Ultimate 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%
✖Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.ⓘ Column Length [l]			+10% -10%
✖The Ultimate Crushing Load for Columns is the ultimate load that column can bear before failure.ⓘ Ultimate Crushing Load for Columns [P_cs]			+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 ultimate load is the absolute maximum magnitude of load that a component or system can sustain, limited only by failure. It is the limit Load multiplied by a prescribed Safety Factor of 1.5.ⓘ Ultimate Unit Load for Bridges using Structural Carbon Steel [P_u]

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Formula

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Ultimate Unit Load for Bridges using Structural Carbon Steel

Formula

`"P"_{"u"} = ("S"_{"y"}/(1+0.25*sec(0.375*"l"*sqrt("P"_{"cs"}/("ε"*"A")))))*"A"`

Example

`"960.2793lbs"=("32000lbf/in²"/(1+0.25*sec(0.375*"120in"*sqrt("520kN"/("29000000lbf/in²"*"81in²")))))*"81in²"`

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Ultimate Unit Load for Bridges using Structural Carbon Steel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
P_u = (S_y/(1+0.25*sec(0.375*l*sqrt(P_cs/(ε*A)))))*A
This formula uses 2 Functions, 6 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

Ultimate Load - (Measured in Pound) - The ultimate load is the absolute maximum magnitude of load that a component or system can sustain, limited only by failure. It is the limit Load multiplied by a prescribed Safety Factor of 1.5.
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.
Column Length - (Measured in Inch) - Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
Ultimate Crushing Load for Columns - (Measured in Newton) - The Ultimate Crushing Load for Columns is the ultimate load that column can bear before failure.
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
Column Length: 120 Inch --> 120 Inch No Conversion Required
Ultimate Crushing Load for Columns: 520 Kilonewton --> 520000 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

P_u = (S_y/(1+0.25*sec(0.375*l*sqrt(P_cs/(ε*A)))))*A --> (32000/(1+0.25*sec(0.375*120*sqrt(520000/(29000000*0.0522579600004181)))))*0.0522579600004181

Evaluating ... ...

P_u = 960.279305488873

STEP 3: Convert Result to Output's Unit

435.575366048289 Kilogram -->960.279305488873 Pound (Check conversion here)

FINAL ANSWER

960.279305488873 ≈ 960.2793 Pound <-- Ultimate Load

(Calculation completed in 00.009 seconds)

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Home » Engineering » Civil » Bridge and Suspension Cable » Load, Stress and Fasteners » Additional Bridge Column Formulas » Ultimate Unit Load for Bridges using Structural Carbon Steel

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< 6 Additional Bridge Column Formulas Calculators

Allowable Unit Load for Bridges using Structural Carbon Steel

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

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 when Column Ends are Pinned

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

Allowable Load for Bridges using Structural Carbon Steel

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

Ultimate Load for Bridges using Structural Carbon Steel when Columns are Pinned

Go Ultimate Load = (25600-0.566*Critical Slenderness Ratio^2)*Section Area of Column

Ultimate Load for Bridges using Structural Carbon Steel

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

Ultimate Unit Load for Bridges using Structural Carbon Steel Formula

What is Ultimate Load?

It the maximum load up which when the load is reached to ultimate load the plastic strain will be developed in material. After ultimate load material can not be able to take the extra load. If the load is developed in material after ultimate load the material will fail.

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 Ultimate Unit Load for Bridges using Structural Carbon Steel?

Ultimate Unit Load for Bridges using Structural Carbon Steel calculator uses 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 to calculate the Ultimate Load, The Ultimate Unit Load for Bridges using Structural Carbon Steel formula is defined as the maximum magnitude of load a component or system can sustain, limited only by failure when the factor of safety and modulus of elasticity are predetermined. Ultimate Load is denoted by P_u symbol.

How to calculate Ultimate Unit Load for Bridges using Structural Carbon Steel using this online calculator? To use this online calculator for Ultimate Unit Load for Bridges using Structural Carbon Steel, enter Yield Point of Material (S_y), Column Length (l), Ultimate Crushing Load for Columns (P_cs), Modulus of Elasticity of Material (ε) & Section Area of Column (A) and hit the calculate button. Here is how the Ultimate Unit Load for Bridges using Structural Carbon Steel calculation can be explained with given input values -> 2117.053 = (220632233.379338/(1+0.25*sec(0.375*3.04800000001219*sqrt(520000/(199947961500.025*0.0522579600004181)))))*0.0522579600004181.

FAQ

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

The Ultimate Unit Load for Bridges using Structural Carbon Steel formula is defined as the maximum magnitude of load a component or system can sustain, limited only by failure when the factor of safety and modulus of elasticity are predetermined and is represented as P_u = (S_y/(1+0.25*sec(0.375*l*sqrt(P_cs/(ε*A)))))*A or 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. 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, Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions, The Ultimate Crushing Load for Columns is the ultimate load that column can bear before failure, 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 Ultimate Unit Load for Bridges using Structural Carbon Steel?

The Ultimate Unit Load for Bridges using Structural Carbon Steel formula is defined as the maximum magnitude of load a component or system can sustain, limited only by failure when the factor of safety and modulus of elasticity are predetermined is calculated using 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. To calculate Ultimate Unit Load for Bridges using Structural Carbon Steel, you need Yield Point of Material (S_y), Column Length (l), Ultimate Crushing Load for Columns (P_cs), 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, Column Length, Ultimate Crushing Load for Columns, 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 Ultimate Load?

In this formula, Ultimate Load uses Yield Point of Material, Column Length, Ultimate Crushing Load for Columns, 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 -

Ultimate Load = (26500-0.425*Critical Slenderness Ratio^2)*Section Area of Column
Ultimate Load = (25600-0.566*Critical Slenderness Ratio^2)*Section Area of Column

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