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Ultimate Strength for No Compression Reinforcement Formula

GoUltimate Strength for Symmetrical Reinforcement in Single Layers 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 \cdot m) + 1 - (\frac{e'}{d}) + \sqrt{({(1 - (\frac{e'}{d}))}^{2}) + 2 \cdot (Rho \cdot e' \cdot \frac{m}{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?m - Force Ratio of Strengths of Reinforcements?e' - Eccentricity by Method of Frame Analysis?

Ultimate Strength for No Compression Reinforcement Example

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Here is how the Ultimate Strength for No Compression Reinforcement equation looks like.

689.8837 = 0.85 \cdot 55 \cdot 5 \cdot 20 \cdot 0.85 \cdot ((- 0.5 \cdot 0.4) + 1 - (\frac{35}{20}) + \sqrt{({(1 - (\frac{35}{20}))}^{2}) + 2 \cdot (0.5 \cdot 35 \cdot \frac{0.4}{20})})

689.8837N = 0.85 \cdot 55MPa \cdot 5mm \cdot 20mm \cdot 0.85 \cdot ((- 0.5 \cdot 0.4) + 1 - (\frac{35mm}{20mm}) + \sqrt{({(1 - (\frac{35mm}{20mm}))}^{2}) + 2 \cdot (0.5 \cdot 35mm \cdot \frac{0.4}{20mm})})

689.8837 = 0.85 \cdot 55 \cdot 5 \cdot 20 \cdot 0.85 \cdot ((- 0.5 \cdot 0.4) + 1 - (\frac{35}{20}) + \sqrt{({(1 - (\frac{35}{20}))}^{2}) + 2 \cdot (0.5 \cdot 35 \cdot \frac{0.4}{20})})

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Ultimate Strength for No Compression Reinforcement Solution

Follow our step by step solution on how to calculate Ultimate Strength for No Compression Reinforcement?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

P u = 0.85 \cdot 5.5E+7Pa \cdot 0.005m \cdot 0.02m \cdot 0.85 \cdot ((- 0.5 \cdot 0.4) + 1 - (\frac{0.035m}{0.02m}) + \sqrt{({(1 - (\frac{0.035m}{0.02m}))}^{2}) + 2 \cdot (0.5 \cdot 0.035m \cdot \frac{0.4}{0.02m})})

Next Step Prepare to Evaluate

∴

P u = 0.85 \cdot 5.5E+7 \cdot 0.005 \cdot 0.02 \cdot 0.85 \cdot ((- 0.5 \cdot 0.4) + 1 - (\frac{0.035}{0.02}) + \sqrt{({(1 - (\frac{0.035}{0.02}))}^{2}) + 2 \cdot (0.5 \cdot 0.035 \cdot \frac{0.4}{0.02})})

Next Step Evaluate

∴

P u = 689.883741715151N

LAST Step Rounding Answer

∴

P u = 689.8837N

Ultimate Strength for No Compression 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

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

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

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 Ultimate Strength for Symmetrical Reinforcement in Single Layers

P u = Phi \cdot ((A' s \cdot \frac{f y}{(\frac{e}{d}) - d' + 0.5}) + (b \cdot L \cdot \frac{f' c}{(3 \cdot L \cdot \frac{e}{d^{2}}) + 1.18}))

How to Evaluate Ultimate Strength for No Compression Reinforcement?

Ultimate Strength for No Compression 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*Force Ratio of Strengths of Reinforcements)+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*Eccentricity by Method of Frame Analysis*Force Ratio of Strengths of Reinforcements/Distance from Compression to Tensile Reinforcement))) to evaluate the Axial Load Capacity, The Ultimate Strength for No Compression 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 No Compression Reinforcement using this online evaluator? To use this online evaluator for Ultimate Strength for No Compression 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), Force Ratio of Strengths of Reinforcements (m) & Eccentricity by Method of Frame Analysis (e') and hit the calculate button.

FAQs on Ultimate Strength for No Compression Reinforcement

What is the formula to find Ultimate Strength for No Compression Reinforcement?

The formula of Ultimate Strength for No Compression 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*Force Ratio of Strengths of Reinforcements)+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*Eccentricity by Method of Frame Analysis*Force Ratio of Strengths of Reinforcements/Distance from Compression to Tensile Reinforcement))). Here is an example- 689.8837 = 0.85*55000000*0.005*0.02*0.85*((-0.5*0.4)+1-(0.035/0.02)+sqrt(((1-(0.035/0.02))^2)+2*(0.5*0.035*0.4/0.02))).

How to calculate Ultimate Strength for No Compression 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), Force Ratio of Strengths of Reinforcements (m) & Eccentricity by Method of Frame Analysis (e') we can find Ultimate Strength for No Compression 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*Force Ratio of Strengths of Reinforcements)+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*Eccentricity by Method of Frame Analysis*Force Ratio of Strengths of Reinforcements/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=Capacity Reduction Factor*((Area of Compressive Reinforcement*Yield Strength of Reinforcing Steel/((Eccentricity of Column/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of Compression Face*Effective Length of Column*28-Day Compressive Strength of Concrete/((3*Effective Length of Column*Eccentricity of Column/(Distance from Compression to Tensile Reinforcement^2))+1.18)))

Can the Ultimate Strength for No Compression Reinforcement be negative?

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

Which unit is used to measure Ultimate Strength for No Compression Reinforcement?

Ultimate Strength for No Compression 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 No Compression Reinforcement can be measured.

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Ultimate Strength for No Compression Reinforcement Formula

​GoUltimate Strength for Symmetrical Reinforcement in Single Layers Formula

Ultimate Strength for No Compression Reinforcement Example

Ultimate Strength for No Compression Reinforcement Solution

Ultimate Strength for No Compression Reinforcement Formula Elements

Other Formulas to find Axial Load Capacity

How to Evaluate Ultimate Strength for No Compression Reinforcement?

FAQs on Ultimate Strength for No Compression Reinforcement

Variable Name

GoUltimate Strength for Symmetrical Reinforcement in Single Layers Formula