Instructions for Using the Projected Area Calculator

Appendix B of ACI 349 and many other modern codes base the design strength of concrete for an anchor on the concrete's calculated pullout capacity. The following criteria form the basis for the calculation.

  • The tensile capacity of concrete is generally accepted as ranging from 6 to 7 times the square root of the compressive strength of concrete (in psi).
  • The principal stress in the concrete describes a cone originating at the anchor head and radiating toward the surface of concrete at 45 degrees from the axis of the anchor.
  • The principal stress varies from a maximum at the anchor head to zero at the concrete surface.


    • Taken together, the above criteria indicate an average resistance on the part of the concrete of 6 to 7 times the square root of the compressive strength of concrete acting on the lateral surface area of the cone. This translates to approximately 4 times the square root of concrete compressive strength on the projected area of concrete at the concrete surface. See Figures B.4.1 and B.4.2 of the Code

    Section B.4.2 of Appendix B defines the design strength of concrete as times the projected area of concrete and details the appropriate factors. It states that, "The effective area shall be limited by overlapping stress cones, by the intersection of the cones with concrete surfaces, by the bearing area of anchor heads, and by the overall thickness of the concrete."

    In practice, then, the calculation of concrete design strength is elementary except in cases where closely spaced anchors result in overlapping projected circles on the concrete surface. Manual calculation in these cases is tedious and error prone, the more so since the calculation must often be iterated at successively greater embedments (circle radii) until the required design strength is achieved. The concrete projected area calulator is intended to simplify these calculations by providing a form based interface to a program which will calculate the projected area of an arbitrary bolt pattern.

    To use the program simply input the bolt diameter, position and embedment for each anchor in the pattern and then use the calculate button to calculate the projected area. Bolt position is specified by entering the anchor's x, y grid coordinates as in a plan view. All entered parameters should be expressed in inches and the calculated result is given in square inches. Please bear in mind that while the program takes overlapping stress cones and the bearing area of anchor heads into account, it does not account for concrete edge distances, the effects of other nearby anchor groups nor the overall thickness of the concrete. Please see the appropriate code sections for guidance on these issues.


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