Allowable Unit Load for Bridges using Structural Carbon Steel Calculator

✖The yield point of material is a point on the stress–strain curve beyond which the material enters the phase of nonlinear pattern and irrecoverable strain or permanent (plastic) tensile deformation.ⓘ Yield Point of Material [S_y]			+10% -10%
✖Factor of Safety for bridge column expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety for Bridge Column [f_s]			+10% -10%
✖The critical slenderness ratio is the ratio of the column length in meters, millimeters, and inches to the least radius of gyration in meters, millimeters and inches. The value ranges from 120-160.ⓘ Critical Slenderness Ratio [L\|r]			+10% -10%
✖Total allowable load for bridges is the capacity or can say the maximum load allowed.ⓘ Total Allowable Load for Bridges [P]			+10% -10%
✖The modulus of elasticity of material is the slope of its stress–strain curve in the elastic deformation region. It is the measure of the stiffness of a material.ⓘ Modulus of Elasticity of Material [ε]			+10% -10%
✖The section area of column is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.ⓘ Section Area of Column [A]			+10% -10%

✖The allowable load is the load which induces the maximum permissible unit stress at a critical section of a structural member.ⓘ Allowable Unit Load for Bridges using Structural Carbon Steel [Q]

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Allowable Unit Load for Bridges using Structural Carbon Steel Solution

STEP 0: Pre-Calculation Summary

Formula Used

Allowable Load = (Yield Point of Material/Factor of Safety for Bridge Column)/(1+(0.25*sec(0.375*Critical Slenderness Ratio)*sqrt((Factor of Safety for Bridge Column*Total Allowable Load for Bridges)/(Modulus of Elasticity of Material*Section Area of Column))))*Section Area of Column
Q = (S_y/f_s)/(1+(0.25*sec(0.375*L|r)*sqrt((f_s*P)/(ε*A))))*A
This formula uses 2 Functions, 7 Variables

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Allowable Load - (Measured in Pound) - The allowable load is the load which induces the maximum permissible unit stress at a critical section of a structural member.
Yield Point of Material - (Measured in Pound-Force per Square Inch) - The yield point of material is a point on the stress–strain curve beyond which the material enters the phase of nonlinear pattern and irrecoverable strain or permanent (plastic) tensile deformation.
Factor of Safety for Bridge Column - Factor of Safety for bridge column expresses how much stronger a system is than it needs to be for an intended load.
Critical Slenderness Ratio - The critical slenderness ratio is the ratio of the column length in meters, millimeters, and inches to the least radius of gyration in meters, millimeters and inches. The value ranges from 120-160.
Total Allowable Load for Bridges - (Measured in Newton) - Total allowable load for bridges is the capacity or can say the maximum load allowed.
Modulus of Elasticity of Material - (Measured in Pound-Force per Square Inch) - The modulus of elasticity of material is the slope of its stress–strain curve in the elastic deformation region. It is the measure of the stiffness of a material.
Section Area of Column - (Measured in Square Meter) - The section area of column is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.

STEP 1: Convert Input(s) to Base Unit

Yield Point of Material: 32000 Pound-Force per Square Inch --> 32000 Pound-Force per Square Inch No Conversion Required
Factor of Safety for Bridge Column: 3 --> No Conversion Required
Critical Slenderness Ratio: 140 --> No Conversion Required
Total Allowable Load for Bridges: 10.5 Kilonewton --> 10500 Newton (Check conversion here)
Modulus of Elasticity of Material: 29000000 Pound-Force per Square Inch --> 29000000 Pound-Force per Square Inch No Conversion Required
Section Area of Column: 81 Square Inch --> 0.0522579600004181 Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = (S_y/f_s)/(1+(0.25*sec(0.375*L|r)*sqrt((f_s*P)/(ε*A))))*A --> (32000/3)/(1+(0.25*sec(0.375*140)*sqrt((3*10500)/(29000000*0.0522579600004181))))*0.0522579600004181

Evaluating ... ...

Q = 592.057308231909

STEP 3: Convert Result to Output's Unit

268.552677622674 Kilogram -->592.057308231909 Pound (Check conversion here)

FINAL ANSWER

592.057308231909 ≈ 592.0573 Pound <-- Allowable Load

(Calculation completed in 00.004 seconds)

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< Additional Bridge Column Formulas Calculators

Allowable Unit Load for Bridges using Structural Carbon Steel

LaTeX Go Allowable Load = (Yield Point of Material/Factor of Safety for Bridge Column)/(1+(0.25*sec(0.375*Critical Slenderness Ratio)*sqrt((Factor of Safety for Bridge Column*Total Allowable Load for Bridges)/(Modulus of Elasticity of Material*Section Area of Column))))*Section Area of Column

Ultimate Unit Load for Bridges using Structural Carbon Steel

LaTeX Go Ultimate Load = (Yield Point of Material/(1+0.25*sec(0.375*Column Length*sqrt(Ultimate Crushing Load for Columns/(Modulus of Elasticity of Material*Section Area of Column)))))*Section Area of Column

Allowable Load for Bridges using Structural Carbon Steel

LaTeX Go Allowable Load = (15000-(1/4)*Critical Slenderness Ratio^2)*Section Area of Column

Ultimate Load for Bridges using Structural Carbon Steel

LaTeX Go Ultimate Load = (26500-0.425*Critical Slenderness Ratio^2)*Section Area of Column

Allowable Unit Load for Bridges using Structural Carbon Steel Formula

LaTeX Go

What is Allowable Load?

The allowable load is based on the application of a safety factor to the mean result of laboratory testing to failure (ultimate load), regardless of the controlling failure mode observed in the tests.

Define Carbon Steel

Carbon steel is a steel with carbon content from about 0.05-2.1% by weight. The American Iron and Steel Institute (AISI) states:
- no minimum content is specified or required for chromium, cobalt, molybdenum, nickel, niobium, titanium, tungsten, vanadium, zirconium, or any other element to be added to obtain a desired alloying effect,
- the specified minimum for copper does not exceed 0.40%,
- or the maximum content specified for any of the following elements does not exceed the percentages noted: manganese 1.65%, silicon 0.60%; copper 0.60%

How to Calculate Allowable Unit Load for Bridges using Structural Carbon Steel?

Allowable Unit Load for Bridges using Structural Carbon Steel calculator uses Allowable Load = (Yield Point of Material/Factor of Safety for Bridge Column)/(1+(0.25*sec(0.375*Critical Slenderness Ratio)*sqrt((Factor of Safety for Bridge Column*Total Allowable Load for Bridges)/(Modulus of Elasticity of Material*Section Area of Column))))*Section Area of Column to calculate the Allowable Load, The Allowable Unit Load for Bridges using Structural Carbon Steel formula is defined as the load that induces the maximum permissible unit stress at a critical section of a structural member when the factor of safety and modulus of elasticity are predetermined. Allowable Load is denoted by Q symbol.

How to calculate Allowable Unit Load for Bridges using Structural Carbon Steel using this online calculator? To use this online calculator for Allowable Unit Load for Bridges using Structural Carbon Steel, enter Yield Point of Material (S_y), Factor of Safety for Bridge Column (f_s), Critical Slenderness Ratio (L|r), Total Allowable Load for Bridges (P), Modulus of Elasticity of Material (ε) & Section Area of Column (A) and hit the calculate button. Here is how the Allowable Unit Load for Bridges using Structural Carbon Steel calculation can be explained with given input values -> 1305.263 = (220632233.379338/3)/(1+(0.25*sec(0.375*140)*sqrt((3*10500)/(199947961500.025*0.0522579600004181))))*0.0522579600004181.

FAQ

What is Allowable Unit Load for Bridges using Structural Carbon Steel?

The Allowable Unit Load for Bridges using Structural Carbon Steel formula is defined as the load that induces the maximum permissible unit stress at a critical section of a structural member when the factor of safety and modulus of elasticity are predetermined and is represented as Q = (S_y/f_s)/(1+(0.25*sec(0.375*L|r)*sqrt((f_s*P)/(ε*A))))*A or Allowable Load = (Yield Point of Material/Factor of Safety for Bridge Column)/(1+(0.25*sec(0.375*Critical Slenderness Ratio)*sqrt((Factor of Safety for Bridge Column*Total Allowable Load for Bridges)/(Modulus of Elasticity of Material*Section Area of Column))))*Section Area of Column. The yield point of material is a point on the stress–strain curve beyond which the material enters the phase of nonlinear pattern and irrecoverable strain or permanent (plastic) tensile deformation, Factor of Safety for bridge column expresses how much stronger a system is than it needs to be for an intended load, The critical slenderness ratio is the ratio of the column length in meters, millimeters, and inches to the least radius of gyration in meters, millimeters and inches. The value ranges from 120-160, Total allowable load for bridges is the capacity or can say the maximum load allowed, The modulus of elasticity of material is the slope of its stress–strain curve in the elastic deformation region. It is the measure of the stiffness of a material & The section area of column is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.

How to calculate Allowable Unit Load for Bridges using Structural Carbon Steel?

The Allowable Unit Load for Bridges using Structural Carbon Steel formula is defined as the load that induces the maximum permissible unit stress at a critical section of a structural member when the factor of safety and modulus of elasticity are predetermined is calculated using Allowable Load = (Yield Point of Material/Factor of Safety for Bridge Column)/(1+(0.25*sec(0.375*Critical Slenderness Ratio)*sqrt((Factor of Safety for Bridge Column*Total Allowable Load for Bridges)/(Modulus of Elasticity of Material*Section Area of Column))))*Section Area of Column. To calculate Allowable Unit Load for Bridges using Structural Carbon Steel, you need Yield Point of Material (S_y), Factor of Safety for Bridge Column (f_s), Critical Slenderness Ratio (L|r), Total Allowable Load for Bridges (P), Modulus of Elasticity of Material (ε) & Section Area of Column (A). With our tool, you need to enter the respective value for Yield Point of Material, Factor of Safety for Bridge Column, Critical Slenderness Ratio, Total Allowable Load for Bridges, Modulus of Elasticity of Material & Section Area of Column and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Allowable Load?

In this formula, Allowable Load uses Yield Point of Material, Factor of Safety for Bridge Column, Critical Slenderness Ratio, Total Allowable Load for Bridges, Modulus of Elasticity of Material & Section Area of Column. We can use 2 other way(s) to calculate the same, which is/are as follows -

Allowable Load = (15000-(1/4)*Critical Slenderness Ratio^2)*Section Area of Column
Allowable Load = (15000-(1/3)*Critical Slenderness Ratio^2)*Section Area of Column

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