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Ultimate Strength for Short, Square Members when Governed by Compression Formula

GoUltimate Strength for Short, Square Members when Controlled by Tension Formula

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Axial Load Capacity is defined as the maximum load along the direction of the drive train. Check FAQs

P u = Φ \cdot ((A st \cdot \frac{f y}{(3 \cdot \frac{e}{D b}) + 1}) + (A g \cdot \frac{f' c}{(12 \cdot L \cdot \frac{e}{{(L + 0.67 \cdot D b)}^{2}}) + 1.18}))

P_u - Axial Load Capacity?Φ - Resistance Factor?A_st - Area of Steel Reinforcement?f_y - Yield Strength of Reinforcing Steel?e - Eccentricity of Column?D_b - Bar Diameter?A_g - Gross Area of Column?f'_c - 28-Day Compressive Strength of Concrete?L - Effective Length of Column?

Ultimate Strength for Short, Square Members when Governed by Compression Example

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Here is how the Ultimate Strength for Short, Square Members when Governed by Compression equation looks like with Values.

Here is how the Ultimate Strength for Short, Square Members when Governed by Compression equation looks like with Units.

Here is how the Ultimate Strength for Short, Square Members when Governed by Compression equation looks like.

1321.9762 = 0.85 \cdot ((7 \cdot \frac{250}{(3 \cdot \frac{35}{12}) + 1}) + (33 \cdot \frac{55}{(12 \cdot 3000 \cdot \frac{35}{{(3000 + 0.67 \cdot 12)}^{2}}) + 1.18}))

1321.9762N = 0.85 \cdot ((7mm² \cdot \frac{250MPa}{(3 \cdot \frac{35mm}{12mm}) + 1}) + (33mm² \cdot \frac{55MPa}{(12 \cdot 3000mm \cdot \frac{35mm}{{(3000mm + 0.67 \cdot 12mm)}^{2}}) + 1.18}))

1321.9762 = 0.85 \cdot ((7 \cdot \frac{250}{(3 \cdot \frac{35}{12}) + 1}) + (33 \cdot \frac{55}{(12 \cdot 3000 \cdot \frac{35}{{(3000 + 0.67 \cdot 12)}^{2}}) + 1.18}))

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

Follow our step by step solution on how to calculate Ultimate Strength for Short, Square Members when Governed by Compression?

FIRST Step Consider the formula

P u = Φ \cdot ((A st \cdot \frac{f y}{(3 \cdot \frac{e}{D b}) + 1}) + (A g \cdot \frac{f' c}{(12 \cdot L \cdot \frac{e}{{(L + 0.67 \cdot D b)}^{2}}) + 1.18}))

Next Step Substitute values of Variables

∴

P u = 0.85 \cdot ((7mm² \cdot \frac{250MPa}{(3 \cdot \frac{35mm}{12mm}) + 1}) + (33mm² \cdot \frac{55MPa}{(12 \cdot 3000mm \cdot \frac{35mm}{{(3000mm + 0.67 \cdot 12mm)}^{2}}) + 1.18}))

Next Step Convert Units

∴

P u = 0.85 \cdot ((7mm² \cdot \frac{250MPa}{(3 \cdot \frac{0.035m}{0.012m}) + 1}) + (33mm² \cdot \frac{55MPa}{(12 \cdot 3m \cdot \frac{0.035m}{{(3m + 0.67 \cdot 0.012m)}^{2}}) + 1.18}))

Next Step Prepare to Evaluate

∴

P u = 0.85 \cdot ((7 \cdot \frac{250}{(3 \cdot \frac{0.035}{0.012}) + 1}) + (33 \cdot \frac{55}{(12 \cdot 3 \cdot \frac{0.035}{{(3 + 0.67 \cdot 0.012)}^{2}}) + 1.18}))

Next Step Evaluate

∴

P u = 1321.97623269127N

LAST Step Rounding Answer

∴

P u = 1321.9762N

Ultimate Strength for Short, Square Members when Governed by Compression Formula Elements

Variables

Axial Load Capacity

Axial Load Capacity is defined as the maximum load along the direction of the drive train.

Symbol: P_u

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Axial Load Capacity

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.

Symbol: Φ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Resistance Factor

Area of Steel Reinforcement

The Area of Steel Reinforcement is the cross-sectional area of steel reinforcement.

Symbol: A_st

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Steel Reinforcement

Yield Strength of Reinforcing Steel

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.

Symbol: f_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Strength of Reinforcing Steel

Eccentricity of Column

The Eccentricity of Column is the distance between the middle of the column's cross-section and the eccentric load.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity of Column

Bar Diameter

Bar Diameter are most usually comprised to 12, 16, 20, and 25 mm.

Symbol: D_b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Bar Diameter

Gross Area of Column

The Gross Area of Column is the total area enclosed by the column.

Symbol: A_g

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Gross Area of Column

28-Day Compressive Strength of Concrete

The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days.

Symbol: f'_c

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find 28-Day Compressive Strength of Concrete

Effective Length of Column

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.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Other Formulas to find Axial Load Capacity

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

P u = 0.85 \cdot b \cdot L \cdot f' c \cdot Φ \cdot ((\sqrt{({((\frac{e}{L}) - 0.5)}^{2}) + (0.67 \cdot (\frac{D b}{L}) \cdot Rho' \cdot m)}) - ((\frac{e}{L}) - 0.5))

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

Ultimate Strength for Short, Square Members when Governed by Compression evaluator 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 evaluate 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 evaluate Ultimate Strength for Short, Square Members when Governed by Compression using this online evaluator? To use this online evaluator 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.

FAQs on Ultimate Strength for Short, Square Members when Governed by Compression

What is the formula to find Ultimate Strength for Short, Square Members when Governed by Compression?

The formula of Ultimate Strength for Short, Square Members when Governed by Compression is expressed as 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))). Here is an example- 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))).

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

With 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) we can find Ultimate Strength for Short, Square Members when Governed by Compression using the formula - 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))).

What are the other ways to Calculate Axial Load Capacity?

Here are the different ways to Calculate Axial Load Capacity-

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))

Can the Ultimate Strength for Short, Square Members when Governed by Compression be negative?

No, the Ultimate Strength for Short, Square Members when Governed by Compression, measured in Force cannot be negative.

Which unit is used to measure Ultimate Strength for Short, Square Members when Governed by Compression?

Ultimate Strength for Short, Square Members when Governed by Compression is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Ultimate Strength for Short, Square Members when Governed by Compression can be measured.

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Ultimate Strength for Short, Square Members when Governed by Compression Formula

​GoUltimate Strength for Short, Square Members when Controlled by Tension Formula

Ultimate Strength for Short, Square Members when Governed by Compression Example

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

Ultimate Strength for Short, Square Members when Governed by Compression Formula Elements

Other Formulas to find Axial Load Capacity

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

FAQs on Ultimate Strength for Short, Square Members when Governed by Compression

Variable Name

GoUltimate Strength for Short, Square Members when Controlled by Tension Formula