Tension and Shear on L-Bracket Offset From Wall

Question

I’m planning to mount a mantle on a brick fireplace wall using two iron L-brackets that are 5” wide and 1/4” thick. Each bracket has four 5/16” mounting holes…two at the top and two at the bottom. The bracket is 5-3/4” deep including the lip at the front and the back portion of the bracket is 8-7/16” tall. The brackets weigh about 7-1/2 lbs each.

The mantle weighs about 50 lbs and is about 3-1/2” x 5-1/2”. So once mounted, the COG of the mantle will be about 2-3/4” from the wall. The distance from the center of the top mounting holes to the bottom of the bracket is 7-3/16”.

Without accounting for the weight of the brackets themselves, the tension load from the mantle on the top four screws would be…

Force = (2.75 / 7.1875) * 50

Force = 19.13 lbs

1. Am I calculating this correctly?
2. How do you account for the weight of the brackets?

All that said, my primary issue is that the brick is not plumb and is somewhat uneven. I would like to use some steel shims/washers/spacers between the bracket and the brick wall in order to make the brackets plumb. Spacers would likely be about 1/8” or 3/16”. I assume that adding spacers to the bottom mounting holes would have a different impact than adding spacers to the top holes since my understanding is that only the top screws/anchors are under tension and the bottom fasteners are only under shear.

3. How would adding these spacers affect the tension and shear loads on the screws and anchors? What if I’m only adding spacers to one or two of the corners while the other corners maintain direct contact with the brick? What if spacers were added to all four corners, and perhaps to a thickness that removed all direct contact between the bracket and the brick where the bracket was completely offset from the brick wall? How significantly would these scenarios affect the tension and shear loads on the screws and anchors?

Answer 1

Your calculations are correct but give the total raw tension on four screws. If you divide it by 4 you get the tensile force on each screw. As for adding washers as spacers to make the wall plumb, it is okay as long as you keep them as fit and as tight as possible. And preferably use lock washers. Avoid using multiple washers in the same anchor. The idea is the washer becomes an integral part of the wall, not a fastener.

Are you not ever going to hang something on the mantel or put a picture frame on it?

I would add 100lbs to the self-weight, as a safety factor to cover the effect of the brackets and possible future objects placed on the mantel. The stresses on the top screws will be tension and shear and shear alone on the bottom.

In these kinds of applications, chances are the distribution of the loads is uneven e.g. possibly the screws on the top position don't share the load evenly. You want to tighten the screws gradually going from one to the other in small steps.