Ultimate Strength for Symmetrical Reinforcement in Single Layers Calculator

✖Capacity Reduction Factor is derived for reinforced concrete structures based on a reliability-based calibration of the Australian Concrete Structures Standard AS3600.ⓘ Capacity Reduction Factor [Phi]			+10% -10%
✖The Area of Compressive Reinforcement is the amount of steel required in the compression zone.ⓘ Area of Compressive Reinforcement [A'_s]			+10% -10%
✖The Yield Strength of Reinforcing Steel is the maximum stress that can be applied before it begins to change shape permanently. This is an approximation of the elastic limit of the steel.ⓘ Yield Strength of Reinforcing Steel [f_y]			+10% -10%
✖The Eccentricity of Column is the distance between the middle of the column's cross-section and the eccentric load.ⓘ Eccentricity of Column [e]			+10% -10%
✖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 Tensile Reinforcement [d]			+10% -10%
✖Distance from Compression to Centroid Reinforcment is defined as the distance from extreme compression surface to the centroid of compression reinforcement, in (mm).ⓘ Distance from Compression to Centroid Reinforcment [d']			+10% -10%
✖Width of Compression Face is the measurement or extent of something from side to side.ⓘ Width of Compression Face [b]			+10% -10%
✖The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.ⓘ Effective Length of Column [L]			+10% -10%
✖The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days.ⓘ 28-Day Compressive Strength of Concrete [f'_c]			+10% -10%

✖Axial Load Capacity is defined as the maximum load along the direction of the drive train.ⓘ Ultimate Strength for Symmetrical Reinforcement in Single Layers [P_u]

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Ultimate Strength for Symmetrical Reinforcement in Single Layers

Formula

`"P"_{"u"} = "Phi"*(("A'"_{"s"}*"f"_{"y"}/(("e"/"d")-"d'"+0.5))+("b"*"L"*"f'"_{"c"}/((3*"L"*"e"/("d"^2))+1.18)))`

Example

`"889.1433N"="0.85"*(("20.0mm²"*"250.0MPa"/(("35mm"/"20mm")-"10mm"+0.5))+("5mm"*"3000mm"*"55.0MPa"/((3*"3000mm"*"35mm"/(("20mm")^2))+1.18)))`

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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 of Column/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete/((3*Effective Length of Column*Eccentricity of Column/(Distance from Compression to Tensile Reinforcement^2))+1.18)))
P_u = Phi*((A'_s*f_y/((e/d)-d'+0.5))+(b*L*f'_c/((3*L*e/(d^2))+1.18)))
This formula uses 10 Variables

Variables Used

Axial Load Capacity - (Measured in Newton) - Axial Load Capacity is defined as the maximum load along the direction of the drive train.
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 - (Measured in Square Meter) - The Area of Compressive Reinforcement is the amount of steel required in the compression zone.
Yield Strength of Reinforcing Steel - (Measured in Megapascal) - The Yield Strength of Reinforcing Steel is the maximum stress that can be applied before it begins to change shape permanently. This is an approximation of the elastic limit of the steel.
Eccentricity of Column - (Measured in Millimeter) - The Eccentricity of Column is the distance between the middle of the column's cross-section and the eccentric load.
Distance from Compression to Tensile Reinforcement - (Measured in Millimeter) - 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 - (Measured in Millimeter) - 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 - (Measured in Millimeter) - Width of Compression Face is the measurement or extent of something from side to side.
Effective Length of Column - (Measured in Millimeter) - The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.
28-Day Compressive Strength of Concrete - (Measured in Megapascal) - The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days.

STEP 1: Convert Input(s) to Base Unit

Capacity Reduction Factor: 0.85 --> No Conversion Required
Area of Compressive Reinforcement: 20 Square Millimeter --> 2E-05 Square Meter (Check conversion here)
Yield Strength of Reinforcing Steel: 250 Megapascal --> 250 Megapascal No Conversion Required
Eccentricity of Column: 35 Millimeter --> 35 Millimeter No Conversion Required
Distance from Compression to Tensile Reinforcement: 20 Millimeter --> 20 Millimeter No Conversion Required
Distance from Compression to Centroid Reinforcment: 10 Millimeter --> 10 Millimeter No Conversion Required
Width of Compression Face: 5 Millimeter --> 5 Millimeter No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3000 Millimeter No Conversion Required
28-Day Compressive Strength of Concrete: 55 Megapascal --> 55 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_u = Phi*((A'_s*f_y/((e/d)-d'+0.5))+(b*L*f'_c/((3*L*e/(d^2))+1.18))) --> 0.85*((2E-05*250/((35/20)-10+0.5))+(5*3000*55/((3*3000*35/(20^2))+1.18)))

Evaluating ... ...

P_u = 889.143337599615

STEP 3: Convert Result to Output's Unit

889.143337599615 Newton --> No Conversion Required

FINAL ANSWER

889.143337599615 ≈ 889.1433 Newton <-- Axial Load Capacity

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Columns » Ultimate Strength Design of Concrete Columns » Column Strength when Compression Governs » Ultimate Strength for Symmetrical Reinforcement in Single Layers

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< 2 Column Strength when Compression Governs Calculators

Ultimate Strength for No Compression Reinforcement

Go 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)))

Ultimate Strength for Symmetrical Reinforcement in Single Layers

Go Axial Load Capacity = Capacity Reduction Factor*((Area of Compressive Reinforcement*Yield Strength of Reinforcing Steel/((Eccentricity of Column/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete/((3*Effective Length of Column*Eccentricity of Column/(Distance from Compression to Tensile Reinforcement^2))+1.18)))

Ultimate Strength for Symmetrical Reinforcement in Single Layers Formula

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 of Column/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete/((3*Effective Length of Column*Eccentricity of Column/(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 is denoted by P_u 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 (A'_s), Yield Strength of Reinforcing Steel (f_y), Eccentricity of Column (e), Distance from Compression to Tensile Reinforcement (d), Distance from Compression to Centroid Reinforcment (d'), Width of Compression Face (b), Effective Length of Column (L) & 28-Day Compressive Strength of Concrete (f'_c) 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 -> 889.1433 = 0.85*((2E-05*250000000/((0.035/0.02)-0.01+0.5))+(0.005*3*55000000/((3*3*0.035/(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 P_u = Phi*((A'_s*f_y/((e/d)-d'+0.5))+(b*L*f'_c/((3*L*e/(d^2))+1.18))) or Axial Load Capacity = Capacity Reduction Factor*((Area of Compressive Reinforcement*Yield Strength of Reinforcing Steel/((Eccentricity of Column/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete/((3*Effective Length of Column*Eccentricity of Column/(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, The Area of Compressive Reinforcement is the amount of steel required in the compression zone, The Yield Strength of Reinforcing Steel is the maximum stress that can be applied before it begins to change shape permanently. This is an approximation of the elastic limit of the steel, The Eccentricity of Column is the distance between the middle of the column's cross-section and the eccentric load, 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, The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration & The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days.

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 of Column/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete/((3*Effective Length of Column*Eccentricity of Column/(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 (A'_s), Yield Strength of Reinforcing Steel (f_y), Eccentricity of Column (e), Distance from Compression to Tensile Reinforcement (d), Distance from Compression to Centroid Reinforcment (d'), Width of Compression Face (b), Effective Length of Column (L) & 28-Day Compressive Strength of Concrete (f'_c). With our tool, you need to enter the respective value for Capacity Reduction Factor, Area of Compressive Reinforcement, Yield Strength of Reinforcing Steel, Eccentricity of Column, Distance from Compression to Tensile Reinforcement, Distance from Compression to Centroid Reinforcment, Width of Compression Face, Effective Length of Column & 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 of Column, Distance from Compression to Tensile Reinforcement, Distance from Compression to Centroid Reinforcment, Width of Compression Face, Effective Length of Column & 28-Day Compressive Strength of Concrete. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)))

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