Reinforced concrete analysis is performed at a given section for either axial force and bending moment or transverse shear loads. The axial force and bending moment analysis usually idealizes the stress-strain behavior of the concrete with a rectangular stress block to simplify the calculations. More detailed, moment curvature analysis may be performed with more complex stress-strain relationships.
[↑] Axial Force and Bending Moment:
Reinforced concrete analysis for axial force and bending moment is usually performed by assuming a given strain value at the extreme compression fiber with a linear strain distribution over the depth of the section. The stress distribution typically assumes a rectangular stress block with a depth equal to some fraction of the neutral axis depth and a magnitude equal to some fraction of the concrete compressive strength.[*]
Design Parameters:
a. Stress and strain
Depth to neutral axis = c
Maximum concrete strain = ε
Concrete compressive strength = ƒ'c
Reinforcing yield strength = ƒy
b. Stress block
Ratio of average concrete stress = α1
Ratio of stress block depth = β1
c. Reduction factors (American, ACI 318)
Reinf reduction factor for tension and flexure = ф
Reinf reduction factor for comp and flexure = ф
- Note: Strength reduction factors are used in the American codes, both ultimate strength design and load-resistance factor design. These factors are applied to the computed strength based on the mode of failure.
d. Resistance factors (Canadian, CSA A23.3)
Concrete resistance factor = фc
Reinforcement resistance factor = фr
- Note: Resistance factors are used in the Canadian codes and are applied directly to the material strengths without regard to the mode of failure.
