
5.25*(0.31 sq in) = 1.628 sq in
Top Mat:
(84/21) = 4 bars
4*(0.31 sq in) + 0.113 sq in/ft * 84/12 = 2.031 sq in
Supplemental Over Pier:
4 Sets of #8 bars @ 42”
(84/42)*4=8
8*(0.79 sq in) = 6.32 sq in
1 Set of #8 bars @ 84”
(84/84) = 1 Bar => 0.79 sq in
Total = 1.628 + 2.031 + 6.32 + 0.79 = 10.769 sq in.

It can be seen that the two different models have nominally the same amount of reinforcing which for 40 ksi steel should lead to a tension force in the deck of (10.8 sq in)*(40 ksi) = 432 kips.
The problem is when I look at the tension force in the Negative Moment Capacity Details in the Spaced Reinforcing Model over Pier 3, it tells me that there is 610 kips.
I am having a difficult time understanding where the extra 40% of tensile force is coming from. Could you take another look at this? Let me know if there is something I am misunderstanding.