Long Strands Sag Calculation

[Dinosaur]

It is my understanding that precast prestressed girder plants strive to cast several girders in one long bed for economy. It is very sensible to me because one bit of labor to get the initial tension into the strands serves the requirements of many girders. However, this brings up a question concerning the precautions necessary to insure sag in the strands doesn't become significant or is addressed in some manner during forming and casting the girders.

Do the end forms provide support to the strands that would reduce sag within a beam? Or, are the holes in the end forms too generous (much greater than the diameter of the strand) to be relied upon for this purpose?

For example, according to my calculations, pulling a 270 ksi strand to 0.75 GUTS with 0.153 in^2 area and limiting the sag to no more than 1/8 inch requires supports no farther than 70 feet apart. This is interesting if the end forms are not comparatively tight to support the strand or other measures are taken.

Of course, this is also assuming the only load acting on the strands is the strand's self weight. In my experience the resteel is tied to the strand and supported this way. This causes a dramatic increase in the sag of the strand.

Also of interest (to me, anyway) is the impact of temperature on the problem. Assuming E=28,000 ksi for strand and the strand is locked off at each end appropriately, a 25 degree (F) change in temperature (typical of a daily swing without any dramatic weather event) changes the strain 0.000163, for a stress of 4.55 ksi. This is 1.7% of GUTS for a 270 ksi strand. It may be that we should consider the impact of temperature in establishing tolerances for this stuff.

Has anyone here looked at the problem of sag in the strand and come to any conclusions or have any recommendations? Thanks.

 

[MichSt]

Very interesting thoughts, but I have never heard of this being a problem. How did you calc the sag in the strand? It doesn’t seem like a tensioned strand could sag that much.

You may want to call up some local precasters to discuss.

 

[Dinosaur]

According to Beer & Johnston, 3rd ed. Statics, Ch. 7 p.290, for parabolic cables y = [w (x)^2]/[2 x To] where:
y is the vertical position along the cable
x is the horizontal position along the cable
w is the weight per unit length of the cable
To is the tension in the cable
setting y = 0.125", w = (0.52 plf / 12 in/ft), x = span/2, and To = 0.75 x GUTS = 31.0 kips (All values for 1/2 in. dia. grade 270 7-wire strand) the only unknown is span. Span = 70.48 feet. So a 0.75 GUTS pull supported at 70 feet will result in 1/8 inch sag in a grade 270 half-inch dia. 7-wire strand.

I agree that it sounds like a lot when you think of the forces and all that, which is why I posted my query. If the bed is only pulling for a TYPE III 70 ft. girder, 1/8 inch is no big deal. But if you are casting several in one big long bed, the sag can start to be something significant.

I checked into our construction specs, and for Bulb-T girders the strand group is permitted a 1/4 inch tolerance in position. One-quarter inch is the 75% GUTS sag for a 100 foot pull. If you're casting more than 100 feet in a bed, you have to have supports or really tight bulkheads or both. The last precaster I visited had supports near mid-span that were suspended from above, however, the embeded steel was not epoxy coated or otherwise protected in accordance with the specs. I will be on the lookout as I make my rounds to our suppliers.

 

[civilperson]

In a four hundred foot bed. Dividers are placed at the location for finished length of the double tee or girder. The normal length is approximately 135 foot or less. These intermediate dividers support and locate the strands. Interior supports, (inverted harps), which depress the strands at third points or at mid-span are some times used. The change in length for the strand is used to prestress the steel, from 2000 pounds set to 70% to 80% of ultimate. The temperature increase in length is in both conditions, initial and stressed. The gauge pressure is compared to calculated increase in length and usually agree within 3/8",(which is the set distance for the chucks).

 

[spagetti]

just a couple thoughts,
First is that use of a long form is to allow for multiple members to be casted at the same time, between each member is a header, placed to achive the desired lengths. If the members are long enough that sag would become an issue you would probably have insufficient force on the strand and would not support the designed load because you would have to over yeild the stand to remove the sag. On those longer members harp points are used thereby effectively reducing the distance between support points and eliminating any potential for sag.
The second, is temperature. when calculating thermal effect, you must first know if the form is self stressing or abuttment. Self-stressing beds require no temperature adjustment. as they realize the same thermal effects as the strand, in this instance, bed shortening is part of your calculation. With abuttments however, thermal effects must be calculated. If the difference between, the ambient temperature at the time of stressing is 25 deg. or more than the temperature of the concrete being placed, than an adjustment of 1% per 10 deg is required.
Two issues to remember are if you are close it will be acceptable, where I work we calculate elongation in the morning, possibly 2 to 3 hrs before the bed is actually going to be stressed, if the ambient temp., we think will be 40 deg at the time of stressing and the concrete temp we think will be 80 deg. we calculate based on those assumptions. if the actual ambient temp at time of stressing is actually 50 deg, and the concrete actually comes out at 85 degrees, we are still good because there is less than a 25 deg differrence between our assumptions and actual.
Another issue to keep in mind, where I work it is not unheard of to be stressing the bed with an ambient temperature of 10 deg. and when required we add live steam to the mix to maintain an 80 deg. concrete temp when it is placed. when you are pulling the tendon to within 75% of yeild and have to add in your adjustment for temperature it could be possible to over yeild the strand.
I hope this has helped