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Cross-Sectional Area of Compressive Reinforcing Formula

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Area of Compression Reinforcement is the amount of steel required in the compression zone. Check FAQs

A s' = \frac{B M - M'}{m \cdot f EC \cdot d eff}

A_s' - Area of Compression Reinforcement?B_M - Bending Moment of Considered Section?M' - Bending Moment of Singly reinforced Beam?m - Modular Ratio?f_EC - Extreme Compressive Stress of Concrete?d_eff - Effective Depth of Beam?

Cross-Sectional Area of Compressive Reinforcing Example

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Here is how the Cross-Sectional Area of Compressive Reinforcing equation looks like with Values.

Here is how the Cross-Sectional Area of Compressive Reinforcing equation looks like with Units.

Here is how the Cross-Sectional Area of Compressive Reinforcing equation looks like.

20.6126 = \frac{49.5 - 16.5}{8 \cdot 50.03 \cdot 4}

20.6126mm² = \frac{49.5kN*m - 16.5kN*m}{8 \cdot 50.03MPa \cdot 4m}

20.6126 = \frac{49.5 - 16.5}{8 \cdot 50.03 \cdot 4}

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Cross-Sectional Area of Compressive Reinforcing Solution

Follow our step by step solution on how to calculate Cross-Sectional Area of Compressive Reinforcing?

FIRST Step Consider the formula

A s' = \frac{B M - M'}{m \cdot f EC \cdot d eff}

Next Step Substitute values of Variables

∴

A s' = \frac{49.5kN*m - 16.5kN*m}{8 \cdot 50.03MPa \cdot 4m}

Next Step Convert Units

∴

A s' = \frac{49500N*m - 16500N*m}{8 \cdot 5E+7Pa \cdot 4m}

Next Step Prepare to Evaluate

∴

A s' = \frac{49500 - 16500}{8 \cdot 5E+7 \cdot 4}

Next Step Evaluate

∴

A s' = 2.06126324205477E-05m²

Next Step Convert to Output's Unit

∴

A s' = 20.6126324205477mm²

LAST Step Rounding Answer

∴

A s' = 20.6126mm²

Cross-Sectional Area of Compressive Reinforcing Formula Elements

Variables

Area of Compression Reinforcement

Area of Compression Reinforcement is the amount of steel required in the compression zone.

Symbol: A_s'

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Compression Reinforcement

Bending Moment of Considered Section

Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section.

Symbol: B_M

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Bending Moment of Considered Section

Bending Moment of Singly reinforced Beam

Bending Moment of Singly reinforced Beam is the bending moment that would be carried by a beam of balanced design and same dimensions with tensile reinforcing only.

Symbol: M'

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Bending Moment of Singly reinforced Beam

Modular Ratio

Modular Ratio is the ratio of modulus of elasticity of steel and concrete. Concrete has varying moduli as it is not a perfectly elastic material. essentially, m= Es/Ec.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Modular Ratio

Extreme Compressive Stress of Concrete

Extreme Compressive Stress of Concrete is the stress on the extreme fiber of concrete surface.

Symbol: f_EC

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Extreme Compressive Stress of Concrete

Effective Depth of Beam

Effective Depth of Beam is the distance from the centroid of tension steel to the outermost face of the compression fiber.

Symbol: d_eff

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Effective Depth of Beam

Other formulas in Doubly Reinforced Rectangular Sections category

Go Total Cross-Sectional Area of Tensile Reinforcing

A cs = 8 \cdot \frac{Mb R}{7 \cdot f s \cdot D B}

Go Bending Moment given Total Cross-Sectional Area of Tensile Reinforcing

Mb R = A cs \cdot 7 \cdot f s \cdot \frac{D B}{8}

How to Evaluate Cross-Sectional Area of Compressive Reinforcing?

Cross-Sectional Area of Compressive Reinforcing evaluator uses Area of Compression Reinforcement = (Bending Moment of Considered Section-Bending Moment of Singly reinforced Beam)/(Modular Ratio*Extreme Compressive Stress of Concrete*Effective Depth of Beam) to evaluate the Area of Compression Reinforcement, The Cross-Sectional Area of Compressive Reinforcing formula is defined as the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point. . Area of Compression Reinforcement is denoted by A_s' symbol.

How to evaluate Cross-Sectional Area of Compressive Reinforcing using this online evaluator? To use this online evaluator for Cross-Sectional Area of Compressive Reinforcing, enter Bending Moment of Considered Section (B_M), Bending Moment of Singly reinforced Beam (M'), Modular Ratio (m), Extreme Compressive Stress of Concrete (f_EC) & Effective Depth of Beam (d_eff) and hit the calculate button.

FAQs on Cross-Sectional Area of Compressive Reinforcing

What is the formula to find Cross-Sectional Area of Compressive Reinforcing?

The formula of Cross-Sectional Area of Compressive Reinforcing is expressed as Area of Compression Reinforcement = (Bending Moment of Considered Section-Bending Moment of Singly reinforced Beam)/(Modular Ratio*Extreme Compressive Stress of Concrete*Effective Depth of Beam). Here is an example- 2.1E+7 = (49500-16500)/(8*50030000*4).

How to calculate Cross-Sectional Area of Compressive Reinforcing?

With Bending Moment of Considered Section (B_M), Bending Moment of Singly reinforced Beam (M'), Modular Ratio (m), Extreme Compressive Stress of Concrete (f_EC) & Effective Depth of Beam (d_eff) we can find Cross-Sectional Area of Compressive Reinforcing using the formula - Area of Compression Reinforcement = (Bending Moment of Considered Section-Bending Moment of Singly reinforced Beam)/(Modular Ratio*Extreme Compressive Stress of Concrete*Effective Depth of Beam).

Can the Cross-Sectional Area of Compressive Reinforcing be negative?

No, the Cross-Sectional Area of Compressive Reinforcing, measured in Area cannot be negative.

Which unit is used to measure Cross-Sectional Area of Compressive Reinforcing?

Cross-Sectional Area of Compressive Reinforcing 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 Cross-Sectional Area of Compressive Reinforcing can be measured.

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Cross-Sectional Area of Compressive Reinforcing Formula

Cross-Sectional Area of Compressive Reinforcing Example

Cross-Sectional Area of Compressive Reinforcing Solution

Cross-Sectional Area of Compressive Reinforcing Formula Elements

Other formulas in Doubly Reinforced Rectangular Sections category

How to Evaluate Cross-Sectional Area of Compressive Reinforcing?

FAQs on Cross-Sectional Area of Compressive Reinforcing

Variable Name