prestressed beam depth of neutral axis

[GoDucks]

I am currently doing a strength design hand check for a 72" Bulb-T. While doing the check for rectangular-vs-T Beam action, I am getting "odd" results for the depth of the neutral axis "c-value" (using equations in LRFD 5.7.3.1.

Using my numbers I get that the rectangular section "c" is more than the depth for T-Beam action, which is counter to what I would expect.

Here are my values:

Aps=7.956 (52 strands)
fpu=270ksi
f`c = 4.35ksi
b1 = 0.832
bf=75in
bw=48in
k=0.28
dp=58.4in

When checking for rectangular beam…..I get c=8.9 in

When checking for T-beam action………I get c=8.5 in


I understand it is not a big difference, it just bugs me that it does not give me results like I expect.

Does this seem odd to you also?
Do you know why I am getting these results?

Thanks for any help that you can provide.

 

[shin25]

Something does not seem right in the information that you have provided. 'bw' I believe is the width of web of bulb-T. Normally, this dimension should be 6" to 9". Also, you did not provide the depth of the deck. Moreover, dp is too small. I think you are not considering the depth of the deck.

 

[GoDucks]

Thanks for the reply...here is the missing info:

Slab thickness = 8in

the "web" is the flange of the Bulb-T = 48", while the "web" is the effective width governed by beam spacing

dp = (beam depth + deck + haunch)-(ycg) therefore..
db = (72" + 8" + 0.5") - (22.1") = 58.4" (falls in draped strand area)

Any other thoughts?

 

[GoDucks]

Error in above post....

line 3 should read....

the "web" is the flange of the Bulb-T = 48", while the "flange" is the effective width governed by beam spacing

 

[shin25]

I have hard time to understand how you are getting the cg of strand group from the bottom of the beam as 22.1". Can you tell me know how did you get this cg?

 

[GoDucks]

Although this "problem" occurs throughout the entire beam, the one that I am primaraly trying to solve falls at the development point of the strand (approx 8' from the end of the beam)

The precast supplier drapes (aka harps) the strand to minimize the prestressed enduced moment near the ends of the beam in an effort to satisfy the service design criterea.

The point that we are looking at is well with the harped area, resulting in the elevated c.o.g. of the strand.

 

[shin25]

I suggest you neglect the strands that are too close to the compression face of the beam.

These strands will have significantly different strain during strength limit than the strands close to the tension face of the beam. I believe PCI also suggests similar recommendation.

Also, since your section is close to the end of the beam, you should consider reduced stress in the strands due to lack of development length.

 

[GoDucks]

I agree....but even if I use a more "reasonable" cog...i.e. center of span...
yc=4.95" for a dp=76"

I still get a rectangular section "c" of 9"
and a T-Beam "c" of 8.7"......

I have went on and it really does not make a difference in the end, just does not feel right

 

[shin25]

It is not 'c' but a=B1*c that defines a rectangular or T action.

 

[GoDucks]

I understand the concept,

in either case, "c" - depth to neutral axis and
"a" depth of Whitney stress block
would be proportionally the same....and the "a" for the T-Beam would be less than that of the rectangular section