Reinforced Concrete Analysis
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 stressstrain behavior of the concrete with a rectangular stress block to simplify the calculations. More detailed, moment curvature analysis may be performed with more complex stressstrain relationships.
Reinforced Concrete Analysis Types:
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:

Stress and strain
 Depth to neutral axis = c
 Maximum concrete strain = e
 Concrete compressive strength = f^{'}_{c}
 Reinforcing yield strength = f_{y}

Stress block
 Ratio of average concrete stress = a_{1}
 Ratio of stress block depth = b_{1}

Reduction factors (American, ACI 318)
 Reinf reduction factor for tension and flexure = f
 Reinf reduction factor for comp and flexure = f
Note: Strength reduction factors are used in the American codes, both ultimate strength design and loadresistance factor design. These factors are applied to the computed strength based on the mode of failure.

Resistance factors (Canadian, CSA A23.3)
 Concrete resistance factor = f_{c}
 Reinforcement resistance factor = f_{r}
Note: Resistance factors are used in the Canadian codes and are applied directly to the material strengths without regard to the mode of failure.
Pure Flexure Design Example:
Determine the bending moment resistance of a rectangular beam with tension reinforcement and no axial loads.
Depth to reinforcing = d = 21 inches
Beam width = b = 12 inches
Reinforcing steel area = A_{s} = 3.0 in^{2}
Concrete compressive strength = f^{'}_{c } = 4000 psi_{
}Reinforcing yield strength = f_{y} = 60000 psi
 Determine moment capacity per ACI 318
Maximum concrete strain = e = 0.003
Reduction factor for flexure = f = 0.90_{ } Ratio of average concrete stress = a_{1 }= 0.85
Ratio of stress block depth = b_{1}= 0.85
 Solve for a using the SF = 0.
A_{s }f_{y} = a b a_{1} f^{'}_{c}
3.0(60000) = a (12)(0.85)(4000)
a = 4.41 inches
 Determine moment from force couple
f M_{n} = f A_{s}f_{y} (d  a / 2)
f M_{n} = 0.9(3.0)(60)(21  4.41 / 2) / 12
f M_{n }= 254 kft
 Determine moment capacity per CSA A23.3
Maximum concrete strain = e = 0.0035
Concrete resistance factor = f_{c} = 0.60_{ } Reinforcement resistance factor = f_{r} = 0.85_{ } Ratio of average concrete stress = a_{1 }= 0.81
Ratio of stress block depth = b_{1}= 0.9
 Solve for "a" using the SF = 0.
f_{r }A_{s }f_{y} = a b a_{1} f_{c }f^{'}_{c}
0.85(3.0)(60000) = a (12)(0.81)(0.6)(4000)
a = 6.56 inches
 Determine moment from force couple
M_{r} = f_{r} A_{s}f_{y} (d  a / 2)
M_{r} = 0.85(3.0)(60)(21  6.56 / 2) / 12
M_{r }= 226 kft