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

✖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%
✖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%
✖Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm.ⓘ Bar Diameter [D_b]			+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%

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

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Ultimate Strength for Short, Square Members when Controlled by Tension

Formula

`"P"_{"u"} = 0.85*"b"*"L"*"f'"_{"c"}*"Φ"*((sqrt(((("e"/"L")-0.5)^2)+(0.67*("D"_{"b"}/"L")*"Rho'"*"m")))-(("e"/"L")-0.5))`

Example

`"582742.6N"=0.85*"5mm"*"3000mm"*"55.0MPa"*"0.850"*((sqrt(((("35mm"/"3000mm")-0.5)^2)+(0.67*("12mm"/"3000mm")*"0.9"*"0.4")))-(("35mm"/"3000mm")-0.5))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Axial Load Capacity = 0.85*Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete*Resistance Factor*((sqrt((((Eccentricity of Column/Effective Length of Column)-0.5)^2)+(0.67*(Bar Diameter/Effective Length of Column)*Area Ratio of Gross Area to Steel Area*Force Ratio of Strengths of Reinforcements)))-((Eccentricity of Column/Effective Length of Column)-0.5))
P_u = 0.85*b*L*f'_c*Φ*((sqrt((((e/L)-0.5)^2)+(0.67*(D_b/L)*Rho'*m)))-((e/L)-0.5))
This formula uses 1 Functions, 9 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.
Width of Compression Face - (Measured in Meter) - Width of Compression Face is the measurement or extent of something from side to side.
Effective Length of Column - (Measured in Meter) - 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 Pascal) - The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days.
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 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.
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.

STEP 1: Convert Input(s) to Base Unit

Width of Compression Face: 5 Millimeter --> 0.005 Meter (Check conversion here)
Effective Length of Column: 3000 Millimeter --> 3 Meter (Check conversion here)
28-Day Compressive Strength of Concrete: 55 Megapascal --> 55000000 Pascal (Check conversion here)
Resistance Factor: 0.85 --> No Conversion Required
Eccentricity of Column: 35 Millimeter --> 0.035 Meter (Check conversion here)
Bar Diameter: 12 Millimeter --> 0.012 Meter (Check conversion here)
Area Ratio of Gross Area to Steel Area: 0.9 --> No Conversion Required
Force Ratio of Strengths of Reinforcements: 0.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_u = 0.85*b*L*f'_c*Φ*((sqrt((((e/L)-0.5)^2)+(0.67*(D_b/L)*Rho'*m)))-((e/L)-0.5)) --> 0.85*0.005*3*55000000*0.85*((sqrt((((0.035/3)-0.5)^2)+(0.67*(0.012/3)*0.9*0.4)))-((0.035/3)-0.5))

Evaluating ... ...

P_u = 582742.600878204

STEP 3: Convert Result to Output's Unit

582742.600878204 Newton --> No Conversion Required

FINAL ANSWER

582742.600878204 ≈ 582742.6 Newton <-- Axial Load Capacity

(Calculation completed in 00.016 seconds)

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Home » Engineering » Civil » Columns » Ultimate Strength Design of Concrete Columns » Short Columns » Ultimate Strength for Short, Square Members when Controlled by Tension

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< 2 Short Columns Calculators

Ultimate Strength for Short, Square Members when Controlled by Tension

Go Axial Load Capacity = 0.85*Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete*Resistance Factor*((sqrt((((Eccentricity of Column/Effective Length of Column)-0.5)^2)+(0.67*(Bar Diameter/Effective Length of Column)*Area Ratio of Gross Area to Steel Area*Force Ratio of Strengths of Reinforcements)))-((Eccentricity of Column/Effective Length of Column)-0.5))

Ultimate Strength for Short, Square 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/((12*Effective Length of Column*Eccentricity of Column/((Effective Length of Column+0.67*Bar Diameter)^2))+1.18)))

Ultimate Strength for Short, Square 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.

How to Calculate Ultimate Strength for Short, Square Members when Controlled by Tension?

Ultimate Strength for Short, Square Members when Controlled by Tension calculator uses Axial Load Capacity = 0.85*Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete*Resistance Factor*((sqrt((((Eccentricity of Column/Effective Length of Column)-0.5)^2)+(0.67*(Bar Diameter/Effective Length of Column)*Area Ratio of Gross Area to Steel Area*Force Ratio of Strengths of Reinforcements)))-((Eccentricity of Column/Effective Length of Column)-0.5)) to calculate the Axial Load Capacity, The Ultimate Strength for Short, Square 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, Square Members when Controlled by Tension using this online calculator? To use this online calculator for Ultimate Strength for Short, Square Members when Controlled by Tension, enter Width of Compression Face (b), Effective Length of Column (L), 28-Day Compressive Strength of Concrete (f'_c), Resistance Factor (Φ), Eccentricity of Column (e), Bar Diameter (D_b), Area Ratio of Gross Area to Steel Area (Rho') & Force Ratio of Strengths of Reinforcements (m) and hit the calculate button. Here is how the Ultimate Strength for Short, Square Members when Controlled by Tension calculation can be explained with given input values -> 582742.6 = 0.85*0.005*3*55000000*0.85*((sqrt((((0.035/3)-0.5)^2)+(0.67*(0.012/3)*0.9*0.4)))-((0.035/3)-0.5)).

FAQ

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

The Ultimate Strength for Short, Square 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*b*L*f'_c*Φ*((sqrt((((e/L)-0.5)^2)+(0.67*(D_b/L)*Rho'*m)))-((e/L)-0.5)) or Axial Load Capacity = 0.85*Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete*Resistance Factor*((sqrt((((Eccentricity of Column/Effective Length of Column)-0.5)^2)+(0.67*(Bar Diameter/Effective Length of Column)*Area Ratio of Gross Area to Steel Area*Force Ratio of Strengths of Reinforcements)))-((Eccentricity of Column/Effective Length of Column)-0.5)). 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, 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, Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm, 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.

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

The Ultimate Strength for Short, Square 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*Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete*Resistance Factor*((sqrt((((Eccentricity of Column/Effective Length of Column)-0.5)^2)+(0.67*(Bar Diameter/Effective Length of Column)*Area Ratio of Gross Area to Steel Area*Force Ratio of Strengths of Reinforcements)))-((Eccentricity of Column/Effective Length of Column)-0.5)). To calculate Ultimate Strength for Short, Square Members when Controlled by Tension, you need Width of Compression Face (b), Effective Length of Column (L), 28-Day Compressive Strength of Concrete (f'_c), Resistance Factor (Φ), Eccentricity of Column (e), Bar Diameter (D_b), Area Ratio of Gross Area to Steel Area (Rho') & Force Ratio of Strengths of Reinforcements (m). With our tool, you need to enter the respective value for Width of Compression Face, Effective Length of Column, 28-Day Compressive Strength of Concrete, Resistance Factor, Eccentricity of Column, Bar Diameter, Area Ratio of Gross Area to Steel Area & Force Ratio of Strengths of Reinforcements 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 Width of Compression Face, Effective Length of Column, 28-Day Compressive Strength of Concrete, Resistance Factor, Eccentricity of Column, Bar Diameter, Area Ratio of Gross Area to Steel Area & Force Ratio of Strengths of Reinforcements. 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/((12*Effective Length of Column*Eccentricity of Column/((Effective Length of Column+0.67*Bar Diameter)^2))+1.18)))

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