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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))))
Pu = 0.85*fc*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, 8 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
28 Day Compressive Strength of Concrete - 28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it. (Measured in Megapascal)
Width of compression face - Width of compression face is the measurement or extent of something from side to side. (Measured in Meter)
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). (Measured in Millimeter)
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 - Eccentricity by method of frame analysis is the eccentricity, of axial load at end of member w.r.t. centroid of tensile reinforcement, calculated by conventional methods of frame analysis. (Measured in Meter)
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 - Distance from Compression to Centroid Reinforcment is defined as the distance from extreme compression surface to the centroid of compression reinforcement, in (mm). (Measured in Millimeter)
STEP 1: Convert Input(s) to Base Unit
28 Day Compressive Strength of Concrete: 100 Megapascal --> 100000000 Pascal (Check conversion here)
Width of compression face: 5 Meter --> 5 Meter No Conversion Required
Distance from Compression to Tensile Reinforcement: 20 Millimeter --> 0.02 Meter (Check conversion here)
Capacity reduction factor: 1 --> No Conversion Required
Area ratio of tensile reinforcement: 1 --> No Conversion Required
Eccentricity by method of frame analysis: 1 Meter --> 1 Meter No Conversion Required
Force ratio of strengths of reinforcements: 1 --> No Conversion Required
Distance from Compression to Centroid Reinforcment: 10 Millimeter --> 0.01 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pu = 0.85*fc*b*d*Phi*((-Rho)+1-(e'/d)+sqrt(((1-(e'/d))^2)+2*Rho*((m-1)*(1-(d'/d))+(e'/d)))) --> 0.85*100000000*5*0.02*1*((-1)+1-(1/0.02)+sqrt(((1-(1/0.02))^2)+2*1*((1-1)*(1-(0.01/0.02))+(1/0.02))))
Evaluating ... ...
Pu = 84991.5016995517
STEP 3: Convert Result to Output's Unit
84991.5016995517 Newton --> No Conversion Required
FINAL ANSWER
84991.5016995517 Newton <-- Axial Load Capacity
(Calculation completed in 00.047 seconds)

11 Other formulas that you can solve using the same Inputs

Ultimate Strength for No Compression Reinforcement
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))) Go
Balanced Moment when Φ is Given
balanced_moment = Resistance Factor*((.85*28 Day Compressive Strength of Concrete*Width of compression face*Depth Rectangular Compressive Stress*(Distance from Compression to Tensile Reinforcement-Distance from Plastic to Tensile Reinforcement-Depth Rectangular Compressive Stress/2))+(Area of Compressive Reinforcement*Yeild Strength of Base Plate*(Distance from Compression to Tensile Reinforcement-Distance from Compression to Centroid Reinforcment-Distance from Plastic to Tensile Reinforcement))+(area of tension reinforcement*Tensile Stress in Steel*Distance from Plastic to Tensile Reinforcement)) Go
Ultimate Strength for Symmetrical Reinforcement in Single Layers
axial_load_capacity = Capacity reduction factor*((Area of Compressive Reinforcement*Yield strength of reinforcing steel/((Eccentricity/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of compression face*Depth of column*28 Day Compressive Strength of Concrete/((3*Depth of column*Eccentricity/(Distance from Compression to Tensile Reinforcement^2))+1.18))) Go
Ultimate Strength for Short, Circular Members when Controlled by Tension
axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*(Overall diameter of section^2)*Capacity reduction factor*(sqrt((((0.85*Eccentricity/Overall diameter of section)-0.38)^2)+(Area ratio of gross area to steel area*Force ratio of strengths of reinforcements*Diameter of reinforcement/(2.5*Overall diameter of section)))-((0.85*Eccentricity/Overall diameter of section)-0.38)) Go
Compressive Reinforcement Area when Axial-Load Capacity of Short Rectangular Members is Given
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*Tensile Stress in Steel))/Yeild Strength of Base Plate Go
Tension Reinforcement Area when Axial-Load Capacity of Short Rectangular Members is Given
area_of_tension_reinforcement = ((.85*28 Day Compressive Strength of Concrete*Width of compression face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yeild Strength of Base Plate)-(Axial Load Capacity/Resistance Factor))/Tensile Stress in Steel Go
Tensile Stress in Steel when Axial-Load Capacity of Short Rectangular Members is Given
tensile_stress_in_steel = ((.85*28 Day Compressive Strength of Concrete*Width of compression face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yeild Strength of Base Plate)-(Axial Load Capacity/Resistance Factor))/area of tension reinforcement Go
Axial-Load Capacity of Short Rectangular Members
axial_load_capacity = Resistance Factor*((.85*28 Day Compressive Strength of Concrete*Width of compression face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yeild Strength of Base Plate)-(area of tension reinforcement*Tensile Stress in Steel)) Go
Yield Strength of Reinforcing Steel when Column Ultimate Strength is Given
yield_strength = (Ultimate strength-0.85*28 Day Compressive Strength of Concrete*(Gross area-Area of Reinforcement))/Area of Reinforcement Go
Column Ultimate Strength with Zero Eccentricity of Load
ultimate_strength = 0.85*28 Day Compressive Strength of Concrete*(Gross area-Area of Reinforcement)+Yield Strength*Area of Reinforcement Go
Allowable Bearing Pressure when Full Area of Support is Occupied by Base Plate
allowable_bearing_pressure = 0.35*28 Day Compressive Strength of Concrete Go

7 Other formulas that calculate the same Output

Ultimate Strength for No Compression Reinforcement
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))) Go
Ultimate Strength for Symmetrical Reinforcement in Single Layers
axial_load_capacity = Capacity reduction factor*((Area of Compressive Reinforcement*Yield strength of reinforcing steel/((Eccentricity/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of compression face*Depth of column*28 Day Compressive Strength of Concrete/((3*Depth of column*Eccentricity/(Distance from Compression to Tensile Reinforcement^2))+1.18))) Go
Ultimate Strength for Short, Circular Members when Controlled by Tension
axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*(Overall diameter of section^2)*Capacity reduction factor*(sqrt((((0.85*Eccentricity/Overall diameter of section)-0.38)^2)+(Area ratio of gross area to steel area*Force ratio of strengths of reinforcements*Diameter of reinforcement/(2.5*Overall diameter of section)))-((0.85*Eccentricity/Overall diameter of section)-0.38)) Go
Ultimate Strength for Short, Square Members when Controlled by Tension
axial_load_capacity = 0.85*Width of compression face*Depth of column*28 Day Compressive Strength of Concrete*Capacity reduction factor*((sqrt((((Eccentricity/Depth of column)-0.5)^2)+(0.67*(Diameter of reinforcement/Depth of column)*Area ratio of gross area to steel area*Force ratio of strengths of reinforcements)))-((Eccentricity/Depth of column)-0.5)) Go
Ultimate Strength for Short, Circular Members when Governed by Compression
axial_load_capacity = Capacity reduction factor*((Area of steel reinforcement*Yield strength of reinforcing steel/((3*Eccentricity/Diameter of reinforcement)+1))+(Gross area*28 Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall diameter of section+0.67*Diameter of reinforcement)^2)+1.18))) Go
Ultimate Strength for Short, Square Members when Governed by Compression
axial_load_capacity = Capacity reduction factor*((Area of steel reinforcement*Yield strength of reinforcing steel/((3*Eccentricity/Diameter of reinforcement)+1))+(Gross area*28 Day Compressive Strength of Concrete/((12*Depth of column*Eccentricity/((Depth of column+0.67*Diameter of reinforcement)^2))+1.18))) Go
Axial-Load Capacity of Short Rectangular Members
axial_load_capacity = Resistance Factor*((.85*28 Day Compressive Strength of Concrete*Width of compression face*Depth Rectangular Compressive Stress)+(Area of Compressive Reinforcement*Yeild Strength of Base Plate)-(area of tension reinforcement*Tensile Stress in Steel)) Go

Ultimate Strength for Symmetrical Reinforcement 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))))
Pu = 0.85*fc*b*d*Phi*((-Rho)+1-(e'/d)+sqrt(((1-(e'/d))^2)+2*Rho*((m-1)*(1-(d'/d))+(e'/d))))

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 and is denoted by Pu 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 (fc), 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) and 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 -> 84991.5 = 0.85*100000000*5*0.02*1*((-1)+1-(1/0.02)+sqrt(((1-(1/0.02))^2)+2*1*((1-1)*(1-(0.01/0.02))+(1/0.02)))).

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 Pu = 0.85*fc*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)))). 28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it, 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, Eccentricity by method of frame analysis is the eccentricity, of axial load at end of member w.r.t. 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 and 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 (fc), 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) and 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 and 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 and Distance from Compression to Centroid Reinforcment. We can use 7 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*Yeild Strength of Base Plate)-(area of tension reinforcement*Tensile Stress in Steel))
  • 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)))
  • axial_load_capacity = Capacity reduction factor*((Area of Compressive Reinforcement*Yield strength of reinforcing steel/((Eccentricity/Distance from Compression to Tensile Reinforcement)-Distance from Compression to Centroid Reinforcment+0.5))+(Width of compression face*Depth of column*28 Day Compressive Strength of Concrete/((3*Depth of column*Eccentricity/(Distance from Compression to Tensile Reinforcement^2))+1.18)))
  • axial_load_capacity = 0.85*28 Day Compressive Strength of Concrete*(Overall diameter of section^2)*Capacity reduction factor*(sqrt((((0.85*Eccentricity/Overall diameter of section)-0.38)^2)+(Area ratio of gross area to steel area*Force ratio of strengths of reinforcements*Diameter of reinforcement/(2.5*Overall diameter of section)))-((0.85*Eccentricity/Overall diameter of section)-0.38))
  • axial_load_capacity = Capacity reduction factor*((Area of steel reinforcement*Yield strength of reinforcing steel/((3*Eccentricity/Diameter of reinforcement)+1))+(Gross area*28 Day Compressive Strength of Concrete/(9.6*Diameter at Eccentricity/((0.8*Overall diameter of section+0.67*Diameter of reinforcement)^2)+1.18)))
  • axial_load_capacity = Capacity reduction factor*((Area of steel reinforcement*Yield strength of reinforcing steel/((3*Eccentricity/Diameter of reinforcement)+1))+(Gross area*28 Day Compressive Strength of Concrete/((12*Depth of column*Eccentricity/((Depth of column+0.67*Diameter of reinforcement)^2))+1.18)))
  • axial_load_capacity = 0.85*Width of compression face*Depth of column*28 Day Compressive Strength of Concrete*Capacity reduction factor*((sqrt((((Eccentricity/Depth of column)-0.5)^2)+(0.67*(Diameter of reinforcement/Depth of column)*Area ratio of gross area to steel area*Force ratio of strengths of reinforcements)))-((Eccentricity/Depth of column)-0.5))
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