Patterned loading on cantilevered beams

[skimboard20]

I have recently been designing some cantilever beams, and have been thinking more and more about a conservatively enveloped design for cantilevers. My question in short is, to what extent is it standard practice to pattern loads on a given beam in order to achieve the worst case shear/moment demand or deflection?

I have attached a simple example with two load cases: 1) dead and live load across the full length of the beam, 2) dead and live only on the back span on the beam. Case 2) yields the worst case for deflection (as with any cantilever beam, the load on the cantilever counteracts the deflection of the back span.

Obviously this only gets more complicated as you introduce more loads, overstrength factors, varying cantilever lengths, etc. I am trying to keep this post as general as possible, and maybe I'm just looking for some other engineer's opinions on how they approach an envelope design for a cantilevered beam.

To what extent should loads be patterned?​

Should you pattern loads within a load combination?​

For example, cantilevered beam carries D, L , S. One case: D+L+S along full beam. Another case: D+L+S along only back span. Another case: D+L along full beam, S only at cantilever ... and so on until every single combination/pattern is exhausted.​

I appreciate anyone's insight on their approach.

Thanks!

 

[MIStructE_IRE]

I don’t see why you would not include the obvious load combination - party on the balcony and no one inside!

 

[Agent666]

Design is looking at every combination, no matter how inconceivable you think it is. People/nature has a way of finding out and demonstrating the consequences otherwise.

Most codes have words to the effect of requiring you to look at the most adverse loading condition for each and every element.

For cantilevered beams, your codes might also require when you look at live load on the cantilever a reduced dead load on the back span, stabilising vs de-stabilising loads. For example, the code I work with requires at the ULS a combination of 1.2G+1.5Q, but to capture the greatest uplift on the right support in your scenario, we would be required to look at 0.9G on the main span and 1.2G+1.5Q on the cantilever for the strength limit state. If you don't do this, you're missing a potentially critical case and possibly not applying any restraint/fixings for uplift.

https://engineervsheep.com

 

[human909]

Agreed on the above. All conceivable loading combinations should be considered at ULS.

However it should be pointed out that the load case 2 you are considering only seems to be a serviceability issue. So there is still likely code flexibility and engineering judgment. If the scenario is quite unlikely and the consequences too much deflection are minor then considering it might be erring on the overly conservative side. However if the likelihood is high and too much deflection would likely damage fixtures then that is problematic.

 

[rscassar]

Statistically I think it would be more probable to achieve full live load on the cantilever and nothing on the backspan then it would be to achieve full live load across all spans.

For ULS, the two cases you have drawn will give you the biggest moment and shear design envelope.
For SLS, the worst case for cantilever deflection will be live load on cantilever and no live load on backspan

 

[rscassar]

actually I am wrong above. Patterning with live load on cantilever and nothing on the backspan will generate the maximum negative moment in the backspan so this will contribute to the governing strength envelope as well.

 

[dik]

and minimum reaction on the RHS...

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

-Dik

 

[Agent666]

For SLS, the worst case for cantilever deflection will be live load on cantilever and no live load on backspan

For shorter cantilevers and longer back spans you'll find live load on the back span will result in the largest cantilever deflection (upwards!).

https://engineervsheep.com

 

[JLNJ]

If you have collateral loads and are considering them dead loads, it compounds the problem. Worse yet, if you are analyzing a drop-in beam system (cantilevers on both ends) getting the patterned loading right is absolutely critical. The controlling combination is often the max load on the cantilevered ends and the min load in the span. Plus, you have the unbraced length of the beam throughout the negative moment region to consider.

Determining a patterned loading “worst case” isn’t necessarily intuitive.