Ultimate Strength for Symmetrical Reinforcement Calculator

✖The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days.ⓘ 28-Day Compressive Strength of Concrete [f'_c]			+10% -10%
✖Width of Compression Face is the measurement or extent of something from side to side.ⓘ Width of Compression Face [b]			+10% -10%
✖Distance from Compression to Tensile Reinforcement is defined as the distance from extreme compression surface to the centroid of tensile reinforcement, in (mm).ⓘ Distance from Compression to Tensile Reinforcement [d]			+10% -10%
✖Capacity Reduction Factor is derived for reinforced concrete structures based on a reliability-based calibration of the Australian Concrete Structures Standard AS3600.ⓘ Capacity Reduction Factor [Phi]			+10% -10%
✖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.ⓘ Area Ratio of Tensile Reinforcement [Rho]			+10% -10%
✖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.ⓘ Eccentricity by Method of Frame Analysis [e']			+10% -10%
✖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.ⓘ Force Ratio of Strengths of Reinforcements [m]			+10% -10%
✖Distance from Compression to Centroid Reinforcment is defined as the distance from extreme compression surface to the centroid of compression reinforcement, in (mm).ⓘ Distance from Compression to Centroid Reinforcment [d']			+10% -10%

✖Axial Load Capacity is defined as the maximum load along the direction of the drive train.ⓘ Ultimate Strength for Symmetrical Reinforcement [P_u]

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Formula

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Ultimate Strength for Symmetrical Reinforcement

Formula

`"P"_{"u"} = 0.85*"f'"_{"c"}*"b"*"d"*"Phi"*((-"Rho")+1-("e'"/"d")+sqrt(((1-("e'"/"d"))^2)+2*"Rho"*(("m"-1)*(1-("d'"/"d"))+("e'"/"d"))))`

Example

`"670.0779N"=0.85*"55.0MPa"*"5mm"*"20mm"*"0.85"*((-"0.5")+1-("35mm"/"20mm")+sqrt(((1-("35mm"/"20mm"))^2)+2*"0.5"*(("0.4"-1)*(1-("10mm"/"20mm"))+("35mm"/"20mm"))))`

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Ultimate Strength for Symmetrical Reinforcement Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
P_u = 0.85*f'_c*b*d*Phi*((-Rho)+1-(e'/d)+sqrt(((1-(e'/d))^2)+2*Rho*((m-1)*(1-(d'/d))+(e'/d))))
This formula uses 1 Functions, 9 Variables

Functions Used

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., sqrt(Number)

Variables Used

Axial Load Capacity - (Measured in Newton) - Axial Load Capacity is defined as the maximum load along the direction of the drive train.
28-Day Compressive Strength of Concrete - (Measured in Megapascal) - The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days.
Width of Compression Face - (Measured in Millimeter) - Width of Compression Face is the measurement or extent of something from side to side.
Distance from Compression to Tensile Reinforcement - (Measured in Millimeter) - Distance from Compression to Tensile Reinforcement is defined as the distance from extreme compression surface to the centroid of tensile reinforcement, in (mm).
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.
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.
Eccentricity by Method of Frame Analysis - (Measured in Millimeter) - 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.
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.
Distance from Compression to Centroid Reinforcment - (Measured in Millimeter) - Distance from Compression to Centroid Reinforcment is defined as the distance from extreme compression surface to the centroid of compression reinforcement, in (mm).

STEP 1: Convert Input(s) to Base Unit

28-Day Compressive Strength of Concrete: 55 Megapascal --> 55 Megapascal No Conversion Required
Width of Compression Face: 5 Millimeter --> 5 Millimeter No Conversion Required
Distance from Compression to Tensile Reinforcement: 20 Millimeter --> 20 Millimeter No Conversion Required
Capacity Reduction Factor: 0.85 --> No Conversion Required
Area Ratio of Tensile Reinforcement: 0.5 --> No Conversion Required
Eccentricity by Method of Frame Analysis: 35 Millimeter --> 35 Millimeter No Conversion Required
Force Ratio of Strengths of Reinforcements: 0.4 --> No Conversion Required
Distance from Compression to Centroid Reinforcment: 10 Millimeter --> 10 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_u = 0.85*f'_c*b*d*Phi*((-Rho)+1-(e'/d)+sqrt(((1-(e'/d))^2)+2*Rho*((m-1)*(1-(d'/d))+(e'/d)))) --> 0.85*55*5*20*0.85*((-0.5)+1-(35/20)+sqrt(((1-(35/20))^2)+2*0.5*((0.4-1)*(1-(10/20))+(35/20))))

Evaluating ... ...

P_u = 670.077948626776

STEP 3: Convert Result to Output's Unit

670.077948626776 Newton --> No Conversion Required

FINAL ANSWER

670.077948626776 ≈ 670.0779 Newton <-- Axial Load Capacity

(Calculation completed in 00.004 seconds)

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< 9 Ultimate Strength Design of Concrete Columns Calculators

Ultimate Strength for Symmetrical Reinforcement

Go 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))))

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

Go 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

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

Go 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

Tensile Stress in Steel for Axial-Load Capacity of Short Rectangular Members

Go Steel Tensile Stress = ((.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))/Area of Tension Reinforcement

Axial Load Capacity of Short Rectangular Members

Go 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))

28-day Concrete Compressive Strength given Column Ultimate Strength

Go 28-Day Compressive Strength of Concrete = (Column Ultimate Strength-Yield Strength of Reinforcing Steel*Area of Steel Reinforcement)/(0.85*(Gross Area of Column-Area of Steel Reinforcement))

Yield Strength of Reinforcing Steel using Column Ultimate Strength

Go Yield Strength of Reinforcing Steel = (Column Ultimate Strength-0.85*28-Day Compressive Strength of Concrete*(Gross Area of Column-Area of Steel Reinforcement))/Area of Steel Reinforcement

Column Ultimate Strength with Zero Eccentricity of Load

Go Column Ultimate Strength = 0.85*28-Day Compressive Strength of Concrete*(Gross Area of Column-Area of Steel Reinforcement)+Yield Strength of Reinforcing Steel*Area of Steel Reinforcement

Balanced Moment given Load and Eccentricity

Go Balanced Moment = Eccentricity of Column*Load Balanced Condition

Ultimate Strength for Symmetrical Reinforcement Formula

What is the ultimate strength of a material?

The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens. For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MPa.

How to Calculate Ultimate Strength for Symmetrical Reinforcement?

Ultimate Strength for Symmetrical Reinforcement calculator 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 calculate 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 calculate Ultimate Strength for Symmetrical Reinforcement using this online calculator? To use this online calculator 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. Here is how the Ultimate Strength for Symmetrical Reinforcement calculation can be explained with given input values -> 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)))).

FAQ

What is Ultimate Strength for Symmetrical Reinforcement?

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 and is represented as P_u = 0.85*f'_c*b*d*Phi*((-Rho)+1-(e'/d)+sqrt(((1-(e'/d))^2)+2*Rho*((m-1)*(1-(d'/d))+(e'/d)))) or 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)))). The 28-Day Compressive Strength of Concrete is the average compressive strength of concrete specimens that have been cured for 28 days, Width of Compression Face is the measurement or extent of something from side to side, Distance from Compression to Tensile Reinforcement is defined as the distance from extreme compression surface to the centroid of tensile reinforcement, in (mm), Capacity Reduction Factor is derived for reinforced concrete structures based on a reliability-based calibration of the Australian Concrete Structures Standard AS3600, 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, 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, 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 & Distance from Compression to Centroid Reinforcment is defined as the distance from extreme compression surface to the centroid of compression reinforcement, in (mm).

How to calculate Ultimate Strength for Symmetrical Reinforcement?

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 is calculated using 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 calculate Ultimate Strength for Symmetrical Reinforcement, you need 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'). With our tool, you need to enter the respective value for 28-Day Compressive Strength of Concrete, Width of Compression Face, Distance from Compression to Tensile Reinforcement, Capacity Reduction Factor, Area Ratio of Tensile Reinforcement, Eccentricity by Method of Frame Analysis, Force Ratio of Strengths of Reinforcements & Distance from Compression to Centroid Reinforcment and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Axial Load Capacity?

In this formula, Axial Load Capacity uses 28-Day Compressive Strength of Concrete, Width of Compression Face, Distance from Compression to Tensile Reinforcement, Capacity Reduction Factor, Area Ratio of Tensile Reinforcement, Eccentricity by Method of Frame Analysis, Force Ratio of Strengths of Reinforcements & Distance from Compression to Centroid Reinforcment. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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