During calculation, beams are represented by their centroidal curve, which coincides with uncracked centre-of-gravity line. The centroids will be moved to a new position when a member cracks, which means that the centre-of-gravity line of the member will differ from the original centre-of-gravity line for an uncracked member. This difference must be considered when the strain-curvature results from the section calculation are translated into effective stiffness. 

As described in the section about effective stiffness the conditions displayed in the figure (axial compressive force with tension in the centroidal curve of the member) cause trouble when calculating the effective area. There must be correspondence between the beam and the section analysis (compatibility) for a valid calculation to take place. The lengthening of the centroidal curve will not be compatible to the axial compressing strain, i.e. compatibility in strain is not at hand. In order to restore compatibility, the program chooses to interpret the difference in strain between the frame calculation and the section analysis as an inelastic deflection that is added to the beam. 

The difference in strain for a member is obtained from

1537735229997-477.pngε = εcg,uncr1537735219412-580.png / L 

where:

  • εcg,uncr = an average strain in the centroidal curve of the member, such as creeping, shrinkage and thermal elongation, 
  • 1537735235943-928.png = an average strain in the centroidal curve of the member, such as creeping, shrinkage and thermal elongation, 
  • L = member length. 

During iteration 1537735242649-279.pngε is added to 1537735285438-258.png1537735246743-461.pngε from the previous step. When a displacement is 1537735251262-273.pngε = 0 during a new iteration step, the strains within the frame calculation and section analysis correspond.

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PRE-Stress Documentation