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Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members Formula

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

A' s = \frac{(\frac{P u}{Φ}) - (.85 \cdot f' c \cdot b \cdot a) + (A s \cdot f s)}{f y}

A'_s - Area of Compressive Reinforcement?P_u - Axial Load Capacity?Φ - Resistance Factor?f'_c - 28-Day Compressive Strength of Concrete?b - Width of Compression Face?a - Depth Rectangular Compressive Stress?A_s - Area of Tension Reinforcement?f_s - Steel Tensile Stress?f_y - Yield Strength of Reinforcing Steel?

Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members Example

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Here is how the Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members equation looks like with Values.

Here is how the Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members equation looks like with Units.

Here is how the Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members equation looks like.

16.8 = \frac{(\frac{680}{0.85}) - (.85 \cdot 55 \cdot 5 \cdot 10.5) + (15 \cdot 280)}{250}

16.8mm² = \frac{(\frac{680N}{0.85}) - (.85 \cdot 55MPa \cdot 5mm \cdot 10.5mm) + (15mm² \cdot 280MPa)}{250MPa}

16.8 = \frac{(\frac{680}{0.85}) - (.85 \cdot 55 \cdot 5 \cdot 10.5) + (15 \cdot 280)}{250}

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Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members Solution

Follow our step by step solution on how to calculate Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members?

FIRST Step Consider the formula

A' s = \frac{(\frac{P u}{Φ}) - (.85 \cdot f' c \cdot b \cdot a) + (A s \cdot f s)}{f y}

Next Step Substitute values of Variables

∴

A' s = \frac{(\frac{680N}{0.85}) - (.85 \cdot 55MPa \cdot 5mm \cdot 10.5mm) + (15mm² \cdot 280MPa)}{250MPa}

Next Step Convert Units

∴

A' s = \frac{(\frac{680N}{0.85}) - (.85 \cdot 5.5E+7Pa \cdot 0.005m \cdot 0.0105m) + (15mm² \cdot 2.8E+8Pa)}{2.5E+8Pa}

Next Step Prepare to Evaluate

∴

A' s = \frac{(\frac{680}{0.85}) - (.85 \cdot 5.5E+7 \cdot 0.005 \cdot 0.0105) + (15 \cdot 2.8E+8)}{2.5E+8}

Next Step Evaluate

∴

A' s = 1.67999933825E-05m²

Next Step Convert to Output's Unit

∴

A' s = 16.7999933825mm²

LAST Step Rounding Answer

∴

A' s = 16.8mm²

Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members Formula Elements

Variables

Area of Compressive Reinforcement

The Area of Compressive 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 Compressive Reinforcement

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

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

Width of Compression Face

Width of Compression Face is the measurement or extent of something from side to side.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Compression Face

Depth Rectangular Compressive Stress

Depth Rectangular Compressive Stress is defined as the depth of equivalent rectangular compressive-stress distribution, in(mm).

Symbol: a

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth Rectangular Compressive Stress

Area of Tension Reinforcement

The Area of Tension Reinforcement is the space occupied by the steel in order to impart tensile strength to the section.

Symbol: A_s

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Tension Reinforcement

Steel Tensile Stress

Steel Tensile Stress is defined as the stress in the steel under tension.

Symbol: f_s

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Steel Tensile Stress

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

Other formulas in Ultimate Strength Design of Concrete Columns category

Go Column Ultimate Strength with Zero Eccentricity of Load

P 0 = 0.85 \cdot f' c \cdot (A g - A st) + f y \cdot A st

Go Yield Strength of Reinforcing Steel using Column Ultimate Strength

f y = \frac{P 0 - 0.85 \cdot f' c \cdot (A g - A st)}{A st}

How to Evaluate Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members?

Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members evaluator uses Area of Compressive Reinforcement = ((Axial Load Capacity/Resistance Factor)-(.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Depth Rectangular Compressive Stress)+(Area of Tension Reinforcement*Steel Tensile Stress))/Yield Strength of Reinforcing Steel to evaluate the Area of Compressive Reinforcement, The Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members formula is usually provided to retain the longitudinal reinforcement and also to take the shear to which the structure is subjected. Area of Compressive Reinforcement is denoted by A'_s symbol.

How to evaluate Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members using this online evaluator? To use this online evaluator for Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members, enter Axial Load Capacity (P_u), Resistance Factor (Φ), 28-Day Compressive Strength of Concrete (f'_c), Width of Compression Face (b), Depth Rectangular Compressive Stress (a), Area of Tension Reinforcement (A_s), Steel Tensile Stress (f_s) & Yield Strength of Reinforcing Steel (f_y) and hit the calculate button.

FAQs on Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members

What is the formula to find Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members?

The formula of Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members is expressed as Area of Compressive Reinforcement = ((Axial Load Capacity/Resistance Factor)-(.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Depth Rectangular Compressive Stress)+(Area of Tension Reinforcement*Steel Tensile Stress))/Yield Strength of Reinforcing Steel. Here is an example- 1.7E+7 = ((680/0.85)-(.85*55000000*0.005*0.0105)+(1.5E-05*280000000))/250000000.

How to calculate Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members?

With Axial Load Capacity (P_u), Resistance Factor (Φ), 28-Day Compressive Strength of Concrete (f'_c), Width of Compression Face (b), Depth Rectangular Compressive Stress (a), Area of Tension Reinforcement (A_s), Steel Tensile Stress (f_s) & Yield Strength of Reinforcing Steel (f_y) we can find Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members using the formula - Area of Compressive Reinforcement = ((Axial Load Capacity/Resistance Factor)-(.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Depth Rectangular Compressive Stress)+(Area of Tension Reinforcement*Steel Tensile Stress))/Yield Strength of Reinforcing Steel.

Can the Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members be negative?

No, the Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members, measured in Area cannot be negative.

Which unit is used to measure Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members?

Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members 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 Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members can be measured.

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Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members Formula

Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members Example

Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members Solution

Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members Formula Elements

Other formulas in Ultimate Strength Design of Concrete Columns category

How to Evaluate Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members?

FAQs on Compressive Reinforcement Area given Axial-Load Capacity of Short Rectangular Members

Variable Name