Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress Calculator

✖Ratio of Web to Flange Yield Strength is a strength ratio.ⓘ Ratio of Web to Flange Yield Strength [α]			+10% -10%
✖The Ratio of Web to Flange Area of the orthotropic-plate bridge is the ratio of web area to the area of tension flange or bottom flange of the orthotropic-plate bridge.ⓘ Ratio of Web to Flange Area [β]			+10% -10%
✖Distance Ratio of Flange to Depth is the ratio of the distance from the outer edge of tension flange or bottom flange of the orthotropic deck to neutral axis divided by the depth of steel section.ⓘ Distance Ratio of Flange to Depth [ψ]			+10% -10%

✖Allowable Stress Multiplier is a factor used in hybrid bridge girders design.ⓘ Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress [R]

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Formula

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Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress

Formula

`"R" = 1-((1-"α")^2*("β"*"ψ")*(3-"ψ"+"ψ"*"α"))/(6+"β"*"ψ"*(3-"ψ"))`

Example

`"0.5"=1-((1-"1.5")^2*("3"*"2.0")*(3-"2.0"+"2.0"*"1.5"))/(6+"3"*"2.0"*(3-"2.0"))`

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Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Allowable Stress Multiplier = 1-((1-Ratio of Web to Flange Yield Strength)^2*(Ratio of Web to Flange Area*Distance Ratio of Flange to Depth)*(3-Distance Ratio of Flange to Depth+Distance Ratio of Flange to Depth*Ratio of Web to Flange Yield Strength))/(6+Ratio of Web to Flange Area*Distance Ratio of Flange to Depth*(3-Distance Ratio of Flange to Depth))
R = 1-((1-α)^2*(β*ψ)*(3-ψ+ψ*α))/(6+β*ψ*(3-ψ))
This formula uses 4 Variables

Variables Used

Allowable Stress Multiplier - Allowable Stress Multiplier is a factor used in hybrid bridge girders design.
Ratio of Web to Flange Yield Strength - Ratio of Web to Flange Yield Strength is a strength ratio.
Ratio of Web to Flange Area - The Ratio of Web to Flange Area of the orthotropic-plate bridge is the ratio of web area to the area of tension flange or bottom flange of the orthotropic-plate bridge.
Distance Ratio of Flange to Depth - Distance Ratio of Flange to Depth is the ratio of the distance from the outer edge of tension flange or bottom flange of the orthotropic deck to neutral axis divided by the depth of steel section.

STEP 1: Convert Input(s) to Base Unit

Ratio of Web to Flange Yield Strength: 1.5 --> No Conversion Required
Ratio of Web to Flange Area: 3 --> No Conversion Required
Distance Ratio of Flange to Depth: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = 1-((1-α)^2*(β*ψ)*(3-ψ+ψ*α))/(6+β*ψ*(3-ψ)) --> 1-((1-1.5)^2*(3*2)*(3-2+2*1.5))/(6+3*2*(3-2))

Evaluating ... ...

R = 0.5

STEP 3: Convert Result to Output's Unit

0.5 --> No Conversion Required

FINAL ANSWER

0.5 <-- Allowable Stress Multiplier

(Calculation completed in 00.004 seconds)

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Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress

Go Allowable Stress Multiplier = 1-((1-Ratio of Web to Flange Yield Strength)^2*(Ratio of Web to Flange Area*Distance Ratio of Flange to Depth)*(3-Distance Ratio of Flange to Depth+Distance Ratio of Flange to Depth*Ratio of Web to Flange Yield Strength))/(6+Ratio of Web to Flange Area*Distance Ratio of Flange to Depth*(3-Distance Ratio of Flange to Depth))

Section Modulus of Transformed Composite Section given Stress in Steel for Unshored Members

Go Section Modulus of Transformed Composite Section = Live Load Moment/(Tensile Steel Stress-(Dead Load Moment for Unshored Member/Section Modulus of Steel Beam))

Section Modulus of Steel Beam given Stress in Steel for Unshored Members

Go Section Modulus of Steel Beam = Dead Load Moment for Unshored Member/(Tensile Steel Stress-(Live Load Moment/Section Modulus of Transformed Composite Section))

Dead Load Moment given Stress in Steel for Unshored Members

Go Dead Load Moment for Unshored Member = Section Modulus of Steel Beam*(Tensile Steel Stress-(Live Load Moment/Section Modulus of Transformed Composite Section))

Stress in Steel for Unshored Members

Go Tensile Steel Stress = (Dead Load Moment for Unshored Member/Section Modulus of Steel Beam)+(Live Load Moment/Section Modulus of Transformed Composite Section)

Live Load Moment given Stress in Steel for Unshored Members

Go Live Load Moment = Section Modulus of Transformed Composite Section*(Tensile Steel Stress-Dead Load Moment for Unshored Member/Section Modulus of Steel Beam)

Section Modulus of Transformed Composite Section given Stress in Steel for Shored Members

Go Section Modulus of Transformed Composite Section = (Dead Load Moment for Shored Member+Live Load Moment)/Tensile Steel Stress

Dead Load Moment given Stress in Steel for Shored Members

Go Dead Load Moment for Shored Member = (Section Modulus of Transformed Composite Section*Tensile Steel Stress)-Live Load Moment

Stress in Steel for Shored Members

Go Tensile Steel Stress = (Dead Load Moment for Shored Member+Live Load Moment)/Section Modulus of Transformed Composite Section

Live Load Moment given Stress in Steel for Shored Members

Go Live Load Moment = Section Modulus of Transformed Composite Section*Tensile Steel Stress-Dead Load Moment for Shored Member

Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress Formula

What are Hybrid Bridge Girders?

These may have flanges with larger yield strength than the web and may be composite or non-composite with a concrete slab, or they may utilize an orthotropic-plate deck as the top flange. Computation of bending stresses and allowable stresses is generally the
same as that for girders with uniform yield strength.

How to Calculate Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress?

Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress calculator uses Allowable Stress Multiplier = 1-((1-Ratio of Web to Flange Yield Strength)^2*(Ratio of Web to Flange Area*Distance Ratio of Flange to Depth)*(3-Distance Ratio of Flange to Depth+Distance Ratio of Flange to Depth*Ratio of Web to Flange Yield Strength))/(6+Ratio of Web to Flange Area*Distance Ratio of Flange to Depth*(3-Distance Ratio of Flange to Depth)) to calculate the Allowable Stress Multiplier, The Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress is defined as a factor used for allowable stress. Allowable Stress Multiplier is denoted by R symbol.

How to calculate Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress using this online calculator? To use this online calculator for Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress, enter Ratio of Web to Flange Yield Strength (α), Ratio of Web to Flange Area (β) & Distance Ratio of Flange to Depth (ψ) and hit the calculate button. Here is how the Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress calculation can be explained with given input values -> 0.5 = 1-((1-1.5)^2*(3*2)*(3-2+2*1.5))/(6+3*2*(3-2)).

FAQ

What is Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress?

The Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress is defined as a factor used for allowable stress and is represented as R = 1-((1-α)^2*(β*ψ)*(3-ψ+ψ*α))/(6+β*ψ*(3-ψ)) or Allowable Stress Multiplier = 1-((1-Ratio of Web to Flange Yield Strength)^2*(Ratio of Web to Flange Area*Distance Ratio of Flange to Depth)*(3-Distance Ratio of Flange to Depth+Distance Ratio of Flange to Depth*Ratio of Web to Flange Yield Strength))/(6+Ratio of Web to Flange Area*Distance Ratio of Flange to Depth*(3-Distance Ratio of Flange to Depth)). Ratio of Web to Flange Yield Strength is a strength ratio, The Ratio of Web to Flange Area of the orthotropic-plate bridge is the ratio of web area to the area of tension flange or bottom flange of the orthotropic-plate bridge & Distance Ratio of Flange to Depth is the ratio of the distance from the outer edge of tension flange or bottom flange of the orthotropic deck to neutral axis divided by the depth of steel section.

How to calculate Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress?

The Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress is defined as a factor used for allowable stress is calculated using Allowable Stress Multiplier = 1-((1-Ratio of Web to Flange Yield Strength)^2*(Ratio of Web to Flange Area*Distance Ratio of Flange to Depth)*(3-Distance Ratio of Flange to Depth+Distance Ratio of Flange to Depth*Ratio of Web to Flange Yield Strength))/(6+Ratio of Web to Flange Area*Distance Ratio of Flange to Depth*(3-Distance Ratio of Flange to Depth)). To calculate Multiplier for Allowable Stress when Flange Bending Stress is lesser than Allowable Stress, you need Ratio of Web to Flange Yield Strength (α), Ratio of Web to Flange Area (β) & Distance Ratio of Flange to Depth (ψ). With our tool, you need to enter the respective value for Ratio of Web to Flange Yield Strength, Ratio of Web to Flange Area & Distance Ratio of Flange to Depth 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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