Simplifying Term for Allowable Stress Equations Calculator

✖Maximum Unbraced Length also known as the unsupported length, is the largest distance along a structural member between the brace points.ⓘ Maximum Unbraced Length [l_max]			+10% -10%
✖Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated.ⓘ Radius of Gyration [r]			+10% -10%
✖Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.ⓘ Yield Stress of Steel [F_y]			+10% -10%
✖Moment Gradient Factor is rate at which moment is changing with length of beam.ⓘ Moment Gradient Factor [C_b]			+10% -10%

✖Simplifying Term for Fb is the term introduced for reducing the complex calculation needed for evaluating allowable stress.ⓘ Simplifying Term for Allowable Stress Equations [Q]

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Simplifying Term for Allowable Stress Equations

Formula

`"Q" = (("l"_{"max"}/"r")^2*"F"_{"y"})/(510000*"C"_{"b"})`

Example

`"0.121935"=(("1921mm"/"87mm")^2*"250MPa")/(510000*"1.960")`

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Simplifying Term for Allowable Stress Equations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Simplifying Term for Fb = ((Maximum Unbraced Length/Radius of Gyration)^2*Yield Stress of Steel)/(510000*Moment Gradient Factor)
Q = ((l_max/r)^2*F_y)/(510000*C_b)
This formula uses 5 Variables

Variables Used

Simplifying Term for Fb - Simplifying Term for Fb is the term introduced for reducing the complex calculation needed for evaluating allowable stress.
Maximum Unbraced Length - (Measured in Meter) - Maximum Unbraced Length also known as the unsupported length, is the largest distance along a structural member between the brace points.
Radius of Gyration - (Measured in Meter) - Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated.
Yield Stress of Steel - (Measured in Megapascal) - Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.
Moment Gradient Factor - Moment Gradient Factor is rate at which moment is changing with length of beam.

STEP 1: Convert Input(s) to Base Unit

Maximum Unbraced Length: 1921 Millimeter --> 1.921 Meter (Check conversion here)
Radius of Gyration: 87 Millimeter --> 0.087 Meter (Check conversion here)
Yield Stress of Steel: 250 Megapascal --> 250 Megapascal No Conversion Required
Moment Gradient Factor: 1.96 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = ((l_max/r)^2*F_y)/(510000*C_b) --> ((1.921/0.087)^2*250)/(510000*1.96)

Evaluating ... ...

Q = 0.121935450094954

STEP 3: Convert Result to Output's Unit

0.121935450094954 --> No Conversion Required

FINAL ANSWER

0.121935450094954 ≈ 0.121935 <-- Simplifying Term for Fb

(Calculation completed in 00.020 seconds)

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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

Simplifying Term for Allowable Stress Equations Formula

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

What is a Compression Flange?

The Compression Flange is defined as the widened portion of a beam or girder, such as the horizontal portion of the cross section of a simple-span T-beam, which is shortened by bending under a normal load.

How to Calculate Simplifying Term for Allowable Stress Equations?

Simplifying Term for Allowable Stress Equations calculator uses Simplifying Term for Fb = ((Maximum Unbraced Length/Radius of Gyration)^2*Yield Stress of Steel)/(510000*Moment Gradient Factor) to calculate the Simplifying Term for Fb, The Simplifying Term for Allowable Stress Equations formula is defined as the determination of a simplifying term that can be used to reduce the calculation complexity while evaluating allowable stress. Simplifying Term for Fb is denoted by Q symbol.

How to calculate Simplifying Term for Allowable Stress Equations using this online calculator? To use this online calculator for Simplifying Term for Allowable Stress Equations, enter Maximum Unbraced Length (l_max), Radius of Gyration (r), Yield Stress of Steel (F_y) & Moment Gradient Factor (C_b) and hit the calculate button. Here is how the Simplifying Term for Allowable Stress Equations calculation can be explained with given input values -> 0.202365 = ((1.921/0.087)^2*250000000)/(510000*1.96).

FAQ

What is Simplifying Term for Allowable Stress Equations?

The Simplifying Term for Allowable Stress Equations formula is defined as the determination of a simplifying term that can be used to reduce the calculation complexity while evaluating allowable stress and is represented as Q = ((l_max/r)^2*F_y)/(510000*C_b) or Simplifying Term for Fb = ((Maximum Unbraced Length/Radius of Gyration)^2*Yield Stress of Steel)/(510000*Moment Gradient Factor). Maximum Unbraced Length also known as the unsupported length, is the largest distance along a structural member between the brace points, Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated, Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed & Moment Gradient Factor is rate at which moment is changing with length of beam.

How to calculate Simplifying Term for Allowable Stress Equations?

The Simplifying Term for Allowable Stress Equations formula is defined as the determination of a simplifying term that can be used to reduce the calculation complexity while evaluating allowable stress is calculated using Simplifying Term for Fb = ((Maximum Unbraced Length/Radius of Gyration)^2*Yield Stress of Steel)/(510000*Moment Gradient Factor). To calculate Simplifying Term for Allowable Stress Equations, you need Maximum Unbraced Length (l_max), Radius of Gyration (r), Yield Stress of Steel (F_y) & Moment Gradient Factor (C_b). With our tool, you need to enter the respective value for Maximum Unbraced Length, Radius of Gyration, Yield Stress of Steel & Moment Gradient Factor 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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