Adding a New Support Point on a Loaded Beam

[metalchair]

Hello All,

A quick conceptual question regarding supporting an existing beam and the sequence of loads. For this conceptual question, assume a uniform load over the length of the beam.

I have a condition where I have a roof beam that is currently supporting load. A client has asked to add additional loading to this beam in which it will now be failing in bending. The beam in question is currently single-span, simply supported. If i were to add a support post at mid-span, creating a two-span continuous condition, would additional load added after the post is installed begin to "cancel" out the original bending stress?

Again, assuming all load is uniform, I believe in theory, there should be a new added load after the post is installed that will effectively reduce the bending stress at the center (original mid-span/new post location) to zero. At center span, the original condition is in positive bending, after the post is added, the same location is now a negative bending location.

 

[ChorasDen]

Assuming you're within the beams elastic limit, I would just use the concept of superposition to find the load required to balance the bending moment at center of the member length to a value of 0. Be aware that the member is already deflected, and that this new load may be difficult to achieve without causing issues with existing finishes and/or water drainage, particularly if this is an older project. It may be difficult as well to induce this vertical load (install post flat and then apply a jacking force?).

 

[Eng16080]

I'm not following how the bending moment would "cancel" out.

In general, adding a post at midspan should significantly increase the beam's capacity. However, be sure to account for the following:
[ol 1]
[li]Currently the beam is simply supported and only experiences positive bending. By introducing the post, now the beam will be in negative bending at the post location. For lateral stability, you may need to brace the bottom of the beam if it isn't currently.[/li]
[li]You should analyze the (now) 2-span beam with live load acting: (a) only on the first span, (b) only on the second span, and (c) on both spans.[/li]
[li]It's not related to your question really, but be sure to properly size the new column and provide a full load path to the foundation. (I know this is probably obvious, but I've often seen this get neglected.)[/li]
[/ol]

 

[metalchair]

Thank you both for your responses.

Eng16080 - I believe it would "cancel", as by adding a post at mid-span to a deflected beam essentially "locks in" the positive bending moment the beam is experiencing under the current loading. By further increasing the loading in the two span condition, you then begin to induce negative bending at the (original) mid-span location, which reduces (cancels out) the positive bending stress on the beam.

 

[rb1957]

I think you need to analyze the three point beam and new loads to show that these are less than the original.

"Wir hoffen, dass dieses Mal alles gut gehen wird!"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Eng16080]

Assuming the beam is simply supported, by adding a post in the middle, I believe the maximum moment will now be half what it was before, except now that maximum moment will be negative.

 

[EZBuilding]

Metalchair,

I believe the appropriate approach is to superimposed the shear and moment diagram from the existing loading conditions (Dead, SID - single span) with the shear and moment diagram from the new loading condition (New dead, new sid, Roof Live - multispan). I don't think considering this as canceling it is appropriate as those moments are still there, just being counteracted by the new demands.

I think it is also appropriate to bracket your design approach and consider your design to be able to support all loads in the two span condition. Should any creep occur, or if during installation the column is jacked up against the beam, you still have a safe design.

 

[Smoulder]

@Metalchair Pretty sure you've got the analysis concept right based on how you've described the process. The main concerns have been mentioned already. My hit list would be

Bracing top of column and beam bottom flange.
Pattern loading.
Specifying shims so no gap and no unknown force jacked into the column during installation.
Creep if applicable.

Creep can be enveloped by immediate elastic stresses and stresses as though column was always there as EZbuilding said. Or the long term case can be calculated using phi/(1+phi) as interpolation factor. Simple calc and gets close enough to the mark for design purpose.

 

[desertfox]

Hi Metalchair

Checkout example 10.4 in the link below:-

https://eng.libretexts.org/Bookshel...3:_Analysis_of_Indeterminate_Beams_and_Frames

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein