Ultimate Strength for Short, Circular Members when Controlled by Tension Calculator

✖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%
✖Overall Diameter of Section is the section without any load.ⓘ Overall Diameter of Section [D]			+10% -10%
✖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 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%
✖Area Ratio of Gross Area to Steel Area is the ratio of gross area of steel and area of steel reinforcement.ⓘ Area Ratio of Gross Area to Steel Area [Rho']			+10% -10%
✖Force Ratio of Strengths of Reinforcements is the ratio of yield strength of reinforcing steel to 0.85 times 28 day compressive strength of concrete.ⓘ Force Ratio of Strengths of Reinforcements [m]			+10% -10%
✖Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm.ⓘ Bar Diameter [D_b]			+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 Controlled by Tension [P_u]

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Formula

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Ultimate Strength for Short, Circular Members when Controlled by Tension

Formula

`"P"_{"u"} = 0.85*"f'"_{"c"}*("D"^2)*"Φ"*(sqrt((((0.85*"e"/"D")-0.38)^2)+("Rho'"*"m"*"D"_{"b"}/(2.5*"D")))-((0.85*"e"/"D")-0.38))`

Example

`"1.3E^6N"=0.85*"55.0MPa"*(("250mm")^2)*"0.850"*(sqrt((((0.85*"35mm"/"250mm")-0.38)^2)+("0.9"*"0.4"*"12mm"/(2.5*"250mm")))-((0.85*"35mm"/"250mm")-0.38))`

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Ultimate Strength for Short, Circular Members when Controlled by Tension Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
P_u = 0.85*f'_c*(D^2)*Φ*(sqrt((((0.85*e/D)-0.38)^2)+(Rho'*m*D_b/(2.5*D)))-((0.85*e/D)-0.38))
This formula uses 1 Functions, 8 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Axial Load Capacity - (Measured in Newton) - Axial Load Capacity is defined as the maximum load along the direction of the drive train.
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.
Overall Diameter of Section - (Measured in Millimeter) - Overall Diameter of Section is the section without any load.
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.
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.
Area Ratio of Gross Area to Steel Area - Area Ratio of Gross Area to Steel Area is the ratio of gross area of steel and area of steel reinforcement.
Force Ratio of Strengths of Reinforcements - Force Ratio of Strengths of Reinforcements is the ratio of yield strength of reinforcing steel to 0.85 times 28 day compressive strength of concrete.
Bar Diameter - (Measured in Millimeter) - Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm.

STEP 1: Convert Input(s) to Base Unit

28-Day Compressive Strength of Concrete: 55 Megapascal --> 55 Megapascal No Conversion Required
Overall Diameter of Section: 250 Millimeter --> 250 Millimeter No Conversion Required
Resistance Factor: 0.85 --> No Conversion Required
Eccentricity of Column: 35 Millimeter --> 35 Millimeter No Conversion Required
Area Ratio of Gross Area to Steel Area: 0.9 --> No Conversion Required
Force Ratio of Strengths of Reinforcements: 0.4 --> No Conversion Required
Bar Diameter: 12 Millimeter --> 12 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_u = 0.85*f'_c*(D^2)*Φ*(sqrt((((0.85*e/D)-0.38)^2)+(Rho'*m*D_b/(2.5*D)))-((0.85*e/D)-0.38)) --> 0.85*55*(250^2)*0.85*(sqrt((((0.85*35/250)-0.38)^2)+(0.9*0.4*12/(2.5*250)))-((0.85*35/250)-0.38))

Evaluating ... ...

P_u = 1328527.74780593

STEP 3: Convert Result to Output's Unit

1328527.74780593 Newton --> No Conversion Required

FINAL ANSWER

1328527.74780593 ≈ 1.3E+6 Newton <-- Axial Load Capacity

(Calculation completed in 00.020 seconds)

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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 Controlled by Tension 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 Controlled by Tension?

Ultimate Strength for Short, Circular Members when Controlled by Tension calculator uses 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)) to calculate the Axial Load Capacity, The Ultimate Strength for Short, Circular Members when Controlled by Tension 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 Controlled by Tension using this online calculator? To use this online calculator for Ultimate Strength for Short, Circular Members when Controlled by Tension, enter 28-Day Compressive Strength of Concrete (f'_c), Overall Diameter of Section (D), Resistance Factor (Φ), Eccentricity of Column (e), Area Ratio of Gross Area to Steel Area (Rho'), Force Ratio of Strengths of Reinforcements (m) & Bar Diameter (D_b) and hit the calculate button. Here is how the Ultimate Strength for Short, Circular Members when Controlled by Tension calculation can be explained with given input values -> 1.3E+6 = 0.85*55000000*(0.25^2)*0.85*(sqrt((((0.85*0.035/0.25)-0.38)^2)+(0.9*0.4*0.012/(2.5*0.25)))-((0.85*0.035/0.25)-0.38)).

FAQ

What is Ultimate Strength for Short, Circular Members when Controlled by Tension?

The Ultimate Strength for Short, Circular Members when Controlled by Tension 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 = 0.85*f'_c*(D^2)*Φ*(sqrt((((0.85*e/D)-0.38)^2)+(Rho'*m*D_b/(2.5*D)))-((0.85*e/D)-0.38)) or 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)). The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days, Overall Diameter of Section is the section without any load, 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 Eccentricity of Column is the distance between the middle of the column's cross-section and the eccentric load, Area Ratio of Gross Area to Steel Area is the ratio of gross area of steel and area of steel reinforcement, Force Ratio of Strengths of Reinforcements is the ratio of yield strength of reinforcing steel to 0.85 times 28 day compressive strength of concrete & Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm.

How to calculate Ultimate Strength for Short, Circular Members when Controlled by Tension?

The Ultimate Strength for Short, Circular Members when Controlled by Tension 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 = 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)). To calculate Ultimate Strength for Short, Circular Members when Controlled by Tension, you need 28-Day Compressive Strength of Concrete (f'_c), Overall Diameter of Section (D), Resistance Factor (Φ), Eccentricity of Column (e), Area Ratio of Gross Area to Steel Area (Rho'), Force Ratio of Strengths of Reinforcements (m) & Bar Diameter (D_b). With our tool, you need to enter the respective value for 28-Day Compressive Strength of Concrete, Overall Diameter of Section, Resistance Factor, Eccentricity of Column, Area Ratio of Gross Area to Steel Area, Force Ratio of Strengths of Reinforcements & Bar Diameter 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 28-Day Compressive Strength of Concrete, Overall Diameter of Section, Resistance Factor, Eccentricity of Column, Area Ratio of Gross Area to Steel Area, Force Ratio of Strengths of Reinforcements & Bar Diameter. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)))

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