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Gross Cross-Sectional Area of Column given Total Allowable Axial Load Formula

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

A g = \frac{P allow}{0.25 \cdot f' c + f' s \cdot p g}

A_g - Gross Area of Column?P_allow - Allowable Load?f'_c - Specified Compressive Strength at 28 Days?f'_s - Allowable Stress in Vertical Reinforcement?p_g - Area Ratio of Cross Sectional Area to Gross Area?

Gross Cross-Sectional Area of Column given Total Allowable Axial Load Example

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Here is how the Gross Cross-Sectional Area of Column given Total Allowable Axial Load equation looks like with Values.

Here is how the Gross Cross-Sectional Area of Column given Total Allowable Axial Load equation looks like with Units.

Here is how the Gross Cross-Sectional Area of Column given Total Allowable Axial Load equation looks like.

499.251 = \frac{16}{0.25 \cdot 80 + 4.001 \cdot 8.01}

499.251mm² = \frac{16kN}{0.25 \cdot 80Pa + 4.001N/mm² \cdot 8.01}

499.251 = \frac{16}{0.25 \cdot 80 + 4.001 \cdot 8.01}

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Gross Cross-Sectional Area of Column given Total Allowable Axial Load Solution

Follow our step by step solution on how to calculate Gross Cross-Sectional Area of Column given Total Allowable Axial Load?

FIRST Step Consider the formula

A g = \frac{P allow}{0.25 \cdot f' c + f' s \cdot p g}

Next Step Substitute values of Variables

∴

A g = \frac{16kN}{0.25 \cdot 80Pa + 4.001N/mm² \cdot 8.01}

Next Step Convert Units

∴

A g = \frac{16000.01N}{0.25 \cdot 80Pa + 4E+6Pa \cdot 8.01}

Next Step Prepare to Evaluate

∴

A g = \frac{16000.01}{0.25 \cdot 80 + 4E+6 \cdot 8.01}

Next Step Evaluate

∴

A g = 0.000499250968000217m²

Next Step Convert to Output's Unit

∴

A g = 499.250968000217mm²

LAST Step Rounding Answer

∴

A g = 499.251mm²

Gross Cross-Sectional Area of Column given Total Allowable Axial Load Formula Elements

Variables

Gross Area of Column

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

Allowable Load

Allowable load is the maximum working load that can be applied on the structure.

Symbol: P_allow

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Allowable Load

Specified Compressive Strength at 28 Days

Specified Compressive Strength at 28 Days is the capacity of a material or structure to withstand loads tending to reduce the size, as opposed to which withstands loads tending to elongate.

Symbol: f'_c

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Specified Compressive Strength at 28 Days

Allowable Stress in Vertical Reinforcement

Allowable Stress in Vertical Reinforcement is equal to 40 percent of the minimum yield strength, but not to exceed 30,000 lb/sq.in(207 MPa).

Symbol: f'_s

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Allowable Stress in Vertical Reinforcement

Area Ratio of Cross Sectional Area to Gross Area

Area Ratio of Cross Sectional Area to Gross Area is the ratio of cross-sectional area of vertical reinforcing steel to gross area of column.

Symbol: p_g

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Area Ratio of Cross Sectional Area to Gross Area

Other formulas in Design of Short Column under Axial Compression category

Go Total Allowable Axial Load for Short Columns

P allow = A g \cdot (0.25 \cdot f' c + f' s \cdot p g)

Go Concrete Compressive Strength given Total Allowable Axial Load

fck = \frac{(\frac{p T}{A g}) - (f' s \cdot p g)}{0.25}

Go Allowable Stress in Vertical Concrete Reinforcing given Total Allowable Axial Load

f' s = \frac{\frac{P allow}{A g} - 0.25 \cdot f' c}{p g}

Go Spiral Volume to Concrete-Core Volume Ratio

p s = 0.45 \cdot (\frac{A g}{A c} - 1) \cdot \frac{f' c}{fy steel}

How to Evaluate Gross Cross-Sectional Area of Column given Total Allowable Axial Load?

Gross Cross-Sectional Area of Column given Total Allowable Axial Load evaluator uses Gross Area of Column = Allowable Load/(0.25*Specified Compressive Strength at 28 Days+Allowable Stress in Vertical Reinforcement*Area Ratio of Cross Sectional Area to Gross Area) to evaluate the Gross Area of Column, The Gross Cross-Sectional Area of Column given Total Allowable Axial Load formula is defined as the total area enclosed by column. Gross Area of Column is denoted by A_g symbol.

How to evaluate Gross Cross-Sectional Area of Column given Total Allowable Axial Load using this online evaluator? To use this online evaluator for Gross Cross-Sectional Area of Column given Total Allowable Axial Load, enter Allowable Load (P_allow), Specified Compressive Strength at 28 Days (f'_c), Allowable Stress in Vertical Reinforcement (f'_s) & Area Ratio of Cross Sectional Area to Gross Area (p_g) and hit the calculate button.

FAQs on Gross Cross-Sectional Area of Column given Total Allowable Axial Load

What is the formula to find Gross Cross-Sectional Area of Column given Total Allowable Axial Load?

The formula of Gross Cross-Sectional Area of Column given Total Allowable Axial Load is expressed as Gross Area of Column = Allowable Load/(0.25*Specified Compressive Strength at 28 Days+Allowable Stress in Vertical Reinforcement*Area Ratio of Cross Sectional Area to Gross Area). Here is an example- 5E+8 = 16000.01/(0.25*80+4001000*8.01).

How to calculate Gross Cross-Sectional Area of Column given Total Allowable Axial Load?

With Allowable Load (P_allow), Specified Compressive Strength at 28 Days (f'_c), Allowable Stress in Vertical Reinforcement (f'_s) & Area Ratio of Cross Sectional Area to Gross Area (p_g) we can find Gross Cross-Sectional Area of Column given Total Allowable Axial Load using the formula - Gross Area of Column = Allowable Load/(0.25*Specified Compressive Strength at 28 Days+Allowable Stress in Vertical Reinforcement*Area Ratio of Cross Sectional Area to Gross Area).

Can the Gross Cross-Sectional Area of Column given Total Allowable Axial Load be negative?

No, the Gross Cross-Sectional Area of Column given Total Allowable Axial Load, measured in Area cannot be negative.

Which unit is used to measure Gross Cross-Sectional Area of Column given Total Allowable Axial Load?

Gross Cross-Sectional Area of Column given Total Allowable Axial Load is usually measured using the Square Millimeter[mm²] for Area. Square Meter[mm²], Square Kilometer[mm²], Square Centimeter[mm²] are the few other units in which Gross Cross-Sectional Area of Column given Total Allowable Axial Load can be measured.

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Gross Cross-Sectional Area of Column given Total Allowable Axial Load Formula

Gross Cross-Sectional Area of Column given Total Allowable Axial Load Example

Gross Cross-Sectional Area of Column given Total Allowable Axial Load Solution

Gross Cross-Sectional Area of Column given Total Allowable Axial Load Formula Elements

Other formulas in Design of Short Column under Axial Compression category

How to Evaluate Gross Cross-Sectional Area of Column given Total Allowable Axial Load?

FAQs on Gross Cross-Sectional Area of Column given Total Allowable Axial Load

Variable Name