Plastic Moment Calculator

✖Specified Minimum Yield Stress represents the minimum tensile stress or yield stress required by the flexural member, say, web.ⓘ Specified Minimum Yield Stress [F_yw]			+10% -10%
✖Plastic modulus is the geometric property of a plastic section which is defined as the ratio of the second moment of area to distance from neutral axis to extreme fibre.ⓘ Plastic modulus [Z_p]			+10% -10%

✖Plastic Moment is the moment at which the entire cross section has reached its yield stress.ⓘ Plastic Moment [M_p]

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Formula

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Plastic Moment

Formula

`"M"_{"p"} = "F"_{"yw"}*"Z"_{"p"}`

Example

`"7E^6N*mm"="139MPa"*"50mm³"`

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Plastic Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Plastic Moment = Specified Minimum Yield Stress*Plastic modulus
M_p = F_yw*Z_p
This formula uses 3 Variables

Variables Used

Plastic Moment - (Measured in Newton Meter) - Plastic Moment is the moment at which the entire cross section has reached its yield stress.
Specified Minimum Yield Stress - (Measured in Megapascal) - Specified Minimum Yield Stress represents the minimum tensile stress or yield stress required by the flexural member, say, web.
Plastic modulus - (Measured in Cubic Millimeter) - Plastic modulus is the geometric property of a plastic section which is defined as the ratio of the second moment of area to distance from neutral axis to extreme fibre.

STEP 1: Convert Input(s) to Base Unit

Specified Minimum Yield Stress: 139 Megapascal --> 139 Megapascal No Conversion Required
Plastic modulus: 50 Cubic Millimeter --> 50 Cubic Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_p = F_yw*Z_p --> 139*50

Evaluating ... ...

M_p = 6950

STEP 3: Convert Result to Output's Unit

6950 Newton Meter -->6950000 Newton Millimeter (Check conversion here)

FINAL ANSWER

6950000 ≈ 7E+6 Newton Millimeter <-- Plastic Moment

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Design of Steel Structures » Load-and-Resistance Factor Design for Buildings » Beams » Plastic Moment

Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 13 Beams Calculators

Critical Elastic Moment

Go Critical Elastic Moment = ((Moment Gradient Factor*pi)/Unbraced Length of Member)*sqrt(((Elastic Modulus of Steel*Y Axis Moment of Inertia*Shear Modulus in Steel Structures*Torsional constant)+(Y Axis Moment of Inertia*Warping Constant*((pi*Elastic Modulus of Steel)/(Unbraced Length of Member)^2))))

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling

Go Limiting Length for Inelastic Buckling = ((Radius of gyration about minor axis*Beam Buckling Factor 1)/(Specified Minimum Yield Stress-Compressive Residual Stress in Flange))*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2)))

Specified Minimum Yield Stress for Web given Limiting Laterally Unbraced Length

Go Specified Minimum Yield Stress = ((Radius of gyration about minor axis*Beam Buckling Factor 1*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2))))/Limiting Length for Inelastic Buckling)+Compressive Residual Stress in Flange

Beam Buckling Factor 1

Go Beam Buckling Factor 1 = (pi/Section Modulus about Major Axis)*sqrt((Elastic Modulus of Steel*Shear Modulus in Steel Structures*Torsional constant*Cross Sectional Area in Steel Structures)/2)

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams

Go Limiting Length for Inelastic Buckling = (2*Radius of gyration about minor axis*Elastic Modulus of Steel*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/Limiting buckling moment

Critical Elastic Moment for Box Sections and Solid Bars

Go Critical Elastic Moment = (57000*Moment Gradient Factor*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of gyration about minor axis)

Beam Buckling Factor 2

Go Beam Buckling Factor 2 = ((4*Warping Constant)/Y Axis Moment of Inertia)*((Section Modulus about Major Axis)/(Shear Modulus in Steel Structures*Torsional constant))^2

Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams

Go Limiting Laterally Unbraced Length = (3750*(Radius of gyration about minor axis/Plastic Moment))/(sqrt(Torsional constant*Cross Sectional Area in Steel Structures))

Maximum Laterally Unbraced Length for Plastic Analysis

Go Laterally Unbraced Length for Plastic Analysis = Radius of gyration about minor axis*(3600+2200*(Smaller Moments of Unbraced Beam/Plastic Moment))/(Minimum Yield Stress of Compression Flange)

Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams

Go Laterally Unbraced Length for Plastic Analysis = (Radius of gyration about minor axis*(5000+3000*(Smaller Moments of Unbraced Beam/Plastic Moment)))/Yield Stress of Steel

Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections

Go Limiting Laterally Unbraced Length = (300*Radius of gyration about minor axis)/sqrt(Flange Yield Stress)

Limiting Buckling Moment

Go Limiting buckling moment = Smaller Yield Stress*Section Modulus about Major Axis

Plastic Moment

Go Plastic Moment = Specified Minimum Yield Stress*Plastic modulus

Plastic Moment Formula

Plastic Moment = Specified Minimum Yield Stress*Plastic modulus
M_p = F_yw*Z_p

What are the principles of Plastic Analysis?

1.Mechanism condition: When the ultimate load is reached collapse mechanism usually formed.
2 Equilibrium condition: Sum of forces =0, Sum of moments=0
3 Plastic moment condition: The bending moment at any section in the structure should not be more than the full plastic moment (moment at which plastic hinges form and structure moves to failure) of the section.

How to Calculate Plastic Moment?

Plastic Moment calculator uses Plastic Moment = Specified Minimum Yield Stress*Plastic modulus to calculate the Plastic Moment, The Plastic Moment formula is defined as the moment at which the entire cross-section has reached its yield stress i.e. theoretically the maximum bending moment that the section can resist and when this point is reached a plastic hinge is formed. Plastic Moment is denoted by M_p symbol.

How to calculate Plastic Moment using this online calculator? To use this online calculator for Plastic Moment, enter Specified Minimum Yield Stress (F_yw) & Plastic modulus (Z_p) and hit the calculate button. Here is how the Plastic Moment calculation can be explained with given input values -> 6.95 = 139000000*5E-08.

FAQ

What is Plastic Moment?

The Plastic Moment formula is defined as the moment at which the entire cross-section has reached its yield stress i.e. theoretically the maximum bending moment that the section can resist and when this point is reached a plastic hinge is formed and is represented as M_p = F_yw*Z_p or Plastic Moment = Specified Minimum Yield Stress*Plastic modulus. Specified Minimum Yield Stress represents the minimum tensile stress or yield stress required by the flexural member, say, web & Plastic modulus is the geometric property of a plastic section which is defined as the ratio of the second moment of area to distance from neutral axis to extreme fibre.

How to calculate Plastic Moment?

The Plastic Moment formula is defined as the moment at which the entire cross-section has reached its yield stress i.e. theoretically the maximum bending moment that the section can resist and when this point is reached a plastic hinge is formed is calculated using Plastic Moment = Specified Minimum Yield Stress*Plastic modulus. To calculate Plastic Moment, you need Specified Minimum Yield Stress (F_yw) & Plastic modulus (Z_p). With our tool, you need to enter the respective value for Specified Minimum Yield Stress & Plastic modulus and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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