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Concrete Compressive Strength given Total Allowable Axial Load Formula

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The characteristic compressive strength is defined as the strength of the concrete below which not more than 5% of the test results are expected to fall. Check FAQs

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

fck - Characteristic Compressive Strength?p_T - Total Allowable Load?A_g - Gross Area of Column?f'_s - Allowable Stress in Vertical Reinforcement?p_g - Area Ratio of Cross Sectional Area to Gross Area?

Concrete Compressive Strength given Total Allowable Axial Load Example

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Here is how the Concrete Compressive Strength given Total Allowable Axial Load equation looks like with Values.

Here is how the Concrete Compressive Strength given Total Allowable Axial Load equation looks like with Units.

Here is how the Concrete Compressive Strength given Total Allowable Axial Load equation looks like.

19.808 = \frac{(\frac{18.5}{500}) - (4.001 \cdot 8.01)}{0.25}

19.808MPa = \frac{(\frac{18.5N}{500mm²}) - (4.001N/mm² \cdot 8.01)}{0.25}

19.808 = \frac{(\frac{18.5}{500}) - (4.001 \cdot 8.01)}{0.25}

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Concrete Compressive Strength given Total Allowable Axial Load Solution

Follow our step by step solution on how to calculate Concrete Compressive Strength given Total Allowable Axial Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

fck = \frac{(\frac{18.5N}{500mm²}) - (4.001N/mm² \cdot 8.01)}{0.25}

Next Step Convert Units

∴

fck = \frac{(\frac{18.5N}{0.0005m²}) - (4001kN/m² \cdot 8.01)}{0.25}

Next Step Prepare to Evaluate

∴

fck = \frac{(\frac{18.5}{0.0005}) - (4001 \cdot 8.01)}{0.25}

Next Step Evaluate

∴

fck = 19807960Pa

Next Step Convert to Output's Unit

∴

fck = 19.80796MPa

LAST Step Rounding Answer

∴

fck = 19.808MPa

Concrete Compressive Strength given Total Allowable Axial Load Formula Elements

Variables

Characteristic Compressive Strength

The characteristic compressive strength is defined as the strength of the concrete below which not more than 5% of the test results are expected to fall.

Symbol: fck

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Characteristic Compressive Strength

Total Allowable Load

Total allowable load is the capacity or can say the maximum load allowed.

Symbol: p_T

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Allowable Load

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

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

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 Concrete Compressive Strength given Total Allowable Axial Load?

Concrete Compressive Strength given Total Allowable Axial Load evaluator uses Characteristic Compressive Strength = ((Total Allowable Load/Gross Area of Column)-(Allowable Stress in Vertical Reinforcement*Area Ratio of Cross Sectional Area to Gross Area))/0.25 to evaluate the Characteristic Compressive Strength, The Concrete Compressive Strength given Total Allowable Axial Load formula is defined as the capacity of a concrete material or structure to withstand total allowable axial loads tending to reduce size, as opposed to which withstands loads tending to elongate. Characteristic Compressive Strength is denoted by fck symbol.

How to evaluate Concrete Compressive Strength given Total Allowable Axial Load using this online evaluator? To use this online evaluator for Concrete Compressive Strength given Total Allowable Axial Load, enter Total Allowable Load (p_T), Gross Area of Column (A_g), 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 Concrete Compressive Strength given Total Allowable Axial Load

What is the formula to find Concrete Compressive Strength given Total Allowable Axial Load?

The formula of Concrete Compressive Strength given Total Allowable Axial Load is expressed as Characteristic Compressive Strength = ((Total Allowable Load/Gross Area of Column)-(Allowable Stress in Vertical Reinforcement*Area Ratio of Cross Sectional Area to Gross Area))/0.25. Here is an example- -0.000128 = ((18.5/0.0005)-(4001000*8.01))/0.25.

How to calculate Concrete Compressive Strength given Total Allowable Axial Load?

With Total Allowable Load (p_T), Gross Area of Column (A_g), Allowable Stress in Vertical Reinforcement (f'_s) & Area Ratio of Cross Sectional Area to Gross Area (p_g) we can find Concrete Compressive Strength given Total Allowable Axial Load using the formula - Characteristic Compressive Strength = ((Total Allowable Load/Gross Area of Column)-(Allowable Stress in Vertical Reinforcement*Area Ratio of Cross Sectional Area to Gross Area))/0.25.

Can the Concrete Compressive Strength given Total Allowable Axial Load be negative?

No, the Concrete Compressive Strength given Total Allowable Axial Load, measured in Pressure cannot be negative.

Which unit is used to measure Concrete Compressive Strength given Total Allowable Axial Load?

Concrete Compressive Strength given Total Allowable Axial Load is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Concrete Compressive Strength given Total Allowable Axial Load can be measured.

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Concrete Compressive Strength given Total Allowable Axial Load Formula

Concrete Compressive Strength given Total Allowable Axial Load Example

Concrete Compressive Strength given Total Allowable Axial Load Solution

Concrete Compressive Strength given Total Allowable Axial Load Formula Elements

Other formulas in Design of Short Column under Axial Compression category

How to Evaluate Concrete Compressive Strength given Total Allowable Axial Load?

FAQs on Concrete Compressive Strength given Total Allowable Axial Load

Variable Name