This text presents an analytical expression to calculate the Concrete Floors maximum tension, at the bottom side of a concrete slab on ground, due to lift truck wheel loads. The Concrete Floors 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.

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 [3] , for a concentrated force distributed over an area A, in the interior point of a plate on elastic foundation, the stresses on the bottom side at a point (x, y) can be written as:

 (1)

 (2)

where,

 (3)

 (4)

Figure 1 shows the geometrical parameters involved in the evaluation of the stresses on the bottom side of the plate at a point (x, y) due to a concentrated force distributed over an area A. The distance from point (x, y) to a point (u, v) inside area A is given by w. The angle of the line between the points (x, y) and (u, v) with the X-axis is given by ω. The difficulty in calculating the stresses lies in the calculation of the integrals I₁ and I₂.

 (5)

 (6)

This design example was taken from reference [8] . For comparison, the original US Customary Units used in the example were used with the analytical expression and with the ANSYS finite element analysis software from reference [9] . Consider a slab on ground with thickness equal to 7.9 in (0.20 m). The modulus of soil reaction is equal to 100 lbf/in³ (2.71E+07 N/m³). The axle load is equal to 25,000 lbf (111,206 N). The tire pressure is equal to 110 lbf/in² (7.58E+05 N/m²). The wheel spacing is equal to 37 in (0.94 m). The modulus of elasticity of concrete is equal to 4,864,000 lbf/in² (3.35E+10 N/m²). 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/in² (2.21 MPa).