CCstruct123
Structural
I have encountered a parking structure PT beam restoration where the beam is two continuous spans and fixed at all three supports. I am trying to roughly match my hand calcs with ADAPTS analysis. At this time, I'm specifically trying to match the moment capacity at the exterior ends of the original undamaged structure. This beam is doubly reinforced across its entire section, but at the exterior ends in question there are specifically;
four #9 rebars at the top (negative reinforcement), so 4-square-inch area total, there is 3 inches of clear cover at top.
while there are four #9 AND four #11 rebars at the bottom (positive moment reinf.), 10.24-square-inch total area. 2 layers with 2 inches of clear cover at the bottom.
and lets say im looking at the point along the beam where the centroid of the 26, 1/2-inch diameter PT strands (3.98-square-inch) is 24 inches above the bottom of the beam (the max height of the strands is 26.5 inches at this end so this 24" is more like the face of column)...
this 28-inch high beam is integral with the 7.5-inch slab, making its total height 35.5 inches. The effective flange width is 138 inches while the b[sub]w[/sub] (web width) is 18 inches. 4,000 psi concrete, grade 60 bars, the Y[sub]b[/sub] (centroid of beam) is located 25.94 inches above the base. The f[sub]ps[/sub] of the strands at this end is ~190.1 ksi. Think that should be everything but let me know if im missing something this is all from memory...
Adapt reports a negative moment capacity and also a positive moment capacity. Basically these capacities are the same in both positive and negative moment directions around 1850 kip-ft +/- 30 k-ft. For ultimate loading the secondary moments actually make this area require negative reinf. at the face but positive reinf. very soon after, not to mention the service load cases that consider the balanced PT moment and not secondary. Intuitively you would think we would want more bars up top, but i understand why after secondary moments, but why such a dramatic increase in mild steel on the bottom? Any ways I am mainly just trying to understand how ADAPT is getting these numbers, I got close using the following method but i was actually around 50-70 k-ft off so im wondering if i got lucky and my methods are incorrect or if adapt is just considering some other factors...
They have to be considering the compression rebar in both directions, or else your capacity numbers are way off from theirs, but this is where my main question comes in... how do you handle a beam that has more compression rebars than tension??... without considering compression rebars, for whitney stress block "a" I was running...
a = (f[sub]ps[/sub]*A[sub]strand[/sub] + f[sub]y[/sub]*A[sub]s[/sub]) / (0.85*f'c*b[sub]w[/sub])
For a non-PT beam, assuming we are in the easier case where both tension and compression steel yields, finding little a is just.. a = (f[sub]y[/sub]*(A[sub]s[/sub]-A'[sub]s[/sub])) / (0.85*f'c*b[sub]w[/sub]).. BUT THIS GIVES YOU A NEGATIVE "a"... so is this even allowed?
COMBINED WITH THE PT STRANDS HOWEVER THIS JUST GIVES YOU A SMALLER "a"...
a = (f[sub]ps[/sub]*A[sub]strand[/sub] + f[sub]y[/sub]*(A[sub]s[/sub]-A'[sub]s[/sub])) / (0.85*f'c*b[sub]w[/sub])
IS THE COMBINATION OF THESE FORMULAS ALLOWED IN THIS WAY??? IF SO WOULD I ALSO BE ABLE TO COMBINE THE M[sub]n[/sub] equations to be
M[sub]n[/sub] = f[sub]ps[/sub]*A[sub]strand[/sub]*(d[sub]strands[/sub]-a/2)+*f[sub]y[/sub]*(A[sub]s[/sub]-A'[sub]s[/sub])*(d-a/2)+f[sub]y[/sub]*A'[sub]s[/sub]*(d-d')
Is there something about the slope of the PT strands that i'm not considering? Or something(s) else i'm missing that adapt is considering. I'm not super concerned with matching ADAPT exactly but more concerned if my hand calc process is conceptually correct! AND IF I CAN APPLY THE SAME TECHNIQUE TO FIND THE MOMENT CAPACITY IN THE OTHER DIRECTION??
four #9 rebars at the top (negative reinforcement), so 4-square-inch area total, there is 3 inches of clear cover at top.
while there are four #9 AND four #11 rebars at the bottom (positive moment reinf.), 10.24-square-inch total area. 2 layers with 2 inches of clear cover at the bottom.
and lets say im looking at the point along the beam where the centroid of the 26, 1/2-inch diameter PT strands (3.98-square-inch) is 24 inches above the bottom of the beam (the max height of the strands is 26.5 inches at this end so this 24" is more like the face of column)...
this 28-inch high beam is integral with the 7.5-inch slab, making its total height 35.5 inches. The effective flange width is 138 inches while the b[sub]w[/sub] (web width) is 18 inches. 4,000 psi concrete, grade 60 bars, the Y[sub]b[/sub] (centroid of beam) is located 25.94 inches above the base. The f[sub]ps[/sub] of the strands at this end is ~190.1 ksi. Think that should be everything but let me know if im missing something this is all from memory...
Adapt reports a negative moment capacity and also a positive moment capacity. Basically these capacities are the same in both positive and negative moment directions around 1850 kip-ft +/- 30 k-ft. For ultimate loading the secondary moments actually make this area require negative reinf. at the face but positive reinf. very soon after, not to mention the service load cases that consider the balanced PT moment and not secondary. Intuitively you would think we would want more bars up top, but i understand why after secondary moments, but why such a dramatic increase in mild steel on the bottom? Any ways I am mainly just trying to understand how ADAPT is getting these numbers, I got close using the following method but i was actually around 50-70 k-ft off so im wondering if i got lucky and my methods are incorrect or if adapt is just considering some other factors...
They have to be considering the compression rebar in both directions, or else your capacity numbers are way off from theirs, but this is where my main question comes in... how do you handle a beam that has more compression rebars than tension??... without considering compression rebars, for whitney stress block "a" I was running...
a = (f[sub]ps[/sub]*A[sub]strand[/sub] + f[sub]y[/sub]*A[sub]s[/sub]) / (0.85*f'c*b[sub]w[/sub])
For a non-PT beam, assuming we are in the easier case where both tension and compression steel yields, finding little a is just.. a = (f[sub]y[/sub]*(A[sub]s[/sub]-A'[sub]s[/sub])) / (0.85*f'c*b[sub]w[/sub]).. BUT THIS GIVES YOU A NEGATIVE "a"... so is this even allowed?
COMBINED WITH THE PT STRANDS HOWEVER THIS JUST GIVES YOU A SMALLER "a"...
a = (f[sub]ps[/sub]*A[sub]strand[/sub] + f[sub]y[/sub]*(A[sub]s[/sub]-A'[sub]s[/sub])) / (0.85*f'c*b[sub]w[/sub])
IS THE COMBINATION OF THESE FORMULAS ALLOWED IN THIS WAY??? IF SO WOULD I ALSO BE ABLE TO COMBINE THE M[sub]n[/sub] equations to be
M[sub]n[/sub] = f[sub]ps[/sub]*A[sub]strand[/sub]*(d[sub]strands[/sub]-a/2)+*f[sub]y[/sub]*(A[sub]s[/sub]-A'[sub]s[/sub])*(d-a/2)+f[sub]y[/sub]*A'[sub]s[/sub]*(d-d')
Is there something about the slope of the PT strands that i'm not considering? Or something(s) else i'm missing that adapt is considering. I'm not super concerned with matching ADAPT exactly but more concerned if my hand calc process is conceptually correct! AND IF I CAN APPLY THE SAME TECHNIQUE TO FIND THE MOMENT CAPACITY IN THE OTHER DIRECTION??
