(Hogging) deflection limit?

[drile007]

I'm wondering if traditional rule for deflection limit (L2/150) apply in the case of "hogging" deflection under cantilever (w2)?

Thank you in advance

 

[csd72]

A we still do not have any specific information on this beam then I will extrapolate on the general information I have already given.

In most countries deflection limits are not mandated as the building codes are generally limited to life safety. Anyway, if a code book could cover everything needed to design a building then we would not need a university degree.

But thats another topic.

Deflection is a very specific phenomenon, there are situations where the standard l/d rules apply but there are also situations where it is the raw deflection that matters regardless of span (try designing a wind post that cantilevers from the floor and stops 200mm below the slab above and you will understand this) there are also other situations where it is the curve of the beam that matters rather than the actual deflection value.

There are also time dependent issues too.

We have no idea what applies in your particular situation.

 

[JStephen]

So if you stand out on that balcony, and someone walks across the inner part, does it bounce the balcony up and down? That could be a bit unnerving.

 

[drile007]

rapt & csd72:
My intention was not to open a debate with specific data. I just want to hear your general thoughts about the problem...and I did...really appreciate them...thanx again!
Why general? To apply general conclusions to various examples, materials,etc.

csd72 just mentioned the time dependant issue! I’m wandering that too. As we know the L/XXX limits are tied to long term deflections which can we approximate with scaling elastic ones (concrete, wood). OK, but what happened under the cantilever (described in my first post)? We scale elastic deflections in upward direction...is that OK? I become a little confused! The only load which can act in that region is self weight…and it acts downward!?

 

[Lion06]

wannabe-

There are two things contributing the the rotational stiffness of the cantilevered beam at the support. One is the rotational stiffness of the backspan, which is a function of EI/L, so as L gets longer the rotational stiffness gets smaller. The other is the rotational stiffness of the support (column, wall, or whatever it happens to be) if it's detailed to behave that way.

In the end, you will get a general flexural deflection (Pl^3)/(3EI), but you will also get a deflection from rigid body rotation due to the rotation of the beam at the support (which is due to the rotational characteristics of the backspan and support (if appropriate)). A modeling program like RISA or RAM Elements will obviously take both into account in doing the analysis, but just know there is more than a simple cantilevered beam deflection that goes into it.

 

[wannabeSE]

SEIT,

I will try it in Elements at work tomarrow. The diagram in the original post depicts simple supports with no fixity and a uniform load on the backspan with no loads on the cantilever. Then I assume that the back span is fixed, say 10 ft, and the cantilever length is variable from 2" to 20'-0". Won't a uniform live load on the backspan cause the same rotaion at the supports despite the variable cantilever length?

 

[BAretired]

Yes, if there is no load on the cantilever, the rotation, [θ] = wL₁³/24EI at each end of the backspan where w is the uniform load per unit length. The upward deflection of the end of the cantilever is [θ]*L₂ neglecting beam dead weight.

If there is no load on the cantilever, why is it there? And why should anyone care how much it lifts up?

BA

 

[Lion06]

wannabe-

As BA notes, the self weight of the cantilever (which could be significant if it's reinforced concrete) will affect the rotation at the support, but you're right if you neglect self-weight.

BA-

My first thought was that the cantilever tip was supporting the building envelope - for which I would care about upward deflection. It sounds like that is not true, though. I would still care about upward deflection - I wouldn't want someone to be uncomfortable walking out on a balcony because it's sticking up in the air some amount that is visually unsettling.