Reinforced Concrete Analysis

موضوع: Reinforced Concrete Analysis الأحد مايو 23, 2010 11:54 pm

	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.

Reinforced Concrete Analysis Types: Axial Force and Bending Moment Pure flexure design example </li> Moment Curvature Analysis

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: <blockquote> Stress and strain <blockquote> Depth to neutral axis = c Maximum concrete strain = e Concrete compressive strength = f^'_c Reinforcing yield strength = f_y </blockquote> </blockquote>
<blockquote> Stress block <blockquote> Ratio of average concrete stress = a₁ Ratio of stress block depth = b₁ </blockquote> </blockquote>
<blockquote> Reduction factors (American, ACI 318) <blockquote> Reinf reduction factor for tension and flexure = f Reinf reduction factor for comp and flexure = f </blockquote> </blockquote> 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.
<blockquote> Resistance factors (Canadian, CSA A23.3) <blockquote> Concrete resistance factor = f_c Reinforcement resistance factor = f_r </blockquote> </blockquote> 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 in² Concrete compressive strength = f^'_c = 4000 psiReinforcing yield strength = f_y = 60000 psi <blockquote> Determine moment capacity per ACI 318 </blockquote> Maximum concrete strain = e = 0.003 Reduction factor for flexure = f = 0.90 Ratio of average concrete stress = a₁= 0.85 Ratio of stress block depth = b₁= 0.85 <blockquote> <blockquote> Solve for a using the SF = 0. </blockquote> </blockquote> A_sf_y = a b b₁ f^'_c 3.0(60000) = a (12)(0.85)(4000) a = 4.41 inches <blockquote> <blockquote> Determine moment from force couple </blockquote> </blockquote> f M_n = f A_sf_y (d - a / 2) f M_n = 0.9(3.0)(60)(21 - 4.41 / 2) / 12 f M_n= 254 k-ft <blockquote> Determine moment capacity per CSA A23.3 </blockquote> 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 = a₁= 0.81 Ratio of stress block depth = b₁= 0.9 <blockquote> <blockquote> Solve for "a" using the SF = 0. </blockquote> </blockquote> f_rA_sf_y = a b b₁ f_cf^'_c 0.85(3.0)(60000) = a (12)(0.81)(0.6)(4000) a = 6.56 inches <blockquote> <blockquote> Determine moment from force couple </blockquote> </blockquote> M_r = f_r A_sf_y (d - a / 2) M_r = 0.85(3.0)(60)(21 - 6.56 / 2) / 12 M_r= 226 k-ft

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