Point Load on Slab on Grade
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.
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What it calculates
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.
Code standards
- ACI 318-19
Who uses this calculator
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.
How it calculates
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 modelled; 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.
Frequently asked questions
What reference methods does this calculator use?
What are the key inputs?
What does the calculator check and output?
How is the concrete modulus and tensile strength determined?
What is the radius of relative stiffness?
What factor of safety should I use?
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