Ultimate Strength for Short, Circular Members when Governed by Compression Calculator

✖The Resistance Factor accounts for the possible conditions that the actual fastener strength may be less than the calculated strength value. It is given by AISC LFRD.ⓘ Resistance Factor [Φ]			+10% -10%
✖The Area of Steel Reinforcement is the cross-sectional area of steel reinforcement.ⓘ Area of Steel Reinforcement [A_st]			+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%
✖Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm.ⓘ Bar Diameter [D_b]			+10% -10%
✖The Gross Area of Column is the total area enclosed by the column.ⓘ Gross Area of Column [A_g]			+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%
✖Diameter at eccentricity is the diameter of section at eccentric distance from the center.ⓘ Diameter at Eccentricity [D_e]			+10% -10%
✖Overall Diameter of Section is the section without any load.ⓘ Overall Diameter of Section [D]			+10% -10%

✖Axial Load Capacity is defined as the maximum load along the direction of the drive train.ⓘ Ultimate Strength for Short, Circular Members when Governed by Compression [P_u]

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Ultimate Strength for Short, Circular Members when Governed by Compression

Formula

`"P"_{"u"} = "Φ"*(("A"_{"st"}*"f"_{"y"}/((3*"e"/"D"_{"b"})+1))+("A"_{"g"}*"f'"_{"c"}/(9.6*"D"_{"e"}/((0.8*"D"+0.67*"D"_{"b"})^2)+1.18)))`

Example

`"0.00018N"="0.850"*(("7mm²"*"250.0MPa"/((3*"35mm"/"12mm")+1))+("33mm²"*"55.0MPa"/(9.6*"0.25m"/((0.8*"250mm"+0.67*"12mm")^2)+1.18)))`

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Ultimate Strength for Short, Circular Members when Governed by Compression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Axial Load Capacity = Resistance Factor*((Area of Steel Reinforcement*Yield Strength of Reinforcing Steel/((3*Eccentricity of Column/Bar Diameter)+1))+(Gross Area of Column*28-Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall Diameter of Section+0.67*Bar Diameter)^2)+1.18)))
P_u = Φ*((A_st*f_y/((3*e/D_b)+1))+(A_g*f'_c/(9.6*D_e/((0.8*D+0.67*D_b)^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.
Resistance Factor - The Resistance Factor accounts for the possible conditions that the actual fastener strength may be less than the calculated strength value. It is given by AISC LFRD.
Area of Steel Reinforcement - (Measured in Square Meter) - The Area of Steel Reinforcement is the cross-sectional area of steel reinforcement.
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 Meter) - The Eccentricity of Column is the distance between the middle of the column's cross-section and the eccentric load.
Bar Diameter - (Measured in Meter) - Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm.
Gross Area of Column - (Measured in Square Meter) - The Gross Area of Column is the total area enclosed by the column.
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.
Diameter at Eccentricity - (Measured in Meter) - Diameter at eccentricity is the diameter of section at eccentric distance from the center.
Overall Diameter of Section - (Measured in Meter) - Overall Diameter of Section is the section without any load.

STEP 1: Convert Input(s) to Base Unit

Resistance Factor: 0.85 --> No Conversion Required
Area of Steel Reinforcement: 7 Square Millimeter --> 7E-06 Square Meter (Check conversion here)
Yield Strength of Reinforcing Steel: 250 Megapascal --> 250 Megapascal No Conversion Required
Eccentricity of Column: 35 Millimeter --> 0.035 Meter (Check conversion here)
Bar Diameter: 12 Millimeter --> 0.012 Meter (Check conversion here)
Gross Area of Column: 33 Square Millimeter --> 3.3E-05 Square Meter (Check conversion here)
28-Day Compressive Strength of Concrete: 55 Megapascal --> 55 Megapascal No Conversion Required
Diameter at Eccentricity: 0.25 Meter --> 0.25 Meter No Conversion Required
Overall Diameter of Section: 250 Millimeter --> 0.25 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_u = Φ*((A_st*f_y/((3*e/D_b)+1))+(A_g*f'_c/(9.6*D_e/((0.8*D+0.67*D_b)^2)+1.18))) --> 0.85*((7E-06*250/((3*0.035/0.012)+1))+(3.3E-05*55/(9.6*0.25/((0.8*0.25+0.67*0.012)^2)+1.18)))

Evaluating ... ...

P_u = 0.000179805747358996

STEP 3: Convert Result to Output's Unit

0.000179805747358996 Newton --> No Conversion Required

FINAL ANSWER

0.000179805747358996 ≈ 0.00018 Newton <-- Axial Load Capacity

(Calculation completed in 00.004 seconds)

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< 3 Circular Columns Calculators

Ultimate Strength for Short, Circular Members when Controlled by Tension

Go Axial Load Capacity = 0.85*28-Day Compressive Strength of Concrete*(Overall Diameter of Section^2)*Resistance Factor*(sqrt((((0.85*Eccentricity of Column/Overall Diameter of Section)-0.38)^2)+(Area Ratio of Gross Area to Steel Area*Force Ratio of Strengths of Reinforcements*Bar Diameter/(2.5*Overall Diameter of Section)))-((0.85*Eccentricity of Column/Overall Diameter of Section)-0.38))

Ultimate Strength for Short, Circular Members when Governed by Compression

Go Axial Load Capacity = Resistance Factor*((Area of Steel Reinforcement*Yield Strength of Reinforcing Steel/((3*Eccentricity of Column/Bar Diameter)+1))+(Gross Area of Column*28-Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall Diameter of Section+0.67*Bar Diameter)^2)+1.18)))

Eccentricity for Balanced Condition for Short, Circular Members

Go Eccentricity with respect to Plastic Load = (0.24-0.39*Area Ratio of Gross Area to Steel Area*Force Ratio of Strengths of Reinforcements)*Overall Diameter of Section

Ultimate Strength for Short, Circular Members when Governed by Compression 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.

What happens when eccentricity is 0?

If the eccentricity is zero, the curve is a circle; if equal to one, a parabola; if less than one, an ellipse; and if greater than one, a hyperbola.

How to Calculate Ultimate Strength for Short, Circular Members when Governed by Compression?

Ultimate Strength for Short, Circular Members when Governed by Compression calculator uses Axial Load Capacity = Resistance Factor*((Area of Steel Reinforcement*Yield Strength of Reinforcing Steel/((3*Eccentricity of Column/Bar Diameter)+1))+(Gross Area of Column*28-Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall Diameter of Section+0.67*Bar Diameter)^2)+1.18))) to calculate the Axial Load Capacity, The Ultimate Strength for Short, Circular Members when Governed by Compression 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 Short, Circular Members when Governed by Compression using this online calculator? To use this online calculator for Ultimate Strength for Short, Circular Members when Governed by Compression, enter Resistance Factor (Φ), Area of Steel Reinforcement (A_st), Yield Strength of Reinforcing Steel (f_y), Eccentricity of Column (e), Bar Diameter (D_b), Gross Area of Column (A_g), 28-Day Compressive Strength of Concrete (f'_c), Diameter at Eccentricity (D_e) & Overall Diameter of Section (D) and hit the calculate button. Here is how the Ultimate Strength for Short, Circular Members when Governed by Compression calculation can be explained with given input values -> 0.00018 = 0.85*((7E-06*250000000/((3*0.035/0.012)+1))+(3.3E-05*55000000/(9.6*0.25/((0.8*0.25+0.67*0.012)^2)+1.18))).

FAQ

What is Ultimate Strength for Short, Circular Members when Governed by Compression?

The Ultimate Strength for Short, Circular Members when Governed by Compression 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 = Φ*((A_st*f_y/((3*e/D_b)+1))+(A_g*f'_c/(9.6*D_e/((0.8*D+0.67*D_b)^2)+1.18))) or Axial Load Capacity = Resistance Factor*((Area of Steel Reinforcement*Yield Strength of Reinforcing Steel/((3*Eccentricity of Column/Bar Diameter)+1))+(Gross Area of Column*28-Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall Diameter of Section+0.67*Bar Diameter)^2)+1.18))). The Resistance Factor accounts for the possible conditions that the actual fastener strength may be less than the calculated strength value. It is given by AISC LFRD, The Area of Steel Reinforcement is the cross-sectional area of steel reinforcement, 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, Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm, The Gross Area of Column is the total area enclosed by the column, The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days, Diameter at eccentricity is the diameter of section at eccentric distance from the center & Overall Diameter of Section is the section without any load.

How to calculate Ultimate Strength for Short, Circular Members when Governed by Compression?

The Ultimate Strength for Short, Circular Members when Governed by Compression 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 = Resistance Factor*((Area of Steel Reinforcement*Yield Strength of Reinforcing Steel/((3*Eccentricity of Column/Bar Diameter)+1))+(Gross Area of Column*28-Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall Diameter of Section+0.67*Bar Diameter)^2)+1.18))). To calculate Ultimate Strength for Short, Circular Members when Governed by Compression, you need Resistance Factor (Φ), Area of Steel Reinforcement (A_st), Yield Strength of Reinforcing Steel (f_y), Eccentricity of Column (e), Bar Diameter (D_b), Gross Area of Column (A_g), 28-Day Compressive Strength of Concrete (f'_c), Diameter at Eccentricity (D_e) & Overall Diameter of Section (D). With our tool, you need to enter the respective value for Resistance Factor, Area of Steel Reinforcement, Yield Strength of Reinforcing Steel, Eccentricity of Column, Bar Diameter, Gross Area of Column, 28-Day Compressive Strength of Concrete, Diameter at Eccentricity & Overall Diameter of Section 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 Resistance Factor, Area of Steel Reinforcement, Yield Strength of Reinforcing Steel, Eccentricity of Column, Bar Diameter, Gross Area of Column, 28-Day Compressive Strength of Concrete, Diameter at Eccentricity & Overall Diameter of Section. 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*(Overall Diameter of Section^2)*Resistance Factor*(sqrt((((0.85*Eccentricity of Column/Overall Diameter of Section)-0.38)^2)+(Area Ratio of Gross Area to Steel Area*Force Ratio of Strengths of Reinforcements*Bar Diameter/(2.5*Overall Diameter of Section)))-((0.85*Eccentricity of Column/Overall Diameter of Section)-0.38))

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