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Propped cantilever deflection

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Enhineyero

Enhineyero

Structural
Sep 1, 2011
283
I notice that the calculated elastic deflection at tip of propped cantilever beam is dependent on backspan. Deflection increases as backspan length go up.
deflection at tip of pure cantilever: PL^3/3EI
Deflection at tip of propped cantilever: P(Lc)^2/3EI x (Lb+Lc)


For example I have a 10kN point load on a 2m long pure cantilever 200UB25 beam, deflection = 6mm. On a propped cantilever with a back span of say 8m, deflection = 28mm. Thats more than 4x increase and it doesnt feel right.

Any thoughts on this.
 
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It is true..

The following fig. from Design Info . pci handbook.

beam_overhang_jkjopa.jpg


If you want similar deflection, ( 6 mm in this case, ) you can apply a point load at the span of the back span beam ( X in this case ) to get rotation zero at prop ( R2).. and the cantilever will be fixed ..

More over, you can increase the point load to get zero deflection or upward deflection at the tip of cantilever depending on the applied force at the back span .

You may try and see with superposition.
 
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It's a good catch Enhineyero, a purely fixed cantilever will have less deflection than one with a backspan as you have noticed (there is now rotation at the joint with the backspan that the fixed cantilever beam does not have, increasing deflection).

I recently reviewed a younger engineers calculations for a cantilevered beam deflection and they used the purely fixed beam calculation. We recalculated with the actual backspan condition and we had to upsize the beam to meet our deflection criteria.



S&T -
 
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Oftentimes the “prop” is not a fixed point but rather a beam spanning between columns. This beam deflects and increases that tip deflection significantly.

The same concept applies to a single column cantilevered up to act as a post for a jib crane.
 
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To me that is just a simple span cantilever... A propped cantilever, in my understanding, the rear support is fixed and there is no cantilever on the outside. It's like a cantilever with a simple support at the cantilever end.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik
 
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Yes, that is a simply supported beam with an inset support. The overhanging bit is magnifying the slope at the inset support. A cantilever by definition is encastre at the fixed end, zero slope, zero deflection.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
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Another way of writing it is P(Lc)^3/3EI x [(Lb+Lc)/Lc], so it becomes the fixed cantilever deflection times a ratio based on the spans. This ignores the support deflection mentioned by JLNJ. For UDL, the ratio is [(4Lb+3Lc)/3Lc].

In your case, the span/depth of the backspan is 40, so quite floppy.
 
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Not too often that I disagree with dik and GregLocock, and perhaps they are right, technically. But the beam in HTURKAK's illustration is what I have always called a propped cantilever.
 
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I call this a beam with overhang. Propped cantilever has always meant what Dik says when I've heard it (until now). I avoid the term because why would you call no cantilever a cantilever?
 
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It's OK Hokie... it's not often that I think you're incorrect... [pipe]



It sort of looks like a cantilever with the end propped up. [pipe]

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik
 
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Even if the back end is encastre, the part beyond the roller support is still a cantilever.
 
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20211024_150544_hyhs0g.jpg


Don't know why we have the term 'simply-supported beam' when 'propped unstable structure' could be used.

Better yet: propped cantilever with rotational restraint released.
 
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Hokie, the picture I posted is a propped cantilever. I inferred from your comment that you expect a propped cantilever to have an overhang, but it doesn't. You could have an overhang, but the conventional meaning is prop at the end without overhang.

A simply-supported beam isn't unstable, the same way a propped cantilever isn't a cantilever.
 
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I can also find images on the internet of 'propped cantilevers' with 'overhangs'.

A couple of the most common usages of the word cantilever in structural engineering are cantilevered balconies, and the roof girder system of cantilever and drop-in beams, which was one called the "Gerber system". Neither of these involve an encastre support.
 
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A longer backspan is softer spring, so yes the cantilever rotates more with a longer backspan.


I’ve never heard this arrangement described as propped cantilever. To me propped cantilever is what steveh shows - a perfect cantilever (rigid support), except with a pin support (the prop) at the normally free end.
 
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To me that is just a simple span cantilever... A propped cantilever, in my understanding, the rear support is fixed and there is no cantilever on the outside. It's like a cantilever with a simple support at the cantilever end.
Click to expand...

Didn't expect this post to turn into a discussion of is it called fries or chips.

Agree with Hokie, where I practice it's called a propped cantilever. Must be a local thing.

The overhanging bit is magnifying the slope at the inset support
Click to expand...
This makes sense (particularly for us who studied theory of structures). Was wondering how to explain this to a layman, as it doesnt make intuitive sense.
 
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After explaining to him what a cantilever is, then have him imagine that one end is propped up...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik
 
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I think you can explain the difference in deflection of the propped v. rigid cantilever by looking at only the cantilever region. In one case the support is perfectly rigid and does not rotate. With the back span, the support point support point can rotate. How much the support rotates depends on the backspan and stiffness of the member used. Leave out all the engineering mumbo jumbo.
 
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