Historic true 3 by 10 eastern pine floor joists spanning 20' length, 16" centers. I have a center marble island measuring 5' by 7' weighing 60lbs per sf, approx. 3,000lbs of weight. Trying to assess if the joists will hold this weight. Joists are pocketed into side brick walls. I have additional weight at the sides close to the walls, but its the center I'm most concerned with.
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Two methods come to mind.
Do an experiment. Pull a string line over three adjacent joists, apply a known load on the middle one, and record the deflections. Using the load/deflection relation for the loading condition, back calculate a modulus of elasticity. Using the NDS Supplement for Spruce-Pine-Fir values, map the modulus of elasticity to a lumber grade. From the grade, look up the Fb of the joists and compute capacities.
Visually grade the lumber. ASTM D245 provides a methodology for computing strength reductions based on grain straightness, knot location, knot size, and knot frequency. Look up the Structural Select Fb for Spruce-Pine-Fir in the NDS Supplement and reduce that Fb to a design value.
Given a design Fb, the strength follows as
(1.2)(1.15)Fb(1/6)(3in)(10in)² = Fb(69in³).
1000# applied at midspan of a 20 ft long joist implies a demand of (1000#)(20ft)(12in/ft) / 4 = 60000#-in. Setting capacity and demand equal and solving for Fb yields Fb = 870 psi, and that's ignoring additional sources of load. Modern #2 SPF has Fb = 875 psi.
It smells like you're pushing your luck, so some investigation is warranted. Or you could just throw some sister joists in there without investigation to err on the side of caution.
popham
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