Are you Smarter than a...

Are you smarter than a 10th grader?  I used to think I was....that is until I tried designing the staircase for my mancave project.  As you may recall from prior posts, my plan was to construct a contemporary monostringer staircase for accessing the loft area above my mancave. 


To establish the conceptual design, I did what anyone with exceptionally strong opinions and limited creativity would do...I plagiarized.  With the help of good old uncle Google, I found dozens of monostringer staircase examples by doing an image search for "contemporary monostringer stairs."  After a little browsing, I found a few examples of stairs I thought would blend nicely with my design.  I settled on a design I found on  acadiastairs.com:
 

Monostringer Staircase (aka, "single stringer" staircase).  The person providing the quote informed me that each tread is rated for a 300lb load

Acadia stairs is a New York-based custom stair fabrication company...they ship these types of stair cases (and others) all over the country...just goes to show, you can buy ANYTHING off the internet!

Appreciating the deceiving complexity of this particular design, I solicited a quote from them in hopes I could just outsource this portion of my project and save some time.  Based on my project's dimensions, the bid came back at a budget-crushing $3,500 (not including the wooden stair treads, which I was planning to do myself).  Oh yeah, and if I didn't have the spare time to drive to NY to get it, it was going to cost another $1,000 for shipping and handling.

Make it rain up in this Bi*ch!!!

Now I may be ridiculous, but I'm not insane....after all, this IS a garage we are talking about here!  While I certainly want this project to be cool, I'm not about to liquidate my child's college fund to pay for it.  So with outsourcing out of the question, it was time to take matter into my own hands.  After some careful consideration, I concluded that between the information specified in the quote and that which is published on their website that I should be able to design and fabricate this staircase myself. 

As anyone who has ever designed and built stairs will tell you, they are incredibly easy to screw up--even professionals who design and build stairs on a regular basis will attest to this.  Unfazed by such cautions, I set forth designing the aforementioned staircase.  In a nutshell, I was going to have to figure out some very specific things to pull this off:

1.  The length of i-beam needed for my particular project
2.  The angles at which to cut each end of the i-beam so it meets up with the floor and side of  the mancave correctly
3.  The exact dimensions of the unique, polygonal-shaped metal pieces connecting the stair treads to the i-beam (I call these "riser wedges")

I studied the design carefully and concluded that these dimensions were entirely obtainable provided I would be able to recall some basic high school math...in essence, it really just boils down to 10th grade level geometry and a little 9th grade algebra.

 

Step one was to measure the the staircase's total rise.  This is done by measuring from finished floor height to finished floor height--which in my case equates to 102 9/16."  The next step, was to determine how many steps (or landings) my staircase will need.  As a general rule of thumb, most steps are around 7 inches high....so if you divide the total rise (i.e 102 9/16") by seven, you get 14.651 stairs.  Obviously, I can't install a fraction of a step...so I rounded up for a total of 15 steps.  Having established there will be 15 steps, the next step is to divide the total rise of 102 9/16" by 15 to calculate each individual step's rise.  Here's how it would all look if I were submitting this as a math problem to my 10th grade geometry teacher, Mrs. Simmons:

With my total number of steps determined, I then need to determine the staircase's run (i.e. how far from the mancave's wall the stairs will project).  To determine the total run, I then multiplied each step's depth (aka, "tread depth") by the number of stairs:

 With my total run calculated, I now had 2 sides of a right triangle:

Finding "X" would give me the length needed for my metal i-beam stringer (or so I thought)

To find "X," I dusted off the cobwebs in my brain and managed to recall the pythagorean theorem...come on everyone, say it with me...I know you all know it: A2 + B2 = C2

Once I figured out the hypotenuse, I would be only a few quick calculations away from determining the angles of my triangle...which of course, would lead me to the angle's needed at each end of my i-beam.  Then, using a series of right triangles and super-imposed perpendicular lines, I could figure out the dimensions of those mysterious "riser wedges" that are so integral to this design.

 

 I'll spare you the play-by-play written narrative for this process, but like a good school boy I will show my work (Ignore the actual numbers used.  The work below came from my very first design which used slightly different dimensions for my tread cover thickness and depth than those previously outlined.  Trust me, the logic is the same regardless of the dimensions used).

Asleep yet?  Man, never would I have predicted I'd be using the Sin, Cos, & Tan functions on my calculator after high school!  Truth be told, I sort of enjoyed the process of figuring this out and was surprised I actually remembered all this math I haven't used in over 20 years.

With my staircase design complete, I proudly forwarded my work to a few friends with engineering and design backgrounds for feedback.  In truth, I anticipated them emailing me back to tell me what a great job I had done.  Of course, my hubris was quickly tempered when my friends kindly pointed out the multitude of oversights I had made...not the least of which was my flawed methodology for calculating my steel i-beam length.

If only my "Fails" were this awesome

Error #1:  My stringer's rise and run dimensions were incorrect because my last step is actually the loft's finished surface.  Unlike a standard staircase made with wooden stingers that attaches level with the second story's finished floor height (picture below on the left), my staircase's stringer will actually attach much lower on the header because the last step will be the actual loft floor (see picture below on right).

Note the different attachment point of the traditional wooden stringer with respect to the second floor's surface compared with the steel monostringer's attachment site (much lower).

Error #2:  I neglected to account for the 1/4" floor plate in my rise calculations

Error #3:  I neglected to factor in the 3/8" header plate needed to attach the i-beam to the header 

Error #4:  I did not use CAD to design my project, I instead used microsoft power point (the 2000 version, no less)

In real life, unlike high school, you don't get "partial credit" for showing your work if your methodology is correct but the final answer is wrong.  Although my basic approach was correct...these critical oversights would have ended up costing me HUGE money because I would have ended up with an expensive steel i-beam cut to the wrong length and with the wrong angles at each end.  Clearly, I am in fact NOT smarter than a 10th grader.  Damn.

Face of a loser (I'm referring to Foxworthy, not the defeated contestant...I can't stand red neck comedy)