United StatesACI 318-19
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
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 / FSFactored 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 ≤ 1.0Assumptions
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
1
Open the calculator
Open it from Run calc in the About this calculator panel above.
2
Enter your inputs
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.
3
Review the results and export
Check the utilization of each governing check in the summary, then export a PDF report. See Views and Export.
Common questions
What reference methods does this calculator use?
What reference methods does this calculator use?
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.
What are the key inputs?
What are the key inputs?
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).
What does the calculator check and output?
What does the calculator check and output?
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.
How is the concrete modulus and tensile strength determined?
How is the concrete modulus and tensile strength determined?
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.
What is the radius of relative stiffness?
What is the radius of relative stiffness?
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.
What factor of safety should I use?
What factor of safety should I use?
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
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