huangyhg

cantilever or not?
good morning all.
the uploaded .pdf shows a condition for which i have to review the design. the dbl c5 is being suspended from an existing precast box beam and will support the bridge deck concrete placement.
i maintain that, since the dbl c5 cannot deflection upward between the hanger rods, the design model shown at the bottom is correct. the left hanger rod carries all gravity load.
if one were to assume a support about 1" to the right of the left hanger rod, then the shear between it and the left hanger rod becomes astronomical, as does the tension in the hanger rod.
am i missing anything?

ralph
structures consulting
northeast usa
the left hanger rod will carry all of the gravity load plus the additional load from the c5 bearing against the concrete girder.
you will have a tension reaction at the left rod, and a bearing reaction of the c5's against the girder. the net vertical sum of these reactions will obviously be the gravity load, and the net moment will be the moment in the c5's just to the left of the left hanger rod.
won't the load in the left hanger exceed the applied loads ? maybe it's just something in your terminology that i'm not familiar with ??
it's easy to calculate the moment in the beam at the left hanger. this moment is reacted by the beam pushing up against the existing precast box beam, maybe a triangular distribution is appropriate. that gives you the moment arm of the reacting couple (2/3 the beam overlap), and so the total load in the left hanger.
i agree with eit, the tension in the left hanger rod will actually be more than the sum of p1, 2, 3, and 4.
if the right support weren't tension only, it would have compression reaction, but it's not so the dbl channel bears against the bottom of the concrete beam.
is there some way to verify that the bottom of the box beam is flat enough to allow bearing.? if concave down just enough the system would act more like a simple beam overhanging one support.
but, if the slope of the dbl c5s very very close to (and to the right of) the left hanger rod is zero (it would have to be, as it cannot deflect upward against the bottom of the precast beam), what its real behaviour?
how can one ever achieve a "pure" cantilever?

ralph
structures consulting
northeast usa
rhtpe-
there is no reason to say that the slope is zero at the left rod. the rod will elongate, which will provide some slope. even a truly fixed cantilever is expected to have some moment-rotation response. even if the rod had infinte axial stiffness, it has almost no flexural stiffness, therefore the beam can't be cantilevered from it. if you didn't extend the c5 under the girder then it would be unstable. imagine that instead of this rod, you have a bar coming down with a single, frictionless pin that goes through the c5. i think you would agree that even if the bar were infinitely stiff (axially) and didn't elongate at all that this wouldn't be fixed. this is, for all intents and purposed, what you have.
to draw out the fbd, i would use a pin-pin-cant. i would put one pin at the left rod, the other pin at the resultant of the bearing against the girder. the moment in the c5 just to the left of the left rod is what it is, it doesn't matter if it's fixed or pinned-pinned. that being said, the reaction on the left rod will definitely be higher than the total gravity load.
consider a simple beam with an overhang. the beam between the supports deflects upwards. in your case this upwards deflection is prevented by the support precast box; actually this gives you a more rational basis for the assumed moment reaction (in lieu of my triangular assumption)... the reaction by the precast box could be proprotional to the deflection of the simple beam ... more like a sinusodal distribution; you could also analyze with an elastic support distributed along the non-overhang portion of the beam.
don't foregt that the idealized model will be stiffer than a model that accounts for the anchor rods and bearing.
is there a deflection criteria that needs to be met for the formwork?
rb-
i was intrigued by your last post re: the sinusoidal bearing distribution. i believe this is only true if you have a second pin support where the right rod is. the right rod may be sufficient, but it may not. if, however, that rod is gone and there is no "pin support back there, i don't believe that the upward deflection has the opportunity to develop because of the lack of a single stiff support point, and that the "backspan" will move more like a rigid body and produce much closer to a triangular pressure distribution.
i would simply assume a cantilevered beam with the right support at 0.85d, where d is the distance from the left support rod to the far side of the concrete beam.

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