Moment Gradient Factor given Smaller and Larger Beam End Moment Calculator

✖Smaller Moment at ends of unbraced length of member.ⓘ Smaller Moment [M¹]			+10% -10%
✖Larger Beam End Moment is maximum moment between two ends of the beam.ⓘ Larger Beam End Moment [M²]			+10% -10%

✖Moment gradient factor for bridge beams is rate at which moment is changing with length of beam.ⓘ Moment Gradient Factor given Smaller and Larger Beam End Moment [C_b]

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Moment Gradient Factor given Smaller and Larger Beam End Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment Gradient Factor for Bridge Beams = 1.75+1.05*(Smaller Moment/Larger Beam End Moment)+0.3*(Smaller 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 for Bridge Beams - Moment gradient factor for bridge beams is rate at which moment is changing with length of beam.
Smaller Moment - (Measured in Newton Meter) - Smaller Moment at ends of unbraced length of member.
Larger Beam End Moment - (Measured in Newton Meter) - Larger Beam End Moment is maximum moment between two ends of the beam.

STEP 1: Convert Input(s) to Base Unit

Smaller Moment: 4 Newton Meter --> 4 Newton Meter No Conversion Required
Larger Beam End Moment: 10 Newton Meter --> 10 Newton Meter No Conversion Required

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*(4/10)+0.3*(4/10)^2

Evaluating ... ...

C_b = 2.218

STEP 3: Convert Result to Output's Unit

2.218 --> No Conversion Required

FINAL ANSWER

2.218 <-- Moment Gradient Factor for Bridge Beams

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< Allowable Stress Design for Bridge Beams Calculators

Moment Gradient Factor given Smaller and Larger Beam End Moment

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

Steel Yield Strength given Allowable Unit Stress in Bending

LaTeX Go Yield Strength of Steel = Allowable Unit Tensile Stress in bending/0.55

Allowable Unit Stress in Bending

LaTeX Go Allowable Unit Tensile Stress in bending = 0.55*Yield Strength of Steel

Moment Gradient Factor given Smaller and Larger Beam End Moment Formula

LaTeX Go

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

What is Moment Gradient Factor?

Moment Gradient Factor is well known that if the moment in an I-beam is not constant throughout, the lateral–torsional buckling moment is greater than the same moment in pure bending. In other words, the value of moment-gradient factor is always greater than unity.

How to Calculate Moment Gradient Factor given Smaller and Larger Beam End Moment?

Moment Gradient Factor given Smaller and Larger Beam End Moment calculator uses Moment Gradient Factor for Bridge Beams = 1.75+1.05*(Smaller Moment/Larger Beam End Moment)+0.3*(Smaller Moment/Larger Beam End Moment)^2 to calculate the Moment Gradient Factor for Bridge Beams, The Moment Gradient Factor given Smaller and Larger Beam End Moment formula is defined as a factor that varies with respect to the length of the beam depending on end conditions. Moment Gradient Factor for Bridge Beams is denoted by C_b symbol.

How to calculate Moment Gradient Factor given Smaller and Larger Beam End Moment using this online calculator? To use this online calculator for Moment Gradient Factor given Smaller and Larger Beam End Moment, enter Smaller Moment (M¹) & Larger Beam End Moment (M²) and hit the calculate button. Here is how the Moment Gradient Factor given Smaller and Larger Beam End Moment calculation can be explained with given input values -> 2.218 = 1.75+1.05*(4/10)+0.3*(4/10)^2.

FAQ

What is Moment Gradient Factor given Smaller and Larger Beam End Moment?

The Moment Gradient Factor given Smaller and Larger Beam End Moment formula is defined as a factor that varies with respect to the length of the beam depending on end conditions and is represented as C_b = 1.75+1.05*(M¹/M²)+0.3*(M¹/M²)^2 or Moment Gradient Factor for Bridge Beams = 1.75+1.05*(Smaller Moment/Larger Beam End Moment)+0.3*(Smaller Moment/Larger Beam End Moment)^2. Smaller Moment at ends of unbraced length of member & Larger Beam End Moment is maximum moment between two ends of the beam.

How to calculate Moment Gradient Factor given Smaller and Larger Beam End Moment?

The Moment Gradient Factor given Smaller and Larger Beam End Moment formula is defined as a factor that varies with respect to the length of the beam depending on end conditions is calculated using Moment Gradient Factor for Bridge Beams = 1.75+1.05*(Smaller Moment/Larger Beam End Moment)+0.3*(Smaller Moment/Larger Beam End Moment)^2. To calculate Moment Gradient Factor given Smaller and Larger Beam End Moment, you need Smaller Moment (M¹) & Larger Beam End Moment (M²). With our tool, you need to enter the respective value for Smaller 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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