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Cantilever or not?

Cantilever or not?

Cantilever or not?

(OP)

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

RE: Cantilever or not?

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.

RE: Cantilever or not?

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.

RE: Cantilever or not?

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.

RE: Cantilever or not?

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.  

RE: Cantilever or not?

(OP)

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

RE: Cantilever or not?

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.

RE: Cantilever or not?

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.

RE: Cantilever or not?

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?

RE: Cantilever or not?

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.

RE: Cantilever or not?

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.

RE: Cantilever or not?

Agree with spats, for design purposes.  I prefer to call this a propped cantilever.  The only "true cantilever" is encastre, with an infinitely stiff support.

RE: Cantilever or not?

I believe spats is being unduly conservative.  It is a cantilevered beam with a tieback of d.  If the moment at the left hanger is M, then the uplift at the right edge of the beam is M/d and the tension on the left hanger is P1 + P2 + P3 + p4 + M/d.

BA

RE: Cantilever or not?

SEIT ... it was only a thought-du-moment ... from the OP's sketch it doesn't look like there's a continuous connection with the precast box.  assume there's a 0.001" gap, then the beam would initially deflect like a simply supported beam, and bear up against the support and the new reaction (with the precast box) would relieve the hanger reactions.

IMHO, BA's approach is possibly unconservative for the left hanger load, 'cause he's maximised the couple arm (therefore minimised the couple).

also i think we're over-reacting to the word "cantilever".  in my lexicon, a cantilever is distinguished by developing a moment that reacts the applied loads, having zero slope at the support.  there are few true cantilevers, but many close approximations.  in this case we have a beam, with an internal moment due to the applied loads, and a redundant support ... how does the beam interact with the pre-cast box ?  the hangers and this distributed reaction to the box beam react the applied loads (by the equilibrium equations).  

maybe the OP is concerned about the deflections of the beam (i've been focusing on the reactions).  in which case, spat's post gives an approach for estimating the slope of the beam at the left hanger.  another idea might be to look at the extension of the left hanger due to it's reaction.  now you've got a gap between the beam and the pre-cast box and so you've got to adjust the bearing surface, etc.

RE: Cantilever or not?

If the left hanger were pretensioned greater than P1 + P2 + P3 + P4 + M/d, then the channels would always remain smashed against the precast beam.  Then wouldn't the slope be zero and the left side be a true cantilever?

RE: Cantilever or not?

BAretired,

I'm not being overly conservative. The resisting couple is left rod tension balanced against concrete compression on the bottom of the beam. The centroid of the compression area is approximated based on a singley reinforced concrete beam analysis. Maybe 0.9d is OK, but not the full d.

RE: Cantilever or not?

RHTPE,

An interesting question for which you have had a surprising variety of answers.

In order to answer this we need to step back to first principles.

The loads on a cantilever induce a shear force and a moment in the beam.

In order to resist this, a classic cantilever support has a vertical reaction opposite to the shear force and a moment reaction opposite to the applied reaction.

Now, for your situation:
As the face of the support is not encastre and cannot resist moment at the face then it must resist this moment by a push/pull couple and therefore the reaction on the rod is always going to be greater than the shear force alone.

As you have surmised, it will bear on the underside of the concrete beam, but where will this occur.

The rod will deflect due to the reaction, but the section of beam under the concrete will be sloped from this deflection anf will be curved due to the bending moment from the cantilever. This will give you a set of simultaneous equations to calculate where the steel beam touched the underside of the concrete.

Add on sufficient length for bearing and you have your lever arm.

Alternatively you can just assume that at ultimate limit state the rod will deflect sufficiently that this intermediate bearing will not be an issue. In this case you would design it like a conc beam or a base plate.  

RE: Cantilever or not?

PMR06 makes a good suggestion, regarding preloading the hanger.  we can quibble about M/d, M/(d/2), M/(0.9*d), ... and about how to ensure the actual preload exceeds the calculatd reaction; but that's all just "grist for the mill".

RE: Cantilever or not?

If you insert a shim between the channels and the box near the right hanger rod, this would ensure that the couple is the distance from the left hanger to the shim.  Then the additional tension is surely M/d.

RE: Cantilever or not?

I guess the answer is variable according to the axial stiffness of the left suspender.  If it is axially stiff, the channels are not able to flex upward between hangers, so the right reaction moves very close to the left rod.

If the left support is axially flexible, the channels can flex upward and the right reaction moves very close to the right rod.   

BA

RE: Cantilever or not?

and the beam would become a simply supported beam, with an overhang.  and this'll have bigger deflections (and smaller reactions) ... depends on what's important to you

RE: Cantilever or not?

It's amazing how this seemingly simple assembly is so difficult to analyze.
The spring stiffness of the threaded rods, the bearing stiffness of the concrete to keep the backspan from arching up, the stiffness of the beam, the pretension (clamping) loads in the bolts, etc.

Seems the easiest solution is to have the contractor install two bolster pads (timber or steel) adjacent to the left and right rods and then you have a clearly defined backspan.

The other alternative is to load test the assembly.

Also, the aluminum shoring joists will also distribute load to adjacent undersung beams based on spacing.  We don't know all the information concerning the assembly so it is difficult to fully comment... i.e., spacing of underslung carrier beams, total load imposed, size of clamping rods, etc.

The contractor probably uses this detail all the time and probably would think we're all nuts for questioning it anyway.

Just one more comment... BA may not be that off by stating to use the full backspan, since, the clamping force in the rods may actually cause the underslung beam to camber downwards  between the left and right fixings and the canteliver to camber up initially, just a little more kindling to add to the conversation.

RE: Cantilever or not?

(OP)

Okay folks, I caved and revised the detail to better match a sensible design model.  Please see the sketch.  The left shim between the top of the channels and bottom of concrete beam is to be removed prior to placing concrete on the deck - it is only there as a erection aid.

If I had the resources, I'd love to do a load test to determine failure mode.

To respond to some of the comments:
-  Deflection is not of concern, either as a "pure" cantilever, or as a simple span + cantilever.
-  Realistically, the contractor's guys will no doubt tighten the S#%& out of both hangers, thus eliminating rod elongation as a concern IF it were a "pure" cantilever.

It's the simple ones that we sometimes look act and realize that it ain't always so simple.  If we only knew as much as we think we do ....
 

Ralph
Structures Consulting
Northeast USA

RE: Cantilever or not?

Maybe the shims should be moved to miss the chamfer.

BA

RE: Cantilever or not?

One of the very first thing I learned when I was just starting out as a structural designer is to avoid any hanging connection whenever possible for primary structural elements. Hanging connections where the bolts are in tension should be a last resort type of thing that needs to be scrutinize thoroughly. It's very easy for the fabricator to fabricate those bottom plates with an oversized hole and you'll be in trouble.

Maybe a better connection is a steel angle bolted or epoxied to the sides of beam 1 to pick up the channels.

RE: Cantilever or not?

I didn't realize this is just a temporary structure so my concern might not be valid at all.

RE: Cantilever or not?

what's the moment on the left hand end ?  sure there's some structure shown, but isn't there a down load associated with it ?  so the (what looks like) two fasteners attached to the beam react load and moment ??

"it is only there as a erection aid." ... "it" refers to the shim or the beam ?

IMHO, the shims at the hangers only simplfy the analysis; i think the guys building this are going to say "wtf?".  are there alignment issues ?? does the beam have to be at a certain height to do it's job ?  could this be a reason for shims ??

also IMHO, don't "cave" to our opinions.  we could be a bunch of lunes. if you accept our advise, that's different "good points guys, things i hadn't consiered" but not "ah geez guys, i'll do it your way 'cause you'll only carp endlessly if i don't".

RE: Cantilever or not?

I agree with rb1957's assessment. I think everyone is over-analyzing this with the "beam can't deflect up" arguement. All you need is a resisting couple to make the mechanism stable. The left rod balanced against the channels pressing against the bottom of the beam provides this. Using shims concentrates the compression on a smaller area, which may/could overstress the concrete in bearing. I think it's much better being tight against the bottom of the beam, and distributing the load.

This can't be as complicated as everyone is making it. As engineers, we make design decisions every day based on assumed mechanisms and structural models. As long as the mechanism exists, it's OK to use it, even if it won't necessarily act exactly the way you assumed. If you design your assumed mechanism properly, it can't fail.

On the other hand, I'm surprised no one is concerned about torsion in the concrete beam.

RE: Cantilever or not?

My mentor here used to say to me: "Don't spend a lot of time to solve the problem, just eliminate it."  With the channel flush up against the bottom of the box, the system is very difficult to analyze.  In fact, I couldn't do it.  One simply needs to size a shim so it doesn't overstress the concrete in bearing, and you have a system that's easy to analyze, build, and defend.  

RE: Cantilever or not?

(OP)

Sometimes we fall into an over-analyzing trap.  For this condition, the principles concerns are:

1.  Falsework safety.  Will this temprary structure safely sustain all anticipated loads?  Of particular concern is the tension load in the left hanger rod, as it will likely exceed the vertical loads on the cantilevered end of the dbl C5s.

2.  Falsework performance.  Primarily deflection that will be reflected in the permanent structure - the cast-in-place bridge deck overhang.

Both of the above are directly affected by the actual behaviour of the dbl C5x6.7s.  Certainly modeling the C5s as a "pure" cantilever will give better deflection & stress numbers than will a model as a simple span + cantilever.  Our role as engineers is to ensure that our analysis & design model can constructed and will behave as modeled.

Yes spats, torsion could be a concern.  Analysis of that issue needs to rest with the bridge designer, not necessarily the falsework designer.  But what is not clearly reflected in my sketch is that the load applied to the right edge of the precast beam by the stay-in-place metal deck will mostly offset the CCW rotation imposed by the suspended falsework.
 

Ralph
Structures Consulting
Northeast USA

RE: Cantilever or not?

i don't understand your terminology "simple span + cantilever"

as drawn (the 2nd time around) the beam is a simmply supported beam.  as drawn originally (and what prompted yr question in the 1st place ... aren't you sorry now !?) i think it is a cantilever, with a distributed reaction along the bearing face.

RE: Cantilever or not?

rb1957,
In terminology used in buildings, it should be called a propped cantilever.  A simple beam (or simple span) has a pinned support at one end, and a roller at the other.

miecz,
I strongly, strongly endorse the argument made by spats.  Analyze the right support anywhere you want to, but the beam will deflect less if placed hard against the concrete soffit.  I don't think that violates the principle which your mentor was trying to impart.

RE: Cantilever or not?

odd and odder ... the original sketch looks nothing like a proped cantilever to me, the later one "could" depending on what's happening on the left end of the beam ...

RE: Cantilever or not?

hokie66-

Quote:

analyze the right support anywhere you want to
Where exactly would you analyze it?

RE: Cantilever or not?

Actually a propped cantilever has one built in support and one simple support (Remember the Fixed End Moment Equations), basically it is a cantilever with the free end propped.

According to the AISC Beam Diagrams & Formulas they just call it a beam overhanging one support.

But now we are getting into semantics, have you ever done a structural plan and noted the overhanging end as a CANT. on the drawings.  So in practice I think it is understood that it is considered a cantilever.

A true cantilever is a perfect assumption anyway and may not actually be attainable in practice, since the bedding material will most likely deform somewhat and allow a slight rotation and shift the reaction away from the true face of the support, even if ever so slightly.

I think the OP was looking for a consensus of opinion or confirmation regarding the modeling assumptions.

I think one of the predicaments that we as structural engineers have to deal with is that we (often) don't get to field test and prototype our designs. They have to work right out of the box based on our best educated guess and hope you didn't miss anything (this becomes more precarious when designing something that there aren't many documented and peer reviewed procedures for or when the assembly deviates from typical tried and true practice).

I don't think you can just arbitrarily pick a resisting moment arm out of your hat and hope to sleep at night when they are loading the formwork with concrete, MEN and materials and hope for the best.

I do a lot of work with temporary as well as permanent structures and I find the temporary structures a lot more challenging at times because they have to be light, easy to carry, easy to install, easy to disassemble and they typically will actually carry the full design loads (which again may not be well documented).

Whereas with permanent structures you can often engineer the Sh** out of it since they will be using cranes and other heavy equipement to safely place the items (or working off of the temporary structure) and then weld/bolt the hell out of it so it doesn't go anywhere, and often they carry less than 50% of the design loads anyway.

RE: Cantilever or not?

miecz,

I said I agreed with spats, so .85d.  But I would be happy with anything in the right half of the beam.  .5d is probably overconservative, 1.0d is unconservative.

RE: Cantilever or not?

MaddEngineer,

Thanks for gently correcting me about the definition of a propped cantilever.  You are indeed right.  Must have been a senior moment, or two.

RE: Cantilever or not?

Ralph, looking at what you have drawn, I think your approach is reasonable. While internally the waler has fixity at the "cantilever," you don't really have absolute fixity at the support, even when the carpenters wail on the bolts of the hanger rod to get it tight.

So a pin-pin analysis seems reasonable, especially in light of the addition of the shims. From a practical standpoint, the shims make sense as it is likely the beam soffit and the waler will not have identical profiles.

Gut check says while shoring loads often approach or exceed design loads, the bridge here likely has a much higher service capacity that what you are applying and for this type of construction, I would anticipate some understanding on the designers part about methods of construction, but that is a fair point to verify.

As for the location of the other shim, I prefer my hold down reaction to be spaced at least as far out as my last applied load. Easier said than done here, but why not check where it can be and come up with a minimum spacing from the rod carrying the load. If the loads/capacities are ok with the shim at 0.75 dist to load, then so be it. Hopefully your load at the shims is low enough for scrap lumber to be used and avoid steel plates.


Sorry to be slow to respond - I was in Honduras when I got your note.

Daniel

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