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Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members Formula

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

A s = \frac{(0.85 \cdot f' c \cdot b \cdot a) + (A' s \cdot f y) - (\frac{P u}{Φ})}{f s}

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

Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members Example

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

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

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

23.7656 = \frac{(0.85 \cdot 55 \cdot 5 \cdot 10.5) + (20 \cdot 250) - (\frac{680}{0.85})}{280}

23.7656mm² = \frac{(0.85 \cdot 55MPa \cdot 5mm \cdot 10.5mm) + (20mm² \cdot 250MPa) - (\frac{680N}{0.85})}{280MPa}

23.7656 = \frac{(0.85 \cdot 55 \cdot 5 \cdot 10.5) + (20 \cdot 250) - (\frac{680}{0.85})}{280}

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Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members Solution

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

FIRST Step Consider the formula

A s = \frac{(0.85 \cdot f' c \cdot b \cdot a) + (A' s \cdot f y) - (\frac{P u}{Φ})}{f s}

Next Step Substitute values of Variables

∴

A s = \frac{(0.85 \cdot 55MPa \cdot 5mm \cdot 10.5mm) + (20mm² \cdot 250MPa) - (\frac{680N}{0.85})}{280MPa}

Next Step Convert Units

∴

A s = \frac{(0.85 \cdot 5.5E+7Pa \cdot 0.005m \cdot 0.0105m) + (2E-5m² \cdot 2.5E+8Pa) - (\frac{680N}{0.85})}{2.8E+8Pa}

Next Step Prepare to Evaluate

∴

A s = \frac{(0.85 \cdot 5.5E+7 \cdot 0.005 \cdot 0.0105) + (2E-5 \cdot 2.5E+8) - (\frac{680}{0.85})}{2.8E+8}

Next Step Evaluate

∴

A s = 2.3765625E-05m²

Next Step Convert to Output's Unit

∴

A s = 23.765625mm²

LAST Step Rounding Answer

∴

A s = 23.7656mm²

Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members Formula Elements

Variables

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

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 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

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

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

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

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 Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members?

Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members evaluator uses Area of Tension Reinforcement = ((0.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yield Strength of Reinforcing Steel)-(Axial Load Capacity/Resistance Factor))/Steel Tensile Stress to evaluate the Area of Tension Reinforcement, The Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members is defined as the area of reinforcement within an effective tension area of concrete. The effective tension area is that area of the concrete cross-section which will crack due to the tension developed in bending. Area of Tension Reinforcement is denoted by A_s symbol.

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

FAQs on Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members

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

The formula of Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members is expressed as Area of Tension Reinforcement = ((0.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yield Strength of Reinforcing Steel)-(Axial Load Capacity/Resistance Factor))/Steel Tensile Stress. Here is an example- 2.4E+7 = ((0.85*55000000*0.005*0.0105)+(2E-05*250000000)-(680/0.85))/280000000.

How to calculate Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members?

With 28-Day Compressive Strength of Concrete (f'_c), Width of Compression Face (b), Depth Rectangular Compressive Stress (a), Area of Compressive Reinforcement (A'_s), Yield Strength of Reinforcing Steel (f_y), Axial Load Capacity (P_u), Resistance Factor (Φ) & Steel Tensile Stress (f_s) we can find Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members using the formula - Area of Tension Reinforcement = ((0.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yield Strength of Reinforcing Steel)-(Axial Load Capacity/Resistance Factor))/Steel Tensile Stress.

Can the Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members be negative?

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

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

Tension Reinforcement Area for 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 Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members can be measured.

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Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members Formula

Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members Example

Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members Solution

Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members Formula Elements

Other formulas in Ultimate Strength Design of Concrete Columns category

How to Evaluate Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members?

FAQs on Tension Reinforcement Area for Axial-Load Capacity of Short Rectangular Members

Variable Name