# Concrete Slab on Grade Analysis Calculator (for Post or Wheel Loading)

For Slab Subjected to Interior Concentrated Post or Wheel Loading

Assuming Slab is Reinforced for Shrinkage and Temperature Only

#### Input Data

#### Result :

#### Check Bearing Stress on Dowels at Construction Joints with Load Transfer:

**References:**

**1.** "Load Testing of Instumented Pavement Sections - Improved Techniques for Appling the Finite Element

Method to Strain Predition in PCC Pavement Structures" - by University of Minnesota, Department of Civil

Engineering (submitted to MN/DOT, March 24, 2002)

** 2.** "Dowel Bar Opimization: Phases I and II - Final Report" - by Max L. Porter (Iowa State University, 2001)

**3.** "Design of Slabs-on-Ground" - ACI 360R-06 - by American Concrete Institute (2006)

**4.** "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D) - by Robert G. Packard

(Portland Cement Association, 1976)

**5.** "Streses and Stains in Rigid Pavements" (Lecture Notes 3) - by Charles Nunoo, Ph.D., P.E.

(Florida International University, Miami FL - Fall 2002)

**Note : **
there will be a few situations where certain combinations of the Concentrated

Load, P, Subgrade Modulus, k, and Contact Area, Ac, result in a #N/A error message

and thus no solution for the minimum slab thickness, t(min), for one or more of the

equations listed above. For those cases, the user would then manually iterate the

input slab thickness to determine the minimum value if desired.

Subgrade Soil Types and Approximate Subgrade Modulus (k) Values | ||
---|---|---|

Type of Soil | Support Provided | k Values Range (pci) |

Fine-grained soils in which silt and clay-size particles predominate | Low | 50 - 120 |

Sands and sand-gravel mixtures with moderate amounts of silt and clay | Medium | 130 - 170 |

Sands and sand-gravel mixtures relatively free of plastic fines | High | 180 - 220 |

Cement-treated subbases | Very high | 250 - 400 |

**Representative Axle Loads and Wheel Spacings for Various Lift Truck Capacities**

Truck Rated Capacity (lbs.) | Total Axle Load (lbs.) | Wheel Spacing (in.) |
---|---|---|

2,000 | 5,600-7,200 | 24-32 |

3,000 | 7,800-9,400 | 26-34 |

4,000 | 9,800-11,600 | 30-36 |

5,000 | 11,600-13,800 | 30-36 |

6,000 | 13,600-15,500 | 30-36 |

7,000 | 15,300-18,100 | 34-37 |

8,000 | 16,700-20,400 | 34-38 |

10,000 | 20,200-23,800 | 37-45 |

12,000 | 23,800-27,500 | 38-40 |

15,000 | 30,000-35,300 | 34-43 |

20,000 | 39,700-43,700 | 36-53 |

Note: Axle loads are given for trucks handling the rated loads at 24 in.

from load center to face of fork with mast vertical.

**Data for Construction Joint Dowels for Load Transfer**

Slab Depth | Dowel Dia., db | Total Dowel Length | Dowel Spacing (c/c), s |
---|---|---|---|

5" - 6" | 3/4" | 16" | 12" |

7" - 8" | 1" | 18" | 12" |

9" - 11" | 1-1/4" | 18" | 12" |

**Slab Thickness Joint Spacing (ft.)**

< 3/4" Aggregate | > 3/4" Aggregate | Slump < 4" | |
---|---|---|---|

5" | 10 | 13 | 15 |

6" | 12 | 15 | 18 |

7" | 14 | 18 | 21 |

8" | 16 | 20 | 24 |

9" | 18 | 23 | 27 |

10" | 20 | 25 | 30 |

It is a linear dimension and represents mathematically the 4th root of

the ratio of the stiffness of the slab to the stiffness of the foundation.

**Values of Portlant Cement Concrete Coefficient of Shrinkage (e)**

**Concrete Strength, Modulus of Rupture, Srinkage Coefficient,**

f 'c (psi) | MR (psi) | e (in./in.) |
---|---|---|

3000 | 493 | 0.00046 |

3500 | 532 | 0.00040 |

4000 | 569 | 0.00035 |

4500 | 604 | 0.00030 |

5000 | 636 | 0.00026 |

5500 | 667 | 0.00023 |

6000 | 697 | 0.00020 |

**Note:**Indirect tensile strength = Modulus of Rupture (MR) = 9*SQRT(f 'c)

**Recommendations for input of Increase for 2nd Wheel (or Post), 'i':**

**1.**For 6" to 10" thick slabs on grade with 'k' values between 100 pci and 200

pci, the increase in stress, 'i', due to a 2nd wheel (or post) load as a

percentage of stress for a single wheel (or post) load is approximately

15% to 20% for a wheel (or post) spacing of 3' to 4'.

**2.**For wheel (or post) spacings of 5' to 15', the increase in stress is

approximately 0% to 5%.

**3.**For a single post load, input a value of i = 0%.

**4.**For situations outside of the above criteria and/or for a more in depth

analysis and evaluation of the effects of a 2nd wheel (or post) load, please

refer to the "BOEF.xls" (Beam On Elastic Foundation) spreadsheet workbook.

**Disclaimer: **This calculator is not intended to be used for the design of actual structures, but only for schematic (preliminary) understanding of structural design principals. For the design of an actual structure, a competent professional should be consulted.

‘Calculations courtesy of Alex Tomanovich, PE ’