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

GoUltimate Strength for Short, Circular Members when Governed by Compression 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 = 0.85 \cdot f' c \cdot (D^{2}) \cdot Φ \cdot (\sqrt{({((0.85 \cdot \frac{e}{D}) - 0.38)}^{2}) + (Rho' \cdot m \cdot \frac{D b}{2.5 \cdot D})} - ((0.85 \cdot \frac{e}{D}) - 0.38))

P_u - Axial Load Capacity?f'_c - 28-Day Compressive Strength of Concrete?D - Overall Diameter of Section?Φ - Resistance Factor?e - Eccentricity of Column?Rho' - Area Ratio of Gross Area to Steel Area?m - Force Ratio of Strengths of Reinforcements?D_b - Bar Diameter?

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

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Here is how the Ultimate Strength for Short, Circular Members when Controlled by Tension equation looks like with Values.

Here is how the Ultimate Strength for Short, Circular Members when Controlled by Tension equation looks like with Units.

Here is how the Ultimate Strength for Short, Circular Members when Controlled by Tension equation looks like.

1.3E+6 = 0.85 \cdot 55 \cdot (250^{2}) \cdot 0.85 \cdot (\sqrt{({((0.85 \cdot \frac{35}{250}) - 0.38)}^{2}) + (0.9 \cdot 0.4 \cdot \frac{12}{2.5 \cdot 250})} - ((0.85 \cdot \frac{35}{250}) - 0.38))

1.3E+6N = 0.85 \cdot 55MPa \cdot ({250mm}^{2}) \cdot 0.85 \cdot (\sqrt{({((0.85 \cdot \frac{35mm}{250mm}) - 0.38)}^{2}) + (0.9 \cdot 0.4 \cdot \frac{12mm}{2.5 \cdot 250mm})} - ((0.85 \cdot \frac{35mm}{250mm}) - 0.38))

1.3E+6 = 0.85 \cdot 55 \cdot (250^{2}) \cdot 0.85 \cdot (\sqrt{({((0.85 \cdot \frac{35}{250}) - 0.38)}^{2}) + (0.9 \cdot 0.4 \cdot \frac{12}{2.5 \cdot 250})} - ((0.85 \cdot \frac{35}{250}) - 0.38))

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

Follow our step by step solution on how to calculate Ultimate Strength for Short, Circular Members when Controlled by Tension?

FIRST Step Consider the formula

P u = 0.85 \cdot f' c \cdot (D^{2}) \cdot Φ \cdot (\sqrt{({((0.85 \cdot \frac{e}{D}) - 0.38)}^{2}) + (Rho' \cdot m \cdot \frac{D b}{2.5 \cdot D})} - ((0.85 \cdot \frac{e}{D}) - 0.38))

Next Step Substitute values of Variables

∴

P u = 0.85 \cdot 55MPa \cdot ({250mm}^{2}) \cdot 0.85 \cdot (\sqrt{({((0.85 \cdot \frac{35mm}{250mm}) - 0.38)}^{2}) + (0.9 \cdot 0.4 \cdot \frac{12mm}{2.5 \cdot 250mm})} - ((0.85 \cdot \frac{35mm}{250mm}) - 0.38))

Next Step Prepare to Evaluate

∴

P u = 0.85 \cdot 55 \cdot (250^{2}) \cdot 0.85 \cdot (\sqrt{({((0.85 \cdot \frac{35}{250}) - 0.38)}^{2}) + (0.9 \cdot 0.4 \cdot \frac{12}{2.5 \cdot 250})} - ((0.85 \cdot \frac{35}{250}) - 0.38))

Next Step Evaluate

∴

P u = 1328527.74780593N

LAST Step Rounding Answer

∴

P u = 1.3E+6N

Ultimate Strength for Short, Circular Members when Controlled by Tension Formula Elements

Variables

Functions

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

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

Overall Diameter of Section

Overall Diameter of Section is the section without any load.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Overall Diameter of Section

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

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

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.

Symbol: Rho'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Area Ratio of Gross Area to Steel Area

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.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Force Ratio of Strengths of Reinforcements

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

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.

Syntax: sqrt(Number)

Other Formulas to find Axial Load Capacity

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

P u = Φ \cdot ((A st \cdot \frac{f y}{(3 \cdot \frac{e}{D b}) + 1}) + (A g \cdot \frac{f' c}{9.6 \cdot \frac{D e}{{(0.8 \cdot D + 0.67 \cdot D b)}^{2}} + 1.18}))

Other formulas in Circular Columns category

Go Eccentricity for Balanced Condition for Short, Circular Members

e b = (0.24 - 0.39 \cdot Rho' \cdot m) \cdot D

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

Ultimate Strength for Short, Circular Members when Controlled by Tension evaluator 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 evaluate 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 evaluate Ultimate Strength for Short, Circular Members when Controlled by Tension using this online evaluator? To use this online evaluator 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.

FAQs on Ultimate Strength for Short, Circular Members when Controlled by Tension

What is the formula to find Ultimate Strength for Short, Circular Members when Controlled by Tension?

The formula of Ultimate Strength for Short, Circular Members when Controlled by Tension is expressed as 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)). Here is an example- 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)).

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

With 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) we can find Ultimate Strength for Short, Circular Members when Controlled by Tension using the formula - 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)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Axial Load Capacity?

Here are the different ways to Calculate Axial Load Capacity-

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)))

Can the Ultimate Strength for Short, Circular Members when Controlled by Tension be negative?

No, the Ultimate Strength for Short, Circular Members when Controlled by Tension, measured in Force cannot be negative.

Which unit is used to measure Ultimate Strength for Short, Circular Members when Controlled by Tension?

Ultimate Strength for Short, Circular Members when Controlled by Tension 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, Circular Members when Controlled by Tension can be measured.

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

​GoUltimate Strength for Short, Circular Members when Governed by Compression Formula

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

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

Ultimate Strength for Short, Circular Members when Controlled by Tension Formula Elements

Other Formulas to find Axial Load Capacity

Other formulas in Circular Columns category

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

FAQs on Ultimate Strength for Short, Circular Members when Controlled by Tension

Variable Name

GoUltimate Strength for Short, Circular Members when Governed by Compression Formula