Flexural Strength per ACI 318-19 with ideCAD
How does ideCAD calculate flexural strength according to ACI 318-19?
Flexural strength is calculated automatically.
Notation
A_{s}_{ } = area of nonprestressed longitudinal tension reinforcement, in^{2}
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}_{ } = concrete compressive 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
β_{1 } = factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis
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Flexural Strength
Nominal flexural strength M_{n} is calculated based on the following Design Assumptions. According to ACI 22.1.3, the design strength of a section is ϕM_{n}.
Design assumptions
The flexural and axial strength of a member calculated by the strength design method, two basic conditions should be satisfied:
equilibrium
compatibility of strains
Equilibrium means balancing of forces acting on the element cross section at nominal strength. Stress-strain relationship for the concrete and the reinforcement at nominal strength is established within the design assumptions described following:
Equilibrium is satisfied in each section.
It is assumed that strain in concrete and reinforcement is proportional to the distance from the neutral axis.
Design strength is calculated by using these assumptions together with design assumptions for concrete described following:
Maximum strain at the extreme concrete compression fiber is assumed equal to 0.003.
The tensile strength of concrete is neglected.
The relationship between concrete compressive stress and strain is represented by the equivalent rectangular concrete stress distribution method.
Concrete stress of 0.85f_{c}^{'} is assumed to be 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:
The distance between the fiber of maximum compressive stress and the neutral axis, c, is perpendicular to the neutral axis.
The value of β_{1} is determined using ACI Table 22.2.2.4.3.
f_{c}' , psi | β_{1} |
---|---|
2500 ≤ f_{c}^{'} ≤ 4000 | 0.85 |
4000 < f_{c}^{'} < 8000 | 0.85 - 0.05(f_{c}^{'} -4000)/1000 |
f_{c}^{'} ≥ 8000 | 0.65 |
Nominal flexural strength M_{n} is calculated as shown below.
The total forces C_{c} and C_{s} resulting from the stresses of concrete and reinforcement are shown below.
From the equation of equilibrium:
Nominal flexural strength M_{n}:
According to ACI 22.1.3, the design strength of a section is taken as the nominal strength multiplied by the applicable strength reduction factor ϕ. Therefore, the design force is ϕM_{n}.
The difference between Design Strength ϕM_{n} and Nominal Strength M_{n} is indicated in the figure below.