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Ultimate Strength for Symmetrical Reinforcement in Single Layers Solution

STEP 0: Pre-Calculation Summary
Formula Used
axial_load_capacity = Capacity reduction factor*((Area of Compressive Reinforcement*Yield strength of reinforcing steel/((Eccentricity/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of compression face*Depth of column*28 Day Compressive Strength of Concrete/((3*Depth of column*Eccentricity/(Distance from Compression to Tensile Reinforcement^2))+1.18)))
Pu = Phi*((As'*fy/((e/d)-d'+0.5))+(b*h*fc/((3*h*e/(d^2))+1.18)))
This formula uses 9 Variables
Variables Used
Capacity reduction factor- Capacity reduction factor is derived for reinforced concrete structures based on a reliability based calibration of the Australian Concrete Structures Standard AS3600.
Area of Compressive Reinforcement - Area of Compressive Reinforcement is common sense to place reinforcement in an area subjected to compressive stress. (Measured in Square Meter)
Yield strength of reinforcing steel - Yield strength of reinforcing steel is the stress at which a predetermined amount of permanent deformation occurs. (Measured in Kilogram-Force per Square Meter)
Eccentricity - Eccentricity of an ellipse is a non-negative real number that uniquely characterizes its shape. (Measured in Centimeter)
Distance from Compression to Tensile Reinforcement - Distance from Compression to Tensile Reinforcement is defined as the distance from extreme compression surface to the centroid of tensile reinforcement, in (mm). (Measured in Millimeter)
Distance from Compression to Centroid Reinforcment - Distance from Compression to Centroid Reinforcment is defined as the distance from extreme compression surface to the centroid of compression reinforcement, in (mm). (Measured in Millimeter)
Width of compression face - Width of compression face is the measurement or extent of something from side to side. (Measured in Meter)
Depth of column - Depth of column is the distance from the top or surface to the bottom of something. (Measured in Meter)
28 Day Compressive Strength of Concrete - 28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it. (Measured in Megapascal)
STEP 1: Convert Input(s) to Base Unit
Capacity reduction factor: 1 --> No Conversion Required
Area of Compressive Reinforcement: 20 Square Meter --> 20 Square Meter No Conversion Required
Yield strength of reinforcing steel: 10 Kilogram-Force per Square Meter --> 98.0664999999931 Pascal (Check conversion here)
Eccentricity: 10 Centimeter --> 0.1 Meter (Check conversion here)
Distance from Compression to Tensile Reinforcement: 20 Millimeter --> 0.02 Meter (Check conversion here)
Distance from Compression to Centroid Reinforcment: 10 Millimeter --> 0.01 Meter (Check conversion here)
Width of compression face: 5 Meter --> 5 Meter No Conversion Required
Depth of column: 8 Meter --> 8 Meter No Conversion Required
28 Day Compressive Strength of Concrete: 100 Megapascal --> 100000000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pu = Phi*((As'*fy/((e/d)-d'+0.5))+(b*h*fc/((3*h*e/(d^2))+1.18))) --> 1*((20*98.0664999999931/((0.1/0.02)-0.01+0.5))+(5*8*100000000/((3*8*0.1/(0.02^2))+1.18)))
Evaluating ... ...
Pu = 666892.836344778
STEP 3: Convert Result to Output's Unit
666892.836344778 Newton --> No Conversion Required
FINAL ANSWER
666892.836344778 Newton <-- Axial Load Capacity
(Calculation completed in 00.062 seconds)

11 Other formulas that you can solve using the same Inputs

Theoretical Maximum Stress for Secant Code Steels
critical_stress = Yield Strength/(1+((Eccentricity*End Fixity Coefficient/(Radius of gyration^2))*(sec((1/Radius of gyration)*sqrt(Concentrated load/(4*Cross sectional area*Modulus Of Elasticity)))))) Go
Column Ultimate Strength with Zero Eccentricity of Load
ultimate_strength = 0.85*28 Day Compressive Strength of Concrete*(Gross area-Area of Reinforcement)+Yield Strength*Area of Reinforcement Go
Maximum Stress For a Circular Cross Section
maximum_stress_for_a_section = Axial Stress*(1+8*Eccentricity/Diameter ) Go
Maximum Stress For a Rectangular Cross Section
maximum_stress_for_a_section = Axial Stress*(1+6*Eccentricity/Width) Go
Latus rectum of an ellipse when focal parameter is given
latus_rectum = Focal parameter of an ellipse*Eccentricity Go
Semi-latus rectum of an ellipse when eccentricity is given
semilatus_rectum = Semi-major axis*(1-(Eccentricity)^2) Go
Linear eccentricity of an ellipse when eccentricity and semimajor axis are given
linear_eccentricity = (Eccentricity*Semi-major axis) Go
Linear eccentricity of ellipse when eccentricity and major axis are given
linear_eccentricity = Eccentricity*Major axis Go
Allowable Bearing Pressure when Full Area of Support is Occupied by Base Plate
allowable_bearing_pressure = 0.35*28 Day Compressive Strength of Concrete Go
Directrix of an ellipse(a>b)
directrix = Major axis/Eccentricity Go
Directrix of an ellipse(b>a)
directrix = Major axis/Eccentricity Go

7 Other formulas that calculate the same Output

Ultimate Strength for Symmetrical Reinforcement
axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*Width of compression face*Distance from Compression to Tensile Reinforcement*Capacity reduction factor*((-Area ratio of tensile reinforcement)+1-(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement)+sqrt(((1-(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement))^2)+2*Area ratio of tensile reinforcement*((Force ratio of strengths of reinforcements-1)*(1-(Distance from Compression to Centroid Reinforcment/Distance from Compression to Tensile Reinforcement))+(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement)))) Go
Ultimate Strength for No Compression Reinforcement
axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*Width of compression face*Distance from Compression to Tensile Reinforcement*Capacity reduction factor*((-Area ratio of tensile reinforcement*Force ratio of strengths of reinforcements)+1-(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement)+sqrt(((1-(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement))^2)+2*(Area ratio of tensile reinforcement*Eccentricity by method of frame analysis*Force ratio of strengths of reinforcements/Distance from Compression to Tensile Reinforcement))) Go
Ultimate Strength for Short, Circular Members when Controlled by Tension
axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*(Overall diameter of section^2)*Capacity reduction factor*(sqrt((((0.85*Eccentricity/Overall diameter of section)-0.38)^2)+(Area ratio of gross area to steel area*Force ratio of strengths of reinforcements*Diameter of reinforcement/(2.5*Overall diameter of section)))-((0.85*Eccentricity/Overall diameter of section)-0.38)) Go
Ultimate Strength for Short, Square Members when Controlled by Tension
axial_load_capacity = 0.85*Width of compression face*Depth of column*28 Day Compressive Strength of Concrete*Capacity reduction factor*((sqrt((((Eccentricity/Depth of column)-0.5)^2)+(0.67*(Diameter of reinforcement/Depth of column)*Area ratio of gross area to steel area*Force ratio of strengths of reinforcements)))-((Eccentricity/Depth of column)-0.5)) Go
Ultimate Strength for Short, Circular Members when Governed by Compression
axial_load_capacity = Capacity reduction factor*((Area of steel reinforcement*Yield strength of reinforcing steel/((3*Eccentricity/Diameter of reinforcement)+1))+(Gross area*28 Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall diameter of section+0.67*Diameter of reinforcement)^2)+1.18))) Go
Ultimate Strength for Short, Square Members when Governed by Compression
axial_load_capacity = Capacity reduction factor*((Area of steel reinforcement*Yield strength of reinforcing steel/((3*Eccentricity/Diameter of reinforcement)+1))+(Gross area*28 Day Compressive Strength of Concrete/((12*Depth of column*Eccentricity/((Depth of column+0.67*Diameter of reinforcement)^2))+1.18))) Go
Axial-Load Capacity of Short Rectangular Members
axial_load_capacity = Resistance Factor*((.85*28 Day Compressive Strength of Concrete*Width of compression face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yeild Strength of Base Plate)-(area of tension reinforcement*Tensile Stress in Steel)) Go

Ultimate Strength for Symmetrical Reinforcement in Single Layers Formula

axial_load_capacity = Capacity reduction factor*((Area of Compressive Reinforcement*Yield strength of reinforcing steel/((Eccentricity/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of compression face*Depth of column*28 Day Compressive Strength of Concrete/((3*Depth of column*Eccentricity/(Distance from Compression to Tensile Reinforcement^2))+1.18)))
Pu = Phi*((As'*fy/((e/d)-d'+0.5))+(b*h*fc/((3*h*e/(d^2))+1.18)))

What is the ultimate strength of a material?

The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens. For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MPa.

How to Calculate Ultimate Strength for Symmetrical Reinforcement in Single Layers?

Ultimate Strength for Symmetrical Reinforcement in Single Layers calculator uses axial_load_capacity = Capacity reduction factor*((Area of Compressive Reinforcement*Yield strength of reinforcing steel/((Eccentricity/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of compression face*Depth of column*28 Day Compressive Strength of Concrete/((3*Depth of column*Eccentricity/(Distance from Compression to Tensile Reinforcement^2))+1.18))) to calculate the Axial Load Capacity, The Ultimate Strength for Symmetrical Reinforcement in Single Layers formula is defined as Ultimate strength is equivalent to the maximum load that can be carried by one square inch of cross-sectional area when the load is applied as simple tension. Axial Load Capacity and is denoted by Pu symbol.

How to calculate Ultimate Strength for Symmetrical Reinforcement in Single Layers using this online calculator? To use this online calculator for Ultimate Strength for Symmetrical Reinforcement in Single Layers, enter Capacity reduction factor (Phi), Area of Compressive Reinforcement (As'), Yield strength of reinforcing steel (fy, Eccentricity (e), Distance from Compression to Tensile Reinforcement (d), Distance from Compression to Centroid Reinforcment (d'), Width of compression face (b), Depth of column (h) and 28 Day Compressive Strength of Concrete (fc) and hit the calculate button. Here is how the Ultimate Strength for Symmetrical Reinforcement in Single Layers calculation can be explained with given input values -> 666892.8 = 1*((20*98.0664999999931/((0.1/0.02)-0.01+0.5))+(5*8*100000000/((3*8*0.1/(0.02^2))+1.18))).

FAQ

What is Ultimate Strength for Symmetrical Reinforcement in Single Layers?
The Ultimate Strength for Symmetrical Reinforcement in Single Layers formula is defined as Ultimate strength is equivalent to the maximum load that can be carried by one square inch of cross-sectional area when the load is applied as simple tension and is represented as Pu = Phi*((As'*fy/((e/d)-d'+0.5))+(b*h*fc/((3*h*e/(d^2))+1.18))) or axial_load_capacity = Capacity reduction factor*((Area of Compressive Reinforcement*Yield strength of reinforcing steel/((Eccentricity/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of compression face*Depth of column*28 Day Compressive Strength of Concrete/((3*Depth of column*Eccentricity/(Distance from Compression to Tensile Reinforcement^2))+1.18))). Capacity reduction factor is derived for reinforced concrete structures based on a reliability based calibration of the Australian Concrete Structures Standard AS3600, Area of Compressive Reinforcement is common sense to place reinforcement in an area subjected to compressive stress, Yield strength of reinforcing steel is the stress at which a predetermined amount of permanent deformation occurs, Eccentricity of an ellipse is a non-negative real number that uniquely characterizes its shape, Distance from Compression to Tensile Reinforcement is defined as the distance from extreme compression surface to the centroid of tensile reinforcement, in (mm), Distance from Compression to Centroid Reinforcment is defined as the distance from extreme compression surface to the centroid of compression reinforcement, in (mm), Width of compression face is the measurement or extent of something from side to side, Depth of column is the distance from the top or surface to the bottom of something and 28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it.
How to calculate Ultimate Strength for Symmetrical Reinforcement in Single Layers?
The Ultimate Strength for Symmetrical Reinforcement in Single Layers formula is defined as Ultimate strength is equivalent to the maximum load that can be carried by one square inch of cross-sectional area when the load is applied as simple tension is calculated using axial_load_capacity = Capacity reduction factor*((Area of Compressive Reinforcement*Yield strength of reinforcing steel/((Eccentricity/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of compression face*Depth of column*28 Day Compressive Strength of Concrete/((3*Depth of column*Eccentricity/(Distance from Compression to Tensile Reinforcement^2))+1.18))). To calculate Ultimate Strength for Symmetrical Reinforcement in Single Layers, you need Capacity reduction factor (Phi), Area of Compressive Reinforcement (As'), Yield strength of reinforcing steel (fy, Eccentricity (e), Distance from Compression to Tensile Reinforcement (d), Distance from Compression to Centroid Reinforcment (d'), Width of compression face (b), Depth of column (h) and 28 Day Compressive Strength of Concrete (fc). With our tool, you need to enter the respective value for Capacity reduction factor, Area of Compressive Reinforcement, Yield strength of reinforcing steel, Eccentricity, Distance from Compression to Tensile Reinforcement, Distance from Compression to Centroid Reinforcment, Width of compression face, Depth of column and 28 Day Compressive Strength of Concrete and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Axial Load Capacity?
In this formula, Axial Load Capacity uses Capacity reduction factor, Area of Compressive Reinforcement, Yield strength of reinforcing steel, Eccentricity, Distance from Compression to Tensile Reinforcement, Distance from Compression to Centroid Reinforcment, Width of compression face, Depth of column and 28 Day Compressive Strength of Concrete. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • axial_load_capacity = Resistance Factor*((.85*28 Day Compressive Strength of Concrete*Width of compression face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yeild Strength of Base Plate)-(area of tension reinforcement*Tensile Stress in Steel))
  • axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*Width of compression face*Distance from Compression to Tensile Reinforcement*Capacity reduction factor*((-Area ratio of tensile reinforcement)+1-(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement)+sqrt(((1-(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement))^2)+2*Area ratio of tensile reinforcement*((Force ratio of strengths of reinforcements-1)*(1-(Distance from Compression to Centroid Reinforcment/Distance from Compression to Tensile Reinforcement))+(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement))))
  • axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*Width of compression face*Distance from Compression to Tensile Reinforcement*Capacity reduction factor*((-Area ratio of tensile reinforcement*Force ratio of strengths of reinforcements)+1-(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement)+sqrt(((1-(Eccentricity by method of frame analysis/Distance from Compression to Tensile Reinforcement))^2)+2*(Area ratio of tensile reinforcement*Eccentricity by method of frame analysis*Force ratio of strengths of reinforcements/Distance from Compression to Tensile Reinforcement)))
  • axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*(Overall diameter of section^2)*Capacity reduction factor*(sqrt((((0.85*Eccentricity/Overall diameter of section)-0.38)^2)+(Area ratio of gross area to steel area*Force ratio of strengths of reinforcements*Diameter of reinforcement/(2.5*Overall diameter of section)))-((0.85*Eccentricity/Overall diameter of section)-0.38))
  • axial_load_capacity = Capacity reduction factor*((Area of steel reinforcement*Yield strength of reinforcing steel/((3*Eccentricity/Diameter of reinforcement)+1))+(Gross area*28 Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall diameter of section+0.67*Diameter of reinforcement)^2)+1.18)))
  • axial_load_capacity = Capacity reduction factor*((Area of steel reinforcement*Yield strength of reinforcing steel/((3*Eccentricity/Diameter of reinforcement)+1))+(Gross area*28 Day Compressive Strength of Concrete/((12*Depth of column*Eccentricity/((Depth of column+0.67*Diameter of reinforcement)^2))+1.18)))
  • axial_load_capacity = 0.85*Width of compression face*Depth of column*28 Day Compressive Strength of Concrete*Capacity reduction factor*((sqrt((((Eccentricity/Depth of column)-0.5)^2)+(0.67*(Diameter of reinforcement/Depth of column)*Area ratio of gross area to steel area*Force ratio of strengths of reinforcements)))-((Eccentricity/Depth of column)-0.5))
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