# Help with cantilever table top questions

I'm hoping someone can help me with some questions to know whether or not the table can be supported by this design and how to calculate the length of the support runners and the width necessary to prevent tipping/rocking along the width as well.

Table length and width ~90" x 36"

Angle of the cantilever arm (terminology?) either 130 degrees or 50 degree

1. Which of the two designs from the elevation view would provide better support (could I use either as long as runners are long enough?) Which would require shorter runners [longer overhang]?
2. What would the minimum width between the two support arms would I need to prevent horizontal tipping?
3. How do I calculate tipping weight on the end of the table (opposite of the support)?

Material is wood. I found some figures for "E = modulus of elasticity" and for the wood I'm using it'd be between 1.6-1.7 and the user posted this note:

units of measure are psi, values must be multiplied by $10^6$.

This is all beyond my math skills, but am willing to try and learn!

• Regardless of CoG calcs, the details of the joinery methods for the 50° and 130° angles will be critical. – Spencer Joplin Sep 1 '18 at 19:44
• We need more details and specifically things such as: 1) maximum load at furthest extension from cantilever support. Usually this would be about 25kg for a regular coffee table but if it is a breakfast bar it will need to be able to support half the weight of an adult for each seating position plus maximum loading of whatever the table is being designed to support (food, machinery, electronics, television, etc) and 2) how you expect to fix the table top to the cantilevered support (glue, screws, nails, dowel rods, dovetail joints etc). – Rhodie Sep 2 '18 at 2:23
• An excellent book on the subject is design of structural elements ISBN 9780415467209 available from www.crcpress.com which will explain loading, bending moments, structural strength and strength of materials. – Rhodie Sep 2 '18 at 2:26
• @SpencerJoplin I will be using bridal joints more than likely. Fine Woodworking magazine shows this is a close second to the half lap in terms of strength and for this project (because of how I'm designing the legs) will be aesthetically please to me – mcoski Sep 2 '18 at 16:30
• @Rhodie This first design will be a desk rather than a table, so lets assume that your 25kg is a good start. My concern is if a 150 or 200lb person comes and sits on the edge will it hold. I'm going to run a couple of mockups with plywood and cheaper wood first to see how close to those weight figures I can get. The top will be sitting on 1/2" - 1" spacers that are on top of the cantilever support. They will be oversized and screwed in to allow for wood movement – mcoski Sep 2 '18 at 16:32

let's say your table and the support weighs 100 lbs. and the support at 90-degree angle projects a rectangle that is 1 foot shorter on each side from the edge of the table, meaning it is a rectangle of the size 66" by 12" and a height of 21".

This support when tilted is $$21\times sin(50) = 16"$$ offset horizontally, standing at the height of $$21\times cos(50) = 13.5"$$

now immediately we observe that as far as stability both 130 and 50 degrees are a mirror image of each other and provide one favorite side, one unfavorite side.

Assuming that CG of the table is at its center of geometry, which is a plausible assumption considering the weight of the two legs touching the floor is much smaller than the top part it is an acceptable assumption.

Now we want to figure how much weight added right on the edge of the table will topple it. At the unfavorable tilt of the support considering the legs or angled out dislocating the CG by 16"out, our restoring moment is the 100 lbs multiplied by 90/2- (16+ 12) = 1700 lbs.inch. now we divide this by

$1700/(16+12 =28)= 60 lbs$...-which is so low that we do not further check for the strength of the legs. of course, this load can be increased as it moves toward the center of the table limited only by the material strength.

now checking for lateral stability, we have a restoring moment of 100 lbs multiplied by 6"= 600 lbs.inch. we dived this by 12" we get 50lbs. Anything larger than 50lbs will laterally topple the table.

• Conclusion: the table is neither child-proof nor idiot-proof, and the geometry should be improved. – Spencer Joplin Sep 2 '18 at 18:12