Concrete Behavior

This elastic modulus of concrete is defined by the user in the materials window. You can choose to use the code equation of BS8110 Figure 2.1 or a specified value.

When you directly specify values, there must be two elastic modulus values:

E_ci = value for initial service (transfer) cross section analyses
E_c = value for all other conditions

When the BS 8110 code equation is selected the following values are used:

E_{c i} = 5, 500 \sqrt{\frac{f_{c u i}}{1.5}}

E_{c} = 5, 500 \sqrt{\frac{f_{c u}}{1.5}}

where

f_cui	=	cube strength at stressing
f_cu	=	28 day cube strength

For calculations based on the "concrete section", concrete is assumed to be a perfectly linear-elastic material with no stress or strain limits.

For detailed cross section analyses, four different stress strain curves are used. All four stress-strain curves are parabolic-linear curves as detailed in. The transition strain from the parabolic to the linear curve is at 2f_c / E_c, where f_c is the peak stress and E_c is the elastic modulus at zero strain.

For initial stress conditions, the peak stress in the stress strain curve is
0.67f_cui
For service stress conditions, the peak stress in the stress-strain curve is
0.67f_cu
For strength conditions, the peak stress in the stress-strain curve is
0.67f_cu / 1.5
For accident (localised damage) strength conditions, the peak stress in the stress-strain curve is
0.67f_cu/ 1.3

The strength stress-strain curves are truncated at a strain of 0.0035. The other stress-strain curves have no limit strain.

For ECR calculations, the maximum tension stress in concrete is assumed to be $0.6 \sqrt{f_{c u}}$ .

For service design crack width calculations and for service design cracked stress analyses, a tension stiffened concrete stress strain curve is used:

Use of this curve is similar, but not technically equivalent, to the provisions of BS 8110-2:1985 Figure 3.1. A comparison of the stress diagrams for the Code provision and the Concept implementation are shown below:

Figure 3.1 provision

RAM Concept implementation

Since RAM Concept ’s crack width design does a cracked stress analysis (with a non tension stiffened concrete stress strain curve) for the 0.8f_y provision, the concrete and rebar stress results for members on which a crack width design is done will represent the range of results between the tension stiffened and the non tension stiffened concrete stress strain curve. Concrete and rebar stress results for all other members will represent use the tension stiffened concrete stress strain curve only.