THE PROBLEM:
I was recently called by concert pianist, Tchl Ivory, who wanted to place not one but two full-sized grand pianos in his family room. Why he needed two is curious to me but that’s beside the point. His house is a rambler, a tract home built in the 70s.
Tchl, a natural-born worrier, was concerned that one day he might find himself playing his very expensive, very heavy pianos in his crawl space. A legitimate concern because residential floors are not typically designed for that kind of load.
Tchl had called a contractor, who crawled under his house, emerged filthy and out of breath and then proclaimed, “It ain’t pretty under there, Tackle. The beams is spaced too far apart to support them two pianees. You need to add a post in the middle o’ the room. I figger me and my boys could do that fer a couple thou. Have ‘er done in a week.”
Tchl wisely opted for a second opinion and called my brother, Mark, who is a contractor specializing in distressed structures and foundation repair. Mark opined that one new post in the middle of the room would be like trying to heal a fractured femur with chap stick. He suggested I take a look and a few days later, under the house I went.
The floor framing consisted of 2×6 joists at 16” OC, supported by 4×6 beams at 8’ OC, supported by posts and piers at 6’ OC.
THE ANALYSIS
Residential floor live load per code is 40 pounds per square foot (psf). I used ConstructionCalc structural design software and calc’d a typical 2×6 joist using this load and found that it was okay.
Each piano weighs 1,500 lbs., with the maximum load on a leg being 700 lbs.
I replaced the 40 psf live load with a 700 lb concentrated load at mid-span, which represents the worst case either of the pianos could apply. The pianos are large enough and the spacing between their legs far enough that it would not be possible for any single joist to be subjected to more than one leg’s load at a time. So this is indeed the worst case loading for any of the joists.
Here is the result section from ConstructionCalc™ ProBeam v4.0™ Structrual Design software:
(Please click the image above to view a larger version)
You can see from the Final Member Results that the joist fails in bending by 43.7%, and in deflection (sag), by 48.4%.
I then checked the 4×6 beam which runs down the middle of the 16’ wide room. To do this I assumed that either piano could bring a 700 lb. point load. With two pianos, that’s 1,400 lbs, total. Depending on the positioning of the pianos the worst case would result in about 75% of this 1,400 lb load = 1,050 lbs at mid-span of this beam. Under this scenario the 4×6 failed in bending by 11.1%.
I could have checked the posts and piers too but I knew at this point that I would be adding new ones, so that analysis was not necessary.
The last thing to check was the 5/8” T&G plywood subfloor. I went to the internet in search of strength data for plywood under a concentrated load and found APA (American Plywood Association) Research Report 135, “Plywood Composite Panels for Floors and Roofs”. It indicated that 5/8” plywood underlayment supported at 16” OC could support an ultimate concentrated load of 1,320 lbs. (ultimate load is the load at which failure occurs, with no factor of safety applied). The testing procedure utilized a 1-inch square load applicator. Our piano legs are on wheels that are about 1-inch in diameter by 3-inches long. Assuming this is approximately equivalent to the test load applicator, we’re looking at a factor of safety of approximately 1320/700 = 1.9. Code generally requires a factor of safety of about 2.5, so this is a little dicey.
THE SOLUTION:
Doubling the joists solves the problem with them, provided the joists under the pianos’ legs are the ones being doubled. The question then becomes, exactly where will the pianos be placed? Mark consulted with Tchl who indicated that due to the pianos’ size there was only one orientation possible in the room. So we doubled all the joists within 3’ of the probable location of all six legs.
The beam fix was simple. We added posts and piers midway between the existing ones, effectively halving the beam’s span. This not only fixed the beam, it also spread the load among twice the number of posts and piers as existed originally. So by doing this we ensured that the beam, posts, and piers were all okay.
Regarding the plywood, I recommended that Tchl place his piano rollers on 4” x 4” x 3/4” plywood bearing “pads”. This applies the concentrated load over an area 5-times larger than the wheel’s 3 square inches, drastically reducing the punching shear on the plywood. Now I feel confident that the plywood factor of safety is at least 2.5
While these upgrades cost a little more than the first contractor’s hoodwink of an estimate, Mr. Ivory needn’t ever worry about hosting a concerto in his crawlspace.
Copyright, Tim Garrison, P.E., 2009
The Builder’s Engineer™
ConstructionCalc Structural Design Software
All rights reserved
Tags: overloaded floor, overloaded floor joists, overspanned floor joists
