Wall bracket engineering calculations 1

[ElectrcBob]

I am mounting a horizontal shelf on a wall and need advice on calculating fasteners.

The wall is 1/2" thick common drywall on 25-gauge (0.018") steel studs. A 1.5" high x 24" wide x 0.25" thick aluminum plate will be attached flat to the drywall with rear-expanding fasteners (Mollys), which puts the drywall in compression at the point of attachment. The shelf will be attached (cantilevered) to the aluminum plate with steel rods (attached sketch).

I'm modeling my shelf after an example sold by Amazon (link below). However, this commercial product meant to be attached to wood studs. My walls don't have lumber in them.

https://www.amazon.com/dp/B09B7PVM49

Weight on the shelf will tend to push the bottom of the plate into the drywall and put the Mollys in tension. My guess is that the weak link will be the Mollys pulling out of the drywall, but there is also some risk of crushing drywall at the bottom edge of the plate. The Mollys will not go into studs. There's no way to get reinforcement behind the drywall. But if there are enough Mollys, it should distribute the load.

I tried to find engineering data for drywall. On one website, they write: "the flexural strength of various drywall types and thicknesses was found to be between 50-100 lbf, depending on the type and thickness of the drywall." On another: "The compressive strength and elastic modulus of the gypsum board were 5.52 MPa and 4350 MPa, respectively"

According to "performance data" on a fastener website, a 3/16" Molly in 1/2" drywall will fail at 175 pounds tension, and they recommend a safety factor of 4 (43.75 pounds max tension per Molly).

Intuitively, it seems best to put Mollys near the top of the plate so the cantilever force is distributed over a wider area of drywall. Is that right?

I plan to build a prototype and test it to failure, but don't believe that is a reasonable way to engineer a dependable solution.

How can I estimate the number of Mollys to use for a 30 pound shelf with the weight 6" out from the wall? Alternately, how can I estimate the weight that a shelf with 6 Mollys can hold, assuming the weight is placed a fixed distance from the wall?

Or is this a flawed design from the start? :-(

Thank you for your advice.

 

[SWComposites]

Go back to simple statics.
You have a moment M of 30 * 6 = 180 in-lbs
Assume this is reacted by a moment between the bolts and bottom of the plate, assuming bolts are 0.3 inch from top of plate, force on bolts is approximately M / (1.5 - 0.3) = 180 / 1.2 = 150 lbs.
Now divide that by the number of bolts.
Hopefully this is a one off for your home and not a commercial product being designed.

 

[dik]

you want to minimise your edge distance at the top... something like 1/2" or 5/8" for a 1/4" hole... 0.3" may be a little too close for the hole and the force will be slightly greater. If that fits the Molly. Use the minimum hole size that the Moly will go through and you should have 1/8" of material from the edge of the hole to the edge of the material. Also, use a stud finder to check that you are not installing them into a steel stud.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[hydtools]

Use the steel studs for backing.

Ted

 

[dik]

They get in the way with expansion (toggle type) fasteners.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[ElectrcBob]

Thank you. Yes, the "simple statics" from SWComposites is what I needed.