• (Edited )

Hi Rocio,
Stress (on a member) = Total Loads (that apply on the member) / Surface Area (that the loads apply on to). You can use this formula to find the Surface Area of the lintel and since you have the length, once you find the area, you can find the width too. Hope I got your question correctly and this answers it.
Best of luck with your studies and exams!
Elif Bayram, AREQuestions

• Thanks so much Elif Bayram but am still super confused. would the load be a triangular load and I would not need to take the full load for the calculation? and do I calculate cross section of beam (WxH) or length by height? For example if I have a load of 10,000 pounds on the lintel in a masonry wall (which would be a triangular load) with 500 PSI stress on the lintel and the lintel is 10" H by 10" W and the total length is what Im trying to solve for. The total length would be 48" for the opening plus the end bearing length of each side that I know it has to be min 4" or max 8" on each side. How do I calculate for that?

• It depends on the load above the lintel. If the lintel is carrying a masonry wall above it (not just its own weight), I don't see why it would be a triangular load. I think, in that case, it will still be a rectangular load. If you can maybe sketch this wall, lintel, and what is above, I can understand it better. When loads apply on a surface area, the third dimension of the load-bearing element is not included. If the lintels width is 10" then, 10 inches x Length (which you are looking for, I believe) is the Area. So, if total loads are 10,000 pounds and stress is 50 psi. Surface Area = 10,000p / 50 psi = 200 square inch = 200/ 10" (width) = 20" would be the length.

Btw, as a general rule for AREs, never assume any dimensions. 4" to 8" end bearing might be a correct assumption while you are practicing architecture, but in the exam, assuming dimensions or information that is not given in the question typically leads to mistakes. I also think that, if a question gives you all this information, like load, stress per square inch, and the width of a lintel, they want you to calculate the length. The total length must be including the end bearings already.

• There are a few assumptions you'll need to make and some context you'll want to establish. . .This is a super-complex question. . . 4-8” is just good practice, not a requirement as far s as I know.

To take the triangular load you need to know that the masonry will corbel over the opening. If you have a relief angle somewhere above the lintel, it might not. Let's assume no relief angle.

Take masonry bearing strength at 1/4 F’m and F’m is usually 1500psi for modern masonry so 375 psi over the bearing area*

A 10,000lb reaction on 2000psi masonry would require 100 square inches of bearing. So a 4” leg brick lintel would need to bear 25” long! A W beam lintel with an 8” flange would need to bear 12.5” long. (Assuming it’s bearing fully - ie grouped cells or solid brick…if it’s hollow masonry you only get to take the bearing area of the face shells and maybe the webs, depending on the mortar technique)

To take a lintel load find your bearing stress allowable (375psi) then subtract the weight of the column of brick above (20’ is 800plf/12”*4” = 17psi give or take) and then check your lintel bearing based on 375-17 psi.

Your example numbers are higher than we'd typically see. . . If you've got a 10,000lb point load on masonry from a lintel you're going to question whether you need a steel column or should be looking at serious reinforcing of the wall end as a column element. You’d also be looking at torsional deflection your my steel lintel - angles and W shapes hate carrying large loads off of their shear center and missing that leads to some very embarrassing discussions with the mason and GC when the brick starts rolling away from the building as they are laying it.

* Read on to geek out. . . what's below goes far beyond what you'd likely find in an ARE exam. . . if you’re looking at long bearing areas be very cautious. Loading your lintel causes deflection - the lintel “smiles.”  As it extends past the face of the support it will want to cantilever over the edge. Load it enough and it will crush that edge; if you don’t have enough “ballast” over the bearing end the smile can lift.

--Michael Ermann, Amber Book creator

• Rocio, your excellent question inspired us…look for a 40 Minutes of Competence Zoom call on this topic October 13th.

• Thank you @michaelermann !