Interaction diagram

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Interaction diagram
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In structural engineering, interaction diagram or interaction surface is typically defined as a set of points representing values of two or more independent forces or stresses at which failure occurs. For example, 2D interaction diagram can represent strength of concrete subjected biaxial stress or 3D interaction surface can represent failure failure of a concrete column subjected to axial force and biaxial bending.

Column axial load plus bending

Analysis method (Nielson 1997):

  • Replace the moment by the axial force acting on the eccentricity.
  • Calculate points on the interaction diagram as follows:
    • Select successive values for the distance of neutral axis from the compression face, ranging from infinity (this represents pure axial load with zero eccentricity) to a very small value found by trial to represent pure bending with zero axial force.
    • Use strain compatibility to calculate stresses and force resultants.
    • The calculated moment and axial force will represent one point on the interaction surface.
    • Repeat for the next location of neutral axis.

Column biaxial bending

Several methods can be used to construct interaction diagram for biaxial bending (Nielson 1997):

  • Load contour method (approximate method)
  • Reciprocal load method (approximate method)
  • Computer analysis (more exact method suitable for computer analysis)


  • Arthur H. Nielson: Design of Concrete Structures, 12th Edition, 1997, ISBN 0-07-046586-X, p. 270 (Section 8.4: Strain compatibility analysis and interaction diagrams)


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