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Ultimate Strength for Symmetrical Reinforcement Formula

GoAxial Load Capacity of Short Rectangular Members Formula

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Axial Load Capacity is defined as the maximum load along the direction of the drive train. Check FAQs

P u = 0.85 \cdot f' c \cdot b \cdot d \cdot Phi \cdot ((- Rho) + 1 - (\frac{e'}{d}) + \sqrt{({(1 - (\frac{e'}{d}))}^{2}) + 2 \cdot Rho \cdot ((m - 1) \cdot (1 - (\frac{d'}{d})) + (\frac{e'}{d}))})

P_u - Axial Load Capacity?f'_c - 28-Day Compressive Strength of Concrete?b - Width of Compression Face?d - Distance from Compression to Tensile Reinforcement?Phi - Capacity Reduction Factor?Rho - Area Ratio of Tensile Reinforcement?e' - Eccentricity by Method of Frame Analysis?m - Force Ratio of Strengths of Reinforcements?d' - Distance from Compression to Centroid Reinforcment?

Ultimate Strength for Symmetrical Reinforcement Example

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Here is how the Ultimate Strength for Symmetrical Reinforcement equation looks like.

670.0779 = 0.85 \cdot 55 \cdot 5 \cdot 20 \cdot 0.85 \cdot ((- 0.5) + 1 - (\frac{35}{20}) + \sqrt{({(1 - (\frac{35}{20}))}^{2}) + 2 \cdot 0.5 \cdot ((0.4 - 1) \cdot (1 - (\frac{10}{20})) + (\frac{35}{20}))})

670.0779N = 0.85 \cdot 55MPa \cdot 5mm \cdot 20mm \cdot 0.85 \cdot ((- 0.5) + 1 - (\frac{35mm}{20mm}) + \sqrt{({(1 - (\frac{35mm}{20mm}))}^{2}) + 2 \cdot 0.5 \cdot ((0.4 - 1) \cdot (1 - (\frac{10mm}{20mm})) + (\frac{35mm}{20mm}))})

670.0779 = 0.85 \cdot 55 \cdot 5 \cdot 20 \cdot 0.85 \cdot ((- 0.5) + 1 - (\frac{35}{20}) + \sqrt{({(1 - (\frac{35}{20}))}^{2}) + 2 \cdot 0.5 \cdot ((0.4 - 1) \cdot (1 - (\frac{10}{20})) + (\frac{35}{20}))})

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Ultimate Strength for Symmetrical Reinforcement Solution

Follow our step by step solution on how to calculate Ultimate Strength for Symmetrical Reinforcement?

FIRST Step Consider the formula

P u = 0.85 \cdot f' c \cdot b \cdot d \cdot Phi \cdot ((- Rho) + 1 - (\frac{e'}{d}) + \sqrt{({(1 - (\frac{e'}{d}))}^{2}) + 2 \cdot Rho \cdot ((m - 1) \cdot (1 - (\frac{d'}{d})) + (\frac{e'}{d}))})

Next Step Substitute values of Variables

∴

P u = 0.85 \cdot 55MPa \cdot 5mm \cdot 20mm \cdot 0.85 \cdot ((- 0.5) + 1 - (\frac{35mm}{20mm}) + \sqrt{({(1 - (\frac{35mm}{20mm}))}^{2}) + 2 \cdot 0.5 \cdot ((0.4 - 1) \cdot (1 - (\frac{10mm}{20mm})) + (\frac{35mm}{20mm}))})

Next Step Prepare to Evaluate

∴

P u = 0.85 \cdot 55 \cdot 5 \cdot 20 \cdot 0.85 \cdot ((- 0.5) + 1 - (\frac{35}{20}) + \sqrt{({(1 - (\frac{35}{20}))}^{2}) + 2 \cdot 0.5 \cdot ((0.4 - 1) \cdot (1 - (\frac{10}{20})) + (\frac{35}{20}))})

Next Step Evaluate

∴

P u = 670.077948626776N

LAST Step Rounding Answer

∴

P u = 670.0779N

Ultimate Strength for Symmetrical Reinforcement Formula Elements

Variables

Functions

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

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

Distance from Compression to Tensile Reinforcement

Distance from Compression to Tensile Reinforcement is defined as the distance from extreme compression surface to the centroid of tensile reinforcement, in (mm).

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Compression to Tensile Reinforcement

Capacity Reduction Factor

Capacity Reduction Factor is derived for reinforced concrete structures based on a reliability-based calibration of the Australian Concrete Structures Standard AS3600.

Symbol: Phi

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Capacity Reduction Factor

Area Ratio of Tensile Reinforcement

Area Ratio of Tensile Reinforcement is the ratio of Area of Compressive Reinforcement to the width of compression face and distance between compression surface to centroid.

Symbol: Rho

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Area Ratio of Tensile Reinforcement

Eccentricity by Method of Frame Analysis

The Eccentricity by Method of Frame Analysis is the eccentricity, of axial load at end of member w.r.t., the centroid of tensile reinforcement, calculated by conventional methods of frame analysis.

Symbol: e'

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity by Method of Frame Analysis

Force Ratio of Strengths of Reinforcements

Force Ratio of Strengths of Reinforcements is the ratio of yield strength of reinforcing steel to 0.85 times 28 day compressive strength of concrete.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Force Ratio of Strengths of Reinforcements

Distance from Compression to Centroid Reinforcment

Distance from Compression to Centroid Reinforcment is defined as the distance from extreme compression surface to the centroid of compression reinforcement, in (mm).

Symbol: d'

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Compression to Centroid Reinforcment

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Axial Load Capacity

Go Axial Load Capacity of Short Rectangular Members

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

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 Ultimate Strength for Symmetrical Reinforcement?

Ultimate Strength for Symmetrical Reinforcement evaluator uses Axial Load Capacity = 0.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Distance from Compression to Tensile Reinforcement*Capacity Reduction Factor*((-Area Ratio of Tensile Reinforcement)+1-(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement)+sqrt(((1-(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement))^2)+2*Area Ratio of Tensile Reinforcement*((Force Ratio of Strengths of Reinforcements-1)*(1-(Distance from Compression to Centroid Reinforcment/Distance from Compression to Tensile Reinforcement))+(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement)))) to evaluate the Axial Load Capacity, The Ultimate Strength for Symmetrical Reinforcement formula is defined as Ultimate strength is equivalent to the maximum load that can be carried by one square inch of cross-sectional area when the load is applied as simple tension. Axial Load Capacity is denoted by P_u symbol.

How to evaluate Ultimate Strength for Symmetrical Reinforcement using this online evaluator? To use this online evaluator for Ultimate Strength for Symmetrical Reinforcement, enter 28-Day Compressive Strength of Concrete (f'_c), Width of Compression Face (b), Distance from Compression to Tensile Reinforcement (d), Capacity Reduction Factor (Phi), Area Ratio of Tensile Reinforcement (Rho), Eccentricity by Method of Frame Analysis (e'), Force Ratio of Strengths of Reinforcements (m) & Distance from Compression to Centroid Reinforcment (d') and hit the calculate button.

FAQs on Ultimate Strength for Symmetrical Reinforcement

What is the formula to find Ultimate Strength for Symmetrical Reinforcement?

The formula of Ultimate Strength for Symmetrical Reinforcement is expressed as Axial Load Capacity = 0.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Distance from Compression to Tensile Reinforcement*Capacity Reduction Factor*((-Area Ratio of Tensile Reinforcement)+1-(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement)+sqrt(((1-(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement))^2)+2*Area Ratio of Tensile Reinforcement*((Force Ratio of Strengths of Reinforcements-1)*(1-(Distance from Compression to Centroid Reinforcment/Distance from Compression to Tensile Reinforcement))+(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement)))). Here is an example- 670.0779 = 0.85*55000000*0.005*0.02*0.85*((-0.5)+1-(0.035/0.02)+sqrt(((1-(0.035/0.02))^2)+2*0.5*((0.4-1)*(1-(0.01/0.02))+(0.035/0.02)))).

How to calculate Ultimate Strength for Symmetrical Reinforcement?

With 28-Day Compressive Strength of Concrete (f'_c), Width of Compression Face (b), Distance from Compression to Tensile Reinforcement (d), Capacity Reduction Factor (Phi), Area Ratio of Tensile Reinforcement (Rho), Eccentricity by Method of Frame Analysis (e'), Force Ratio of Strengths of Reinforcements (m) & Distance from Compression to Centroid Reinforcment (d') we can find Ultimate Strength for Symmetrical Reinforcement using the formula - Axial Load Capacity = 0.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Distance from Compression to Tensile Reinforcement*Capacity Reduction Factor*((-Area Ratio of Tensile Reinforcement)+1-(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement)+sqrt(((1-(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement))^2)+2*Area Ratio of Tensile Reinforcement*((Force Ratio of Strengths of Reinforcements-1)*(1-(Distance from Compression to Centroid Reinforcment/Distance from Compression to Tensile Reinforcement))+(Eccentricity by Method of Frame Analysis/Distance from Compression to Tensile Reinforcement)))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Axial Load Capacity?

Here are the different ways to Calculate Axial Load Capacity-

Axial Load Capacity=Resistance Factor*((.85*28-Day Compressive Strength of Concrete*Width of Compression Face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yield Strength of Reinforcing Steel)-(Area of Tension Reinforcement*Steel Tensile Stress))

Can the Ultimate Strength for Symmetrical Reinforcement be negative?

No, the Ultimate Strength for Symmetrical Reinforcement, measured in Force cannot be negative.

Which unit is used to measure Ultimate Strength for Symmetrical Reinforcement?

Ultimate Strength for Symmetrical Reinforcement is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Ultimate Strength for Symmetrical Reinforcement can be measured.

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Ultimate Strength for Symmetrical Reinforcement Formula

​GoAxial Load Capacity of Short Rectangular Members Formula

Ultimate Strength for Symmetrical Reinforcement Example

Ultimate Strength for Symmetrical Reinforcement Solution

Ultimate Strength for Symmetrical Reinforcement Formula Elements

Other Formulas to find Axial Load Capacity

Other formulas in Ultimate Strength Design of Concrete Columns category

How to Evaluate Ultimate Strength for Symmetrical Reinforcement?

FAQs on Ultimate Strength for Symmetrical Reinforcement

Variable Name

GoAxial Load Capacity of Short Rectangular Members Formula