Introduction
PlastiSpan® insulation has provided designers and building owners with long-term thermal performance for over 45 years as a component in residential, commercial and industrial floor systems. Structural slab design is governed by the types and magnitude of loads on it which generally include wheel loads from forklifts or delivery vehicles, point loads from the legs of storage racks or distributed loads from product stored on the floor.
Review
Selection of a sub-slab insulation product is often based upon its ability
to respond to compressive loads transferred from the slab, without full
and accurate determination of the load distribution characteristics of
the slab. Table 1 below provides sample calculations based upon this
method for structural concrete slab design using two of the load types
noted above.
Table 1 - Examples of Typical Loads on Concrete Slabs
Example 1 - Forklift Wheel Load | Example 2 - Point Load (Storage Racks) | |||||||||
Wheel Load - F | kN | 35 | Point Load - F | kN | 50 | |||||
lb_{f} | 7,875 | lb_{f} | 11,250 | |||||||
Wheel Contact Area | m | 0.203 | x | 0.203 | Base Plate Contact Area | m | 0.152 | x | 0.152 | |
in | 8.0 | 8.0 | in | 6.0 | 6.0 | |||||
Stress Distribution Angle | 45 | Stress Distribution Angle | 45 | |||||||
Slab Thickness | m | 0.152 | Slab Thickness | m | 0.152 | |||||
in | 6.0 | in | 6.0 | |||||||
Loaded Area | m^{2} | 0.26 | Loaded Area | m^{2} | 0.21 | |||||
in^{2} | 398 | in^{2} | 322 | |||||||
EPS Compressive Stress | kPa | 136 | EPS Compressive Stress | kPa | 240 | |||||
psi | 20 | psi | 35 |
The calculations above are based upon the assumption that loads distributed over a contact area on a concrete floor slab area can be "assumed" to be distributed by and through the slab to a largely hypothetical insulation bearing area. The insulation load exposure calculated on this basis would dictate use of a high density, high strength insulation material increasing cost unnecessarily.
Design Considerations
An accepted design procedure to use for structural slab design with these types of loads is the theory of plates on elastic foundations. When a concrete slab is constructed over a compressible or elastic subgrade such as soil or rigid insulation, load distribution and transfer to the sub-slab insulation is controlled by the slab itself and its response to loads. Floor loads will cause slab deflection as a function of both the concrete slab properties and the compressibility of the materials beneath it.
In order to use this method, designers use the insulation or subgrade response
factor referred to as the modulus of subgrade reaction (k) or, in other cases,
foundation modulus, k-modulus, k-value, etc.
The use of k-values in the design of structural slabs as discussed in PCA Concrete
Information^{1} reflects the response of the insulation and subgrade under temporary
(elastic) conditions when small deflections occur. Modulus of subgrade reaction
values expressed in units of NM/m^{3} or lbs/in^{3} (pci) for various PlastiSpan
insulation types and product thickness are listed below.
Table 2 - PlastiSpan Insulation Modulus of Subgrade Reaction (k)
PlastiSpan Insulation Types | Units | PlastiSpan Insulation Thickness - mm (in) | |||
25(1") | 50(2") | 75(3") | 100(4") | ||
PlastiSpan HD Insulation | NM/m^{3} | 176 | 147 | 111 | 92 |
pci | 650 | 540 | 410 | 340 | |
PlastiSpan 20 Insulation | NM/m^{3} | 198 | 163 | 125 | 103 |
pci | 730 | 600 | 460 | 380 | |
PlastiSpan 25 Insulation | NM/m^{3} | 255 | 212 | 160 | 133 |
pci | 940 | 780 | 590 | 490 | |
PlastiSpan
30 Insulation |
NM/m^{3} | 299 | 247 | 187 | 157 |
pci | 1100 | 910 | 690 | 580 | |
PlastiSpan
40 Insulation |
NM/m^{3} | 346 | 285 | 217 | 182 |
pci | 1275 | 1050 | 800 | 670 |
For floor slab designs incorporating multiple insulation layers and a subgrade material, k can be found by adding k values for each layer as follows: 1/k_{T} = 1/k_{1} + 1/k_{2} + …1/k_{n}
Floor slab deflection establishes magnitude of unit load transferred to the
subgrade material, in this case thermal insulation. Based on slab-on-grade
design theory using the theory of plates on elastic foundations^{2},
slab deflection (W) is determined by load exposure, slab strength characteristics
and subgrade (insulation) response to load transfer using the equation below.
where:
W = slab deflection
P = applied load
K = modulus of subgrade reaction
D = Eh^{3}/12(1-μ^{2})
where:
E = modulus of elasticity
of concrete
h = slab thickness, in.
μ = Poisson’s ratio of concrete
The following sample calculations are provided to illustrate a process to
review the effect of the load on the concrete slabs. Slab deflection and
compressive load are calculated using elastic foundation design analysis based
upon the combined characteristics of the insulation and a subgrade material.
Assumptions for Calculations:
- Concrete strength = 28 MPa (4000 psi)
- Concrete thickness (h) as noted in table
- Poisson's ratio for concrete = 0.15
- Insulation thickness = 76 mm (3")
- Subgrade k-value (k_{s}) = 100 NM/m^{3} (368 pci)
- k-value Insulation and soil = 1/k_{T} = 1/k_{i} + 1/k_{s}
- E-modulus of Concrete (E_{c}):
= 24,870 MPa (3.605 x 10^{6} psi)
Step 1: Calculate the modulus of subgrade reaction
for 76 mm (3") insulation plus subgrade material.
1/k_{T} = 1/k_{i} + 1/k_{s}
Table 3 - K-value - PlastiSpan Insulation Plus Subgrade Material (KT)
k_{T} | PlastiSpan
HD Insulation |
PlastiSpan
20 Insulation |
PlastiSpan
25 Insulation |
PlastiSpan
30 Insulation |
PlastiSpan
40 Insulation |
---|---|---|---|---|---|
NM/m^{3} | 53 | 56 | 62 | 65 | 68 |
pci | 194 | 204 | 227 | 240 | 252 |
Step 2: Calculate slab deflection (W) due to load.
Table 4 - Example 1 – Slab Deflection (W) Under Wheel Load
152 mm (6") Concrete Slab |
|||||
---|---|---|---|---|---|
mm^{} | 0.22033 | 0.21459 | 0.20381 | 0.19806 | 0.19326 |
in. | 0.00867 | 0.00845 | 0.00802 | 0.00780 | 0.00761 |
Table 5 - Example 2 – Slab Deflection (W) Under Point Load
152 mm (6") Concrete Slab |
|||||
---|---|---|---|---|---|
mm^{} | 0.31475 | 0.30655 | 0.29116 | 0.28294 | 0.27609 |
in. | 0.01239 | 0.01207 | 0.01146 | 0.01114 | 0.01087 |
Step 3: Check compressive stress (F) in 76 mm (3")
thick EPS insulation. The above slab deflection (W) will transfer load to the insulation material
at intensity directly related to the insulation k-value – F = K_{i}W.
Table 6 - EPS Compressive Stress (F)
PlastiSpan Insulation Types | Example 1 - Wheel Load | Example 2 - Point Load | ||
---|---|---|---|---|
152 mm (6") Slab | 152 mm (6") Slab | |||
kPa | psi | kPa | psi | |
PlastiSpan HD Insulation | 25 | 3.56 | 35 | 5.08 |
PlastiSpan 20 Insulation | 27 | 3.89 | 38 | 5.55 |
PlastiSpan 25 Insulation | 33 | 4.73 | 47 | 6.76 |
PlastiSpan 30 Insulation | 37 | 5.38 | 53 | 7.69 |
PlastiSpan 40 Insulation | 42 | 6.09 | 60 | 8.70 |
Table 7 below provides compressive resistance at 1% strain which should be
used for determination allowable compressive stress for the various PlastiSpan
insulation types based upon long term duration load exposure.
Table 7 - PlastiSpan Insulation Compressive Resistance @ 1% Strain
Units |
PlastiSpan HD Insulation | PlastiSpan 20 Insulation | PlastiSpan 25 Insulation | PlastiSpan 30 Insulation | PlastiSpan 40 Insulation |
---|---|---|---|---|---|
mm^{} | 45 | 50 | 65 | 76 | 100 |
in. | 6.50 | 7.30 | 9.40 | 11.00 | 14.50 |
In the above examples, the compressive load transferred to the PlastiSpan insulation is within the allowable stress range for all insulation types.
Step 4: Check bending stress (fb) in concrete
Where ƒb = Concrete bending stress, h = slab thickness and a = radius of load contact
Table 8 - Concrete Bending Stress (ƒ_{b})
Design Loads | Wheel Load – Load Factor =1.5 | Point load – Load Factor =1.25 | ||
---|---|---|---|---|
kN | lb_{f} | kN | lb_{f} | |
35 | 7,875 | 50 | 11,250 | |
Radius of Contact (a) | 115 mm (4.5") | 86 mm (3.4") | ||
PlastiSpan Insulspan Type | 152 mm (6") Slab | 152 mm (6") Slab | ||
MPa | psi | MPa | psi | |
PlastiSpan HD Insulation | 2.65 | 385 | 3.51 | 509 |
PlastiSpan 20 Insulation | 2.62 | 380 | 3.46 | 502 |
PlastiSpan 25 Insulation | 2.54 | 369 | 3.37 | 489 |
PlastiSpan 30 Insulation | 2.49 | 361 | 3.31 | 481 |
PlastiSpan 40 Insulation | 2.45 | 355 | 3.26 | 473 |
Concrete Tensile Strength (ƒT):
Bending stress should not exceed the concrete tensile strength = 3.41 MPa (495 psi).
Based upon the above analysis, PlastiSpan HD insulation or higher density would be adequate for the wheel load application. PlastiSpan 25 insulation or higher density would be adequate for the point load application.
Summary:
- Under "assumed" or hypothetical load distribution patterns,
the load exposure from the load types typical for
structural slabs would dictate use of a high strength thermal insulation. - Using elastic foundation design theory, a much lower compressive load would
be transferred to the sub-slab
insulation allowing the use of a more cost-effective PlastiSpan insulation alternative.
Limitations of Use:
- It is not the intent of this bulletin to provide comprehensive design guidance.
Concrete slab deflection for each
application must be calculated by the design professional responsible for concrete slab design. - Design approaches expressed in this bulletin are related specifically to
the distribution of floor loads to subgrade
insulation. Final slab design is generally controlled by flexural stresses to which the slab is exposed under long
term or short term rolling load conditions. - Relationships used to establish slab deflection assume load intensities
on the subgrade insulation do not exceed
the elastic limit of the insulation. - Such factors as the bearing capacity and compressibility of subsoil and/or
subgrade slabs below the insulation
must be considered in the design of slab/subgrade insulation composites. - These design considerations are applicable to concrete slabs-on-grade (insulation
serving as grade) exposed to
storage loads, rack storage post loads and vehicle axle or wheel loads causing limited slab deflection. High
intensity column or wall loading on floor slabs requires further consideration. - Soils, concrete, steel and subgrade insulation exhibit creep or cold flow
under long-term load exposures. Such
long-term load exposures must be considered in slab design in order to prevent objectionable slab settlement.
________________
^{1}Portland Cement Association, Concrete
Information, Packard, Robert G., Slab Thickness Design
for Industrial Concrete Floors on Grade, 1996.
^{2}Timoshenko, S. and Woinowsky-Kreiger, S., Theory
of Plates and Shells, McGraw-Hill, 1959.