Q Factor Calculator

✖Effective Length Factor is the factor used for the members in the frame. It depends on the ratio of compression member stiffness to the end restraint stiffness.ⓘ Effective Length Factor [k]			+10% -10%
✖Length of Member between Supports influencing load and resistance factor design for bridge columns.ⓘ Length of Member between Supports [L_c]			+10% -10%
✖Radius of Gyration is used to compare how various structural shapes will behave under compression along an axis. It is used to predict buckling in a compression member or beam.ⓘ Radius of Gyration [r]			+10% -10%
✖Yield strength of steel is the level of stress that corresponds to the yield point.ⓘ Yield Strength of Steel [f_y]			+10% -10%
✖Modulus of Elasticity of a material is a measure of its stiffness.ⓘ Modulus of Elasticity [E_s]			+10% -10%

✖Factor Q is geometrical constant based on the material of the member.ⓘ Q Factor [Q_factor]

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Formula

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Q Factor

Formula

`"Q"_{"factor"} = (("k"*"L"_{"c"}/"r")^2)*("f"_{"y"}/(2*pi*pi*"E"_{"s"}))`

Example

`"0.014248"=(("0.5"*"450mm"/"15mm")^2)*("250MPa"/(2*pi*pi*"200000MPa"))`

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Q Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor Q = ((Effective Length Factor*Length of Member between Supports/Radius of Gyration)^2)*(Yield Strength of Steel/(2*pi*pi*Modulus of Elasticity))
Q_factor = ((k*L_c/r)^2)*(f_y/(2*pi*pi*E_s))
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Factor Q - Factor Q is geometrical constant based on the material of the member.
Effective Length Factor - Effective Length Factor is the factor used for the members in the frame. It depends on the ratio of compression member stiffness to the end restraint stiffness.
Length of Member between Supports - (Measured in Millimeter) - Length of Member between Supports influencing load and resistance factor design for bridge columns.
Radius of Gyration - (Measured in Millimeter) - Radius of Gyration is used to compare how various structural shapes will behave under compression along an axis. It is used to predict buckling in a compression member or beam.
Yield Strength of Steel - (Measured in Pascal) - Yield strength of steel is the level of stress that corresponds to the yield point.
Modulus of Elasticity - (Measured in Pascal) - Modulus of Elasticity of a material is a measure of its stiffness.

STEP 1: Convert Input(s) to Base Unit

Effective Length Factor: 0.5 --> No Conversion Required
Length of Member between Supports: 450 Millimeter --> 450 Millimeter No Conversion Required
Radius of Gyration: 15 Millimeter --> 15 Millimeter No Conversion Required
Yield Strength of Steel: 250 Megapascal --> 250000000 Pascal (Check conversion here)
Modulus of Elasticity: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_factor = ((k*L_c/r)^2)*(f_y/(2*pi*pi*E_s)) --> ((0.5*450/15)^2)*(250000000/(2*pi*pi*200000000000))

Evaluating ... ...

Q_factor = 0.0142482914497037

STEP 3: Convert Result to Output's Unit

0.0142482914497037 --> No Conversion Required

FINAL ANSWER

0.0142482914497037 ≈ 0.014248 <-- Factor Q

(Calculation completed in 00.005 seconds)

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Home » Engineering » Civil » Bridge and Suspension Cable » Load Factor Design (LFD) » Load and Resistance Factor for Bridge Columns » Q Factor

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Bhilai Institute of Technology (BIT), Raipur

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< 9 Load and Resistance Factor for Bridge Columns Calculators

Steel Yield Strength given Q Factor

Go Yield Strength of Steel = (2*Factor Q*pi*pi*(Radius of Gyration^2)*Modulus of Elasticity)/((Effective Length Factor*Length of Member between Supports)^2)

Q Factor

Go Factor Q = ((Effective Length Factor*Length of Member between Supports/Radius of Gyration)^2)*(Yield Strength of Steel/(2*pi*pi*Modulus of Elasticity))

Column Gross Effective Area given Maximum Strength

Go Gross Effective Area of Column = Strength of Column/(0.85*Buckling Stress)

Buckling Stress given Maximum Strength

Go Buckling Stress = Strength of Column/(0.85*Gross Effective Area of Column)

Maximum Strength for Compression Members

Go Strength of Column = 0.85*Gross Effective Area of Column*Buckling Stress

Steel Yield Strength given Buckling Stress for Q Factor Less than or Equal to 1

Go Yield Strength of Steel = Buckling Stress/(1-(Factor Q/2))

Buckling Stress for Q Factor Less than or Equal to 1

Go Buckling Stress = (1-(Factor Q/2))*Yield Strength of Steel

Buckling Stress when Q Factor is Greater than 1

Go Buckling Stress = Yield Strength of Steel/(2*Q Factors)

Steel Yield Strength given Buckling Stress for Q Factor Greater than 1

Go Yield Strength of Steel = Buckling Stress*2*Q Factors

Q Factor Formula

Factor Q = ((Effective Length Factor*Length of Member between Supports/Radius of Gyration)^2)*(Yield Strength of Steel/(2*pi*pi*Modulus of Elasticity))
Q_factor = ((k*L_c/r)^2)*(f_y/(2*pi*pi*E_s))

What is Q Factor?

Q Factor is a unitless quantity depending upon the yield strength and elastic modulus of material, along with the slenderness ratio of the column.

How to Calculate Q Factor?

Q Factor calculator uses Factor Q = ((Effective Length Factor*Length of Member between Supports/Radius of Gyration)^2)*(Yield Strength of Steel/(2*pi*pi*Modulus of Elasticity)) to calculate the Factor Q, The Q Factor formula is defined as geometrical constant depending upon material of member along with slenderness ratio. Factor Q is denoted by Q_factor symbol.

How to calculate Q Factor using this online calculator? To use this online calculator for Q Factor, enter Effective Length Factor (k), Length of Member between Supports (L_c), Radius of Gyration (r), Yield Strength of Steel (f_y) & Modulus of Elasticity (E_s) and hit the calculate button. Here is how the Q Factor calculation can be explained with given input values -> 0.014248 = ((0.5*0.45/0.015)^2)*(250000000/(2*pi*pi*200000000000)).

FAQ

What is Q Factor?

The Q Factor formula is defined as geometrical constant depending upon material of member along with slenderness ratio and is represented as Q_factor = ((k*L_c/r)^2)*(f_y/(2*pi*pi*E_s)) or Factor Q = ((Effective Length Factor*Length of Member between Supports/Radius of Gyration)^2)*(Yield Strength of Steel/(2*pi*pi*Modulus of Elasticity)). Effective Length Factor is the factor used for the members in the frame. It depends on the ratio of compression member stiffness to the end restraint stiffness, Length of Member between Supports influencing load and resistance factor design for bridge columns, Radius of Gyration is used to compare how various structural shapes will behave under compression along an axis. It is used to predict buckling in a compression member or beam, Yield strength of steel is the level of stress that corresponds to the yield point & Modulus of Elasticity of a material is a measure of its stiffness.

How to calculate Q Factor?

The Q Factor formula is defined as geometrical constant depending upon material of member along with slenderness ratio is calculated using Factor Q = ((Effective Length Factor*Length of Member between Supports/Radius of Gyration)^2)*(Yield Strength of Steel/(2*pi*pi*Modulus of Elasticity)). To calculate Q Factor, you need Effective Length Factor (k), Length of Member between Supports (L_c), Radius of Gyration (r), Yield Strength of Steel (f_y) & Modulus of Elasticity (E_s). With our tool, you need to enter the respective value for Effective Length Factor, Length of Member between Supports, Radius of Gyration, Yield Strength of Steel & Modulus of Elasticity 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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