> For the complete documentation index, see [llms.txt](https://enercalc.com/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://enercalc.com/docs/sel-user-manual/calculation-modules/foundation/point-load-on-slab.md). # Point Load on Slab How to evaluate the capacity of an unreinforced slab-on-grade under isolated concentrated loads using ASD or LRFD. ### Design Approach and Sources This module calculates the load-carrying capacity of an unreinforced slab-on-grade under isolated concentrated loads. Typical loads include storage rack legs that aren't supported by the building structure. ACI 318 doesn't cover this application. The module implements the simplified analytical method from Azzi and Laird (2008). The method derives from nonlinear finite element research by Shentu, Jiang, and Hsu (1997). The method uses an elasto-plastic representation of slab behavior to estimate ultimate capacity under concentrated loads. It accounts for concrete cracking and post-cracking behavior. #### Sources 1. Shentu, Jiang, and Hsu (1997). *Load-Carrying Capacity for Concrete Slabs on Grade.* Journal of Structural Engineering, ASCE. 2. Azzi and Laird (2008). *Load-Carrying Capacity of Concrete Slabs-on-Grade Subject to Concentrated Loads.* STRUCTURE Magazine. 3. Jlilati, Brown, and Tang (2019). *Comparative Investigation of Two Design Methods for Slab-on-Grade Foundations Subjected to Concentrated Loads.* ISEC Press. 4. Federal Emergency Management Agency (FEMA). (2005). *Seismic Considerations for Steel Storage Racks Located in Areas Accessible to the Public (FEMA 460).* Prepared by the Building Seismic Safety Council. ### Slab Capacity Equations The module calculates nominal load-carrying capacity using: $$ P\_n = \beta \times 1.72 \left(\frac{k\_s R\_1}{E\_c} \times 10{,}000 + 3.60\right) F\_r d^2 $$ *\[Equation 1, Azzi and Laird (2008)]* Where: * $$P\_{n}$$ is nominal load-carrying capacity. * $$k\_{s}$$ is the soil modulus of subgrade reaction, in pci. * $$R\_{1}$$ is the equivalent bearing radius, in inches: $$ R\_1 = \frac{\sqrt{\text{Plate Width} \times \text{Plate Length}}}{2} $$ * $$E\_{c}$$ is the concrete elastic modulus, in psi. * $$F\_{r}$$ is concrete tensile strength in flexure, in psi: $$ F\_r = f\_t' \sqrt{f\_c'} $$ * $$f\_{c}'$$ is specified concrete compressive strength, in psi. * $$d$$ is slab thickness, in inches. * $$\beta$$ is the thick-slab load reduction factor. Azzi and Laird (2008) use β = 1.0 for slabs thinner than 7 in. They use β = 0.85 for slabs 7 in. thick or thicker. * $$f\_{t}'$$ is the flexural tensile-strength factor. Use 7.5 for normalweight concrete unless engineering judgment and supporting research support another value. #### ASD and LRFD Implementation When you select ASD, the module divides nominal load-carrying capacity ($$P\_{n}$$) by the user-defined factor of safety (FS). It then compares the result with the applied load ($$P\_{u}$$): $$ FS = \frac{P\_n}{P\_u} $$ When you select LRFD, the module applies the user-defined strength reduction factor (ɸ) to nominal load-carrying capacity ($$P\_{n}$$). The factor of safety remains available as an additional input. Set FS to 1.0 when ɸ provides the intended resistance reduction. You can use another value when it matches your design approach and engineering judgment. $$ FS = \frac{\phi P\_n}{P\_u} $$ This module provides flexibility in how resistance reductions are applied. Users should ensure that the combined effect of ɸ and FS reflects their intended design assumptions and should avoid unintentionally double-counting safety margins. #### Factor of Safety Considerations This module allows the user to specify a Factor of Safety (FS) to reduce the nominal load-carrying capacity for design use. Earlier applications of this method commonly used a Factor of Safety of 3. Experimental studies evaluating this approach indicate that a Factor of Safety of 6 may be more appropriate for design applications. Users should select a Factor of Safety consistent with their intended performance objectives and applicable engineering judgment. These Factor of Safety values are most directly applicable when the method is used in an ASD framework. When LRFD is selected, users should ensure that the combined effect of the selected strength reduction factor (ɸ) and any additional Factor of Safety reflects their intended performance objectives. ### Minimum Adjacent Load The nominal load-carrying capacity ($$P\_{n}$$) equation assumes that the load acting on the slab is unique and no other nearby loads are affecting the calculation. To assist in the evaluation of slabs-on-grade, this module also provides a calculation of the distance that the closest load may be without affecting the calculated slab capacity. The calculation given below is based on research by Packard, Pickett and Ray, and Spears and Panarese, and is also discussed in ACI 360R-92. The module calculates the minimum adjacent-load distance as 1.5 times the radius of relative stiffness: $$ b = \left(\frac{E\_c d^3}{12(1-\nu^2)k\_s}\right)^{0.25} $$ *\[Equation 3, Azzi and Laird (2008)]* Where: * $$b$$ is the radius of relative stiffness, in. * $$E\_c$$ is the concrete elastic modulus, in psi. * $$d$$ is the slab thickness, in. * $$\nu$$ is Poisson's ratio. * $$k\_s$$ is the soil modulus of subgrade reaction, in pci. ### Edge Distance Considerations The method used in this module applies to concentrated loads at interior slab locations and does not address loads located near slab edges, joints, or penetrations. In the finite-element analysis on which the method is based, the modeled slab extended approximately three times the radius of relative stiffness (3b) from the load (Shentu et al. 1997; Azzi and Laird 2008). For the module to be applicable, we recommend keeping the load at least 3b from free edges, joints that may open, and slab penetrations. This lower bound keeps the slab surrounding the load at least as extensive as the slab that was analyzed. The source research does not specify an edge-distance limit, and this value has not been verified by testing. Users should evaluate edge distance using applicable engineering judgment. For reference, the Min. Adjacent Load Distance reported on the General tab equals 1.5b, so a distance of 3b is twice that value. ### General ![](https://3283832020-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FiBJmBoewuy4ZcBC7RF3m%2Fuploads%2Fgit-blob-8c102b11c8ae4a45bda608bbd0551c61984493ba%2FPoint%20Load%20on%20Slab%20-%20General.png?alt=media) This module is designed to allow the user to create a table of loads applied to a particular concrete slab and supporting soil with one set of material properties. You can then use the \[**Add**], \[**Edit**] and \[**Delete**] buttons to add a set of applied loads and base plate dimensions. From this data all load combinations are used to determine the maximum axial force. For the plate dimension you specify, the maximum load capacity for the point load application is calculated and compared with your required factor of safety. ### Load Combinations This Load Combination set used is based on the selected design method, ASD or LRFD. ![](https://3283832020-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FiBJmBoewuy4ZcBC7RF3m%2Fuploads%2Fgit-blob-a4f39acb8cc000944629506a5ab8b34510c22893%2FPoint%20Load%20on%20Slab%20-%20LoadCombos.png?alt=media) --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation by asking a question. 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