RAM Concept Help

Calculation of Effective Curvature Ratio

RAM Concept calculates an "effective curvature ratio" at every cross section:

ECR = Ce / Cg

where
ECR
=
the effective curvature ratio
Ce
=
the effective cross section curvature (see calc below)
Cg
=
the gross section curvature

Ce is calculated by the approximate formula:

Ce = (kc BSR Cg) + ((1 – BSR) Cccs)

where
kc
=
the concrete material creep factor (often 3.35) = total strain / elastic strain
BSR
=
Branson’s Stress Ratio or Eurocode 2 Stress Ratio (see "Branson’s Stress Ratio" or "Eurocode 2 Cracking Distribution Stress Ratio")
Cccs
=
the cross section curvature considering cracking, creep and shrinkage (see "Cracked Section Analyses")

Note that if gross-section stresses are kept below the concrete tensile strength, then the effective curvature ratio will be equal to the concrete material creep factor (kc).

If post-tensioning is considered as an internal force (not an external load) for the active design rules, then the gross-section calculations are performed with the post-tensioning primary forces added to the calculated cross section forces.

It is unusual, but possible, for the ECR value to be less than the concrete material creep factor (kc). These cases occur if the amount of reinforcement is so large that the cracked stiffness (including concrete creep) is greater than the gross stiffness (including concrete creep).