Modifier for Moment Gradient Calculator

✖Smaller Beam End Moment is the smaller moment on the section when beam is subjected to unequal end moments.ⓘ Smaller Beam End Moment [M₁]			+10% -10%
✖Larger Beam End Moment is the bigger moment on the beam when it is subjected to unequal end moments.ⓘ Larger Beam End Moment [M₂]			+10% -10%

✖Moment Gradient Factor is rate at which moment is changing with length of beam.ⓘ Modifier for Moment Gradient [C_b]

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Formula

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Modifier for Moment Gradient

Formula

`"C"_{"b"} = 1.75+(1.05*("M"_{"1"}/"M"_{"2"}))+(0.3*("M"_{"1"}/"M"_{"2"})^2)`

Example

`"1.960884"=1.75+(1.05*("10kN*m"/"52.5kN*m"))+(0.3*("10kN*m"/"52.5kN*m")^2)`

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Modifier for Moment Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment Gradient Factor = 1.75+(1.05*(Smaller Beam End Moment/Larger Beam End Moment))+(0.3*(Smaller Beam End Moment/Larger Beam End Moment)^2)
C_b = 1.75+(1.05*(M₁/M₂))+(0.3*(M₁/M₂)^2)
This formula uses 3 Variables

Variables Used

Moment Gradient Factor - Moment Gradient Factor is rate at which moment is changing with length of beam.
Smaller Beam End Moment - (Measured in Newton Meter) - Smaller Beam End Moment is the smaller moment on the section when beam is subjected to unequal end moments.
Larger Beam End Moment - (Measured in Newton Meter) - Larger Beam End Moment is the bigger moment on the beam when it is subjected to unequal end moments.

STEP 1: Convert Input(s) to Base Unit

Smaller Beam End Moment: 10 Kilonewton Meter --> 10000 Newton Meter (Check conversion here)
Larger Beam End Moment: 52.5 Kilonewton Meter --> 52500 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_b = 1.75+(1.05*(M₁/M₂))+(0.3*(M₁/M₂)^2) --> 1.75+(1.05*(10000/52500))+(0.3*(10000/52500)^2)

Evaluating ... ...

C_b = 1.9608843537415

STEP 3: Convert Result to Output's Unit

1.9608843537415 --> No Conversion Required

FINAL ANSWER

1.9608843537415 ≈ 1.960884 <-- Moment Gradient Factor

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 9 Allowable-Stress Design for Building Beams Calculators

Modifier for Moment Gradient

Go Moment Gradient Factor = 1.75+(1.05*(Smaller Beam End Moment/Larger Beam End Moment))+(0.3*(Smaller Beam End Moment/Larger Beam End Moment)^2)

Simplifying Term for Allowable Stress Equations

Go Simplifying Term for Fb = ((Maximum Unbraced Length/Radius of Gyration)^2*Yield Stress of Steel)/(510000*Moment Gradient Factor)

Allowable Stress for Solid Compression Flange having Area not Less than Tension Flange

Go Maximum Fiber Stress = (12000*Moment Gradient Factor)/((Maximum Unbraced Length*Beam Depth)/Area of Compression Flange)

Maximum Unsupported Length of Compression Flange-2

Go Maximum Unbraced Length = 20000/((Yield Stress of Steel*Beam Depth)/Area of Compression Flange)

Maximum Unsupported Length of Compression Flange-1

Go Maximum Unbraced Length = (76.0*Width of Compression Flange)/sqrt(Yield Stress of Steel)

Allowable Stress given Simplifying Term between 0.2 and 1

Go Maximum Fiber Stress = ((2-Simplifying Term for Fb)*Yield Stress of Steel)/3

Allowable Stress when Simplifying Term Greater than 1

Go Maximum Fiber Stress = Yield Stress of Steel/(3*Simplifying Term for Fb)

Maximum Fiber Stress in Bending for Laterally Supported Noncompact Beams and Girders

Go Maximum Fiber Stress = 0.60*Yield Stress of Steel

Maximum Fiber Stress in Bending for Laterally Supported Compact Beams and Girders

Go Maximum Fiber Stress = 0.66*Yield Stress of Steel

Modifier for Moment Gradient Formula

Moment Gradient Factor = 1.75+(1.05*(Smaller Beam End Moment/Larger Beam End Moment))+(0.3*(Smaller Beam End Moment/Larger Beam End Moment)^2)
C_b = 1.75+(1.05*(M₁/M₂))+(0.3*(M₁/M₂)^2)

What is Moment Gradient Factor?

The Moment Gradient Factor, Cb is a modification factor used in the equation for nominal flexural strength when determining Lateral-Torsional Buckling. The reason for this factor is to allow for non-uniform moment diagrams when the ends of a beam segment are braced

How to Calculate Modifier for Moment Gradient?

Modifier for Moment Gradient calculator uses Moment Gradient Factor = 1.75+(1.05*(Smaller Beam End Moment/Larger Beam End Moment))+(0.3*(Smaller Beam End Moment/Larger Beam End Moment)^2) to calculate the Moment Gradient Factor, The Modifier for Moment Gradient formula is defined as the two parameters, smaller end moment and larger end moment if the beam is subjected to two unequal end moments. Moment Gradient Factor is denoted by C_b symbol.

How to calculate Modifier for Moment Gradient using this online calculator? To use this online calculator for Modifier for Moment Gradient, enter Smaller Beam End Moment (M₁) & Larger Beam End Moment (M₂) and hit the calculate button. Here is how the Modifier for Moment Gradient calculation can be explained with given input values -> 1.960884 = 1.75+(1.05*(10000/52500))+(0.3*(10000/52500)^2).

FAQ

What is Modifier for Moment Gradient?

The Modifier for Moment Gradient formula is defined as the two parameters, smaller end moment and larger end moment if the beam is subjected to two unequal end moments and is represented as C_b = 1.75+(1.05*(M₁/M₂))+(0.3*(M₁/M₂)^2) or Moment Gradient Factor = 1.75+(1.05*(Smaller Beam End Moment/Larger Beam End Moment))+(0.3*(Smaller Beam End Moment/Larger Beam End Moment)^2). Smaller Beam End Moment is the smaller moment on the section when beam is subjected to unequal end moments & Larger Beam End Moment is the bigger moment on the beam when it is subjected to unequal end moments.

How to calculate Modifier for Moment Gradient?

The Modifier for Moment Gradient formula is defined as the two parameters, smaller end moment and larger end moment if the beam is subjected to two unequal end moments is calculated using Moment Gradient Factor = 1.75+(1.05*(Smaller Beam End Moment/Larger Beam End Moment))+(0.3*(Smaller Beam End Moment/Larger Beam End Moment)^2). To calculate Modifier for Moment Gradient, you need Smaller Beam End Moment (M₁) & Larger Beam End Moment (M₂). With our tool, you need to enter the respective value for Smaller Beam End Moment & Larger Beam End Moment 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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