Workbench Top Pulling Force With Sloping Leg

[Ian K]

TL;DR Summary

How to calculate outward force of workbench top with slopping leg

Hello,
I am making a workbench for my mancave, the front edge of the bench is supported by legs that slopes inwards at 78 degrees and the back/rear edge of the bench top is fixed to the wall. How do I calculate the force Q pulling the bench top away from the wall please?

Also is the force Q affected by the position of a load on the worktop? eg L1 is quarter distance from front, L2 is in the middle and L3 is three quarters distance from the front. See attached photos of sketches.

Many thanks in advance Ian K
PS I assume L/2 is correct for the shared vertical load supports (Leg and Wall)

 

[jack action]

How do I calculate the force Q pulling the bench top away from the wall please?

$Q$ will oppose the horizontal reaction force between the floor and the legs.

Also is the force Q affected by the position of a load on the worktop?

Yes. You have to do a proper free body diagram and evaluate the sum of forces and the sum of moments for the assembly. Don't assume half of the reaction force will be on the wall and half on the legs.

 

[sophiecentaur]

@Ian K The load L will probably be highest when it is a dynamic load - as you whack an object on the (can you do without one?) bench vise. With vertical front legs, the force Q will be a lot less, of course. Is there a good reason for having diagonal front legs? You could be opening a can of worms here; the stresses on the back wall can usually be relieved by props at the back but here the back support becomes a serious issue.

Wrestling with a big object on a vise can pull a bench from a wall and give a nasty surprise. But, of course, your application may not call for that.

A diagonal member from lower front to just below the rear fixing could help, of course. Triangles are fabulous things in engineering.