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# Check a Point Load on a Slab on Grade
> Check point load capacity on concrete slabs on grade using the Azzi-Laird and Shentu-Jiang-Hsu methods with ACI 318-19 material properties.
Check point load capacity on concrete slabs-on-grade using the Azzi-Laird and Shentu-Jiang-Hsu methods with ACI 318-19 material properties and IBC 2018 load combinations. Covers base plates, racking legs, mezzanine columns, and equipment supports.
## Method & scope
| Property | Detail |
| ---------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Design standards | Load Carrying Capacity: Concrete Slabs on Grade: Azzi and Laird, ACI 318-19 |
| Regions | United States |
| Who it's for | US structural engineers designing isolated column base plates, racking loads, free-standing mezzanine columns, and equipment supports on concrete slabs-on-grade — including warehouse and industrial applications. |
| What it checks | Slab material properties, Radius of relative stiffness, Load carrying capacity, Factored load check (IBC 2018) |
#### What it calculates
US structural engineers designing isolated column base plates, racking loads, free-standing mezzanine columns, and equipment supports on concrete slabs-on-grade, including warehouse and industrial applications. The calculator uses the validated Azzi-Laird and Shentu-Jiang-Hsu methods to check allowable point load capacity and reports a factor of safety against punching and flexural failure.
Provides a validated workflow for a design case not explicitly covered by ACI 318-19 scope, replacing reliance on structural research articles or custom spreadsheets.
#### Calculation method
The Point Load on Slab on Grade calculator checks the allowable point load capacity of an unreinforced or lightly reinforced concrete slab-on-grade using the Azzi-Laird simplified analytical method, cross-referenced against the Shentu, Jiang, and Hsu method. The procedure addresses a design case not explicitly in ACI 318-19 scope, replacing reliance on direct use of journal articles or custom spreadsheets.
##### Slab material properties
Concrete modulus of elasticity (ACI 318-19 Cl 19.2.2.1a):
**E\_c = 33 × w\_c^1.5 × sqrt(f'c)** (psi, valid for w\_c between 90 and 160 pcf)
Flexural tensile strength (ACI 318-19 Cl 14.5.2.1a):
**f\_t' = lambda × 7.5 × sqrt(f'c)**
where lambda is the lightweight concrete modification factor per ACI 318-19 Cl 19.2.4.1 (1.0 for normalweight, 0.75 for lightweight, or custom).
##### Radius of relative stiffness
The radius of relative stiffness b characterizes how far a point load's influence extends in the slab:
**b = (E\_c × d³ / \[12 × (1, nu²) × k\_s])^0.25** (Azzi-Laird Equation 3)
where d is the slab depth, nu is Poisson's ratio (typically 0.15 for concrete), and k\_s is the soil modulus of subgrade reaction (pci). A smaller b indicates a stiffer slab-soil system.
##### Load carrying capacity
The half-width of the column base plate R\_1 is taken as the minimum of L/2 and W/2. A load reduction factor beta accounts for deviation from a theoretical point load when the base plate has finite dimensions.
Nominal load carrying capacity (Azzi-Laird Equation 1):
**P\_n = 1.72 × ((k\_s × R\_1 / E\_c) × 10^4 + 3.6) × f\_t' × beta × d²**
The allowable load capacity with the required factor of safety (Azzi-Laird Equation 1a):
**P\_a = P\_n / FS**
##### Factored load check (IBC 2018)
The maximum factored applied load P is determined from IBC 2018 strength load combinations applied to the user-entered dead and live loads. The governing check is:
**utilization = P / P\_a ≤ 1.0**
##### Assumptions
The slab is assumed to behave as an elastic plate on a Winkler foundation. The method is validated for isolated point loads on interior slab locations, edge and corner conditions require separate analysis. Slab reinforcement is not explicitly modeled; the method applies to plain or lightly reinforced slabs where flexural tensile strength of the concrete governs. No punching shear check per ACI 318-19 is performed.
## How to use it
Open it from **Run calc** in the About this calculator panel above.
Work through the input sections from top to bottom. Click any input label to see its reference explanation, clause, conditions and assumptions. See [Checks, References, Conditions and Assumptions](/docs/running-calculations/checking-results/checks-references-conditions-assumptions).
Check the utilization of each governing check in the summary, then export a PDF report. See [Views and Export](/docs/running-calculations/exporting-reports/views-and-export).
## Common questions
The calculator implements the Azzi and Laird simplified analytical method for slab-on-grade point load capacity, cross-referenced with the Shentu, Jiang, and Hsu method. Both methods are based on concrete modulus of elasticity, tensile flexural strength, and the radius of relative stiffness of the slab-soil system. Load factors use IBC 2018 strength combinations.
Key inputs are concrete compressive strength f'c (psi, minimum 2500 psi per ACI 318-19 Cl 19.2.1.1), slab depth d (inches), concrete weight classification (normalweight or lightweight, per ACI 318-19 Cl 19.2.4.1), column base plate length and width (L and W, inches), soil modulus of subgrade reaction k\_s (pci), applied point loads by load type, and a required factor of safety (FS, typically 3.0).
The calculator outputs: maximum applied factored load P (from IBC 2018 strength combinations), nominal load carrying capacity P\_n (Azzi-Laird Equation 1), allowable load capacity P\_a = P\_n / FS (Azzi-Laird Equation 1a), and the radius of relative stiffness b. A pass/fail check verifies that the applied load does not exceed the allowable capacity.
Concrete modulus of elasticity E\_c is computed per ACI 318-19 Cl 19.2.2.1a as a function of concrete density and f'c, valid for densities between 90 and 160 pcf. Flexural tensile strength f\_t' is taken from ACI 318-19 Cl 14.5.2.1a, approximately 10-15% of compressive strength, modified by the lightweight concrete factor lambda per Cl 19.2.4.1.
The radius of relative stiffness b characterizes the interaction between the slab stiffness and soil support, and is the minimum distance at which an applied load ceases to cause significant deflection. It depends on E\_c, slab depth d, Poisson's ratio, and the soil modulus of subgrade reaction k\_s. A higher k\_s (stiffer soil) reduces b and generally increases allowable load capacity.
Azzi and Laird recommend FS = 3.0 for design of point loads on slabs on grade. A lower FS may be applicable for temporary loads or where slab conditions are well-documented. The calculator allows the engineer to enter any factor of safety, with 3.0 as the default.
## Next steps
Complete list of Calcs.com design calculators available for United States projects (AISC, ACI, NDS, ASCE 7, IBC, and related standards).
Design rectangular concrete columns to ACI 318-19. Checks axial capacity, P-M interaction, biaxial bending and slender column moment magnification.
Design rectangular concrete beams and T-beams to ACI 318-19 across unlimited spans. Checks flexure, shear, and short- and long-term deflection.
Design continuous wall footings to ACI 318-19 per IBC 2021 or IBC 2024. Results cover ultimate load, bearing capacity and serviceability.
