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İnternational Design Codes

ACI 318-19 : Flexural Strength

TSC 2018 : TSC Flexural Strength

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Notation

A_{s =} area of nonprestressed longitudinal tension reinforcement, in²
α = depth of equivalent rectangular stress block, in.
b_w = web width or diameter of circular section, in.
c = distance from extreme compression fiber to neutral axis, in.
C_{c =} concretecompressive force, lb
C_{s =} reinforcement tension force, lb
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
f_c^'₌ specified compressive strength of concrete, psi
f_y = specified yield strength for nonprestressed reinforcement, psi
M_n = nominal flexural strength at section, in.-lb
ϕ = strength reduction factor
ε_t = net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature
β₁ = factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis

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• Maximum strain at the extreme concrete compression fiber is assumed equal to 0.003.

• Tensile strength of concrete is neglected.

• The relationship between concrete compressive stress and strain is represented by equivalent rectangular concrete stress distribution method.

• Concrete stress of 0.85f_c^' is assumed uniformly distributed over. Equivalent rectangular concrete stress zone bounded by edges of the cross section and a line parallel to the neutral axis located a distance α from the fiber of maximum compressive strain, as calculated by:

$$ α = β_1c $$ 

• The distance between the fiber of maximum compressive stress and the neutral axis, c, is perpendicular to the neutral axis.

• The value of β₁ is determined using Codes.

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The total forces C_c and C_s resulting from the stresses of concrete and reinforcement are shown below.

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From the equation of equilibrium:

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Nominal flexural strength M_n:

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