This text presents an analytical expression to calculate the maximum tension, at the bottom side of a concrete slab on ground, due to lift truck wheel loads. The result of the analytical expression is in close agreement with the result of a design chart by the Portland Cement Association and with the result of a finite element analysis. The analytical expression is able to show the relationships among the design variables and it can be used for the thickness design of concrete floors for factories and warehouses. The expression applies only to unreinforced concrete slabs on ground.
In general, the analytical expressions found in the literature about slab on ground present several inconveniences. The expressions were derived before the advent of electronic calculators and the use of slide rules to evaluate mathematical constants resulted in numbers with low accuracy. Typographical mistakes may have been introduced in their subsequent transcription. In references [
Considering E as the modulus of elasticity, ν as the Poisson’s ratio, h as the thickness of the plate and k as the modulus of soil reaction, according to reference [
where,
Due to three dimensional effects, the expressions for the stresses are not accurate in the neighborhood of the center of a very small circle. However, reference [
This suggestion leads to the following expression for the stress, on the bottom side of the plate, at the center of each circle:
The contact area may be estimated for pneumatic tires by dividing wheel load by inflation pressure. According to reference [
This design example was taken from reference [
Applying expression (13) developed for the stress at the center of each circle with the data taken from reference [
The maximum tension at the bottom side of a concrete slab on ground is equal to 348.32 lbf/in2 (2.40 MPa). The maximum tension is about 1% above the value obtained by the analytical expression. The wheel loads were applied at about three times the radius of relative stiffness from the plate edges.
! Enters the model creation preprocessor
/PREP7
! Creates a circular area
CYL4, -18.5, 0.0, 0.0, , 6.014281, , 0.0
! Creates a circular area
CYL4, 18.5, 0.0, 0.0, , 6.014281, , 0.0
! Groups geometry items into a component
CM, Cname, AREA
! Selects a subset of components
CMSEL, ALL, Cname
! Creates a rectangular area by corner points
BLC4, -132.0, -132.0, 264.0, 264.0, 0.0
! Subtracts areas from areas
ASBA, 3, Cname, , DELETE, KEEP
! Generates new areas by gluing areas
AGLUE, ALL
! Define element type
ET, 1, SHELL63
! Define element real constants
R, 1, 7.9, , , , 100.0
! Define material property
MP, EX, 1, 4.864E+06
MP, PRXY, 1, 0.20
! Specify the divisions on unmeshed lines
LESIZE, ALL, 2.0
! Generate nodes and elements
AMESH, ALL
PCA | Expression (13) | FEA |
---|---|---|
320.00 lbf/in2 | 343.72 lbf/in2 | 348.32 lbf/in2 |
2.21 MPa | 2.37 MPa | 2.40 MPa |
! Define constraints
N1 = NODE(-132.0, -132.0, 0.0)
D, N1, UX, 0.0
D, N1, UY, 0.0
! Specifies surface loads on the selected areas
SFA, Cname, 2, PRES, 110.0
FINISH
The analytical expression to calculate the maximum tension, at the bottom side of a concrete slab on ground due to lift truck wheel loads, was evaluated using expressions from theory of Elasticity presented in reference [
Arcaro, V.F. and de Almeida, L.C. (2017) Lift Truck Load Stress in Concrete Floors. Open Journal of Civil Engineering, 7, 245-251. https://doi.org/10.4236/ojce.2017.72015