The Relationship between Stress-Strain Distribution in Concrete for Limit State of Collapse in Compression

The relationship between stress-strain distribution in concrete for limit state of collapse in compression is assumed to be parabolic. This assumption is based on the following reasons:

- Concrete is a brittle material: Concrete is a brittle material, which means that it can withstand compressive stresses only up to a certain limit before it fails. This failure is sudden and catastrophic, and it is accompanied by very little deformation. Therefore, the stress-strain relationship of concrete in compression is nonlinear, and it can be approximated by a parabolic curve.

- Strain hardening is negligible: Unlike steel, concrete does not exhibit strain hardening. This means that the stress-strain relationship of concrete in compression does not show any increase in strength beyond the peak stress. Therefore, a parabolic curve is a good approximation for the stress-strain relationship of concrete in compression.

- Ductility is low: Ductility is the ability of a material to deform under stress without fracturing. Concrete has a low ductility, which means that it cannot sustain large deformations before it fails. Therefore, a parabolic curve is a good approximation for the stress-strain relationship of concrete in compression, as it does not require large deformations.

Conclusion

In conclusion, the relationship between stress-strain distribution in concrete for limit state of collapse in compression is assumed to be parabolic because of the brittle nature of concrete, negligible strain hardening, and low ductility. A parabolic curve is a good approximation for the stress-strain relationship of concrete in compression, as it reflects the nonlinear behavior of the material and does not require large deformations.