# Go Plymouth Foam

Value Engineering  Understanding Compressive Resistance

Value Engineering - Below Grade Insulation  The Theory of Plates on Elastic Foundations The pressure beneath a given slab under a load can be determined using the following formula, found in the
Theory of Plates on Elastic Foundations, as described by Timoshenko and Woinowsky-Krieger:
Pressure on the subgrade = (P/8)√(K/D)

Where:
• P = concentrated load on concrete slab in pounds
• K = Subgrade reaction modulus of total EPS insulation in pounds per cubic inch (k/t)
• k = Stiffness of one inch of EPS insulation in pounds per square inch
• t = EPS insulation thickness in inches
• D = Eh3 / 12(1-u2)
• E = Modulus of elasticity of concrete in pounds per square inch (57000√ f ‘c)
• f ‘c = specified concrete compressive strength in pounds per square inch
• h = Thickness of concrete slab in inches
• u = Poisson’s ratio for concrete (0.15)
An example illustrates the significant difference in the calculated results.
Take the case of a warehouse with a 6-inch-thick, 2,500-psi concrete slab on 2 inches of EPS insulation with a rated stiffness of 360 psi for one inch. Forklifts to be used in the building impart 8,000 pounds of force at the wheel, which has a 6-inch by 10-inch tire footprint on the slab. If the designer assumes that this load distributes at a 45-degree angle through the slab, the 8,000 pounds ends up distributed over approximately 396 square inches [(6 + 6 + 6)(6 + 10 + 6)] of the insulation’s surface, for an average pressure of 20.2 psi.
Taking into account the fact that concrete slabs distribute loads more evenly, using the Modulus of Subgrade Reaction method, the pressure on the insulation is actually much lower – approximately 1.85 psi. Since EPS insulation rated for 1.85 psi costs about 50% less than other rigid foam insulations rated for the much higher value of 20.2 psi, using the more precise method reduces insulation costs substantially. In fact, the 20.2 psi value is beyond the elastic range of the EPS material, and long-term creep effects must be taken into account when using that design approach. With:
P = 8000 pounds, h = 6 inches, f ‘
c = 2,500 psi, E = 57,000√ 2,500 = 2,850,000 psi, u = 0.15, k = 360 psi for 1-inch EPS
K = 360 psi / 2 inches = 180 pci
D = Eh
3/12(1-u2) = 2,850,000 (6)3/12(1–(0.15)2) = 52,480,818 lb-in
Pressure on EPS = (P/8)√(K/D) = 8000/8 √(180 / 52,480,818) = 1.85 psi.

This reprint is a courtesy from Structure Magazine
Plymouth Foam manufactures foundation and below grade insulation for the United Sates including the states of Wisconsin, Illinois, Indiana, Iowa, Minnesota, Michigan and Ohio. Plymouth Foam provides insulation using Expanded Polystyrene (EPS) in the form of flat insulation, tapered insulation, fan fold, laminated insulation, drain boards or drainage boards, insulated footers, mini foundation boards, channeled insulation boards as well as Neopor foundation products and Graphite Expanded Polystyrene Products.

Plymouth Foam’s EPS, the safe insulation, is manufactured in Wisconsin, Minnesota and Ohio. EPS foundation insulation has been known to be used with other products or systems such as Z furring, Form-a-Drain, Dura Drain, Platon, damproofing, waterproofing membranes, as well as many other foundation wall products.