^{1}

^{1}

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,

_{1} and I_{2}.

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 [^{2} e 250 lbf/in^{2}.

This design example was taken from reference [^{3} (2.71E+07 N/m^{3}). The axle load is equal to 25,000 lbf (111,206 N). The tire pressure is equal to 110 lbf/in^{2} (7.58E+05 N/m^{2}). The wheel spacing is equal to 37 in (0.94 m). The modulus of elasticity of concrete is equal to 4,864,000 lbf/in^{2} (3.35E+10 N/m^{2}). The tire contact area can be calculated by dividing the wheel load by the tire pressure. The maximum tension, calculated with the design chart, is equal to 320 lbf/in^{2} (2.21 MPa).

Applying expression (13) developed for the stress at the center of each circle with the data taken from reference [^{2} (2.37 MPa).

The maximum tension at the bottom side of a concrete slab on ground is equal to 348.32 lbf/in^{2} (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/in^{2} | 343.72 lbf/in^{2} | 348.32 lbf/in^{2} |

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