Ultimate Strength for Short, Square 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%
✖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%

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

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Ultimate Strength Design of Concrete Columns Formulas PDF PDF Image

Ultimate Strength for Short, Square 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/((12*Effective Length of Column*Eccentricity of Column/((Effective Length of Column+0.67*Bar Diameter)^2))+1.18)))
P_u = Φ*((A_st*f_y/((3*e/D_b)+1))+(A_g*f'_c/((12*L*e/((L+0.67*D_b)^2))+1.18)))
This formula uses 9 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 Millimeter) - 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 Millimeter) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Resistance Factor: 0.85 --> No Conversion Required
Area of Steel Reinforcement: 7 Square Millimeter --> 7 Square Millimeter No Conversion Required
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 --> 33 Square Millimeter No Conversion Required
28-Day Compressive Strength of Concrete: 55 Megapascal --> 55 Megapascal No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3 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/((12*L*e/((L+0.67*D_b)^2))+1.18))) --> 0.85*((7*250/((3*0.035/0.012)+1))+(33*55/((12*3*0.035/((3+0.67*0.012)^2))+1.18)))

Evaluating ... ...

P_u = 1321.97623269127

STEP 3: Convert Result to Output's Unit

1321.97623269127 Newton --> No Conversion Required

FINAL ANSWER

1321.97623269127 ≈ 1321.976 Newton <-- Axial Load Capacity

(Calculation completed in 00.004 seconds)

You are here -

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

Credits

Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

Rudrani Tidke has created this Calculator and 100+ more calculators!

Verified by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has verified this Calculator and 1200+ more calculators!

< Short Columns Calculators

Ultimate Strength for Short, Square Members when Controlled by Tension

LaTeX 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

LaTeX 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 Governed by Compression Formula

LaTeX Go

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 Governed by Compression?

Ultimate Strength for Short, Square 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/((12*Effective Length of Column*Eccentricity of Column/((Effective Length of Column+0.67*Bar Diameter)^2))+1.18))) to calculate the Axial Load Capacity, The Ultimate Strength for Short, Square 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, Square Members when Governed by Compression using this online calculator? To use this online calculator for Ultimate Strength for Short, Square 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) & Effective Length of Column (L) and hit the calculate button. Here is how the Ultimate Strength for Short, Square Members when Governed by Compression calculation can be explained with given input values -> 1321.976 = 0.85*((7E-06*250000000/((3*0.035/0.012)+1))+(3.3E-05*55000000/((12*3*0.035/((3+0.67*0.012)^2))+1.18))).

FAQ

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

The Ultimate Strength for Short, Square 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/((12*L*e/((L+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/((12*Effective Length of Column*Eccentricity of Column/((Effective Length of Column+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 & 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.

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

The Ultimate Strength for Short, Square 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/((12*Effective Length of Column*Eccentricity of Column/((Effective Length of Column+0.67*Bar Diameter)^2))+1.18))). To calculate Ultimate Strength for Short, Square 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) & Effective Length of Column (L). 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 & Effective Length of Column 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 & Effective Length of Column. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

Home

FREE PDFs

🔍 Search