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Ultimate Unit Load for Bridges using Structural Carbon Steel Formula

GoUltimate Load for Bridges using Structural Carbon Steel Formula

GoUltimate Load for Bridges using Structural Carbon Steel when Columns are Pinned Formula

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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. Check FAQs

P u = (\frac{S y}{1 + 0.25 \cdot \sec (0.375 \cdot l \cdot \sqrt{\frac{P cs}{ε \cdot A}})}) \cdot A

P_u - Ultimate Load?S_y - Yield Point of Material?l - Column Length?P_cs - Ultimate Crushing Load for Columns?ε - Modulus of Elasticity of Material?A - Section Area of Column?

Ultimate Unit Load for Bridges using Structural Carbon Steel Example

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Here is how the Ultimate Unit Load for Bridges using Structural Carbon Steel equation looks like with Values.

Here is how the Ultimate Unit Load for Bridges using Structural Carbon Steel equation looks like with Units.

Here is how the Ultimate Unit Load for Bridges using Structural Carbon Steel equation looks like.

960.2793 = (\frac{32000}{1 + 0.25 \cdot \sec (0.375 \cdot 120 \cdot \sqrt{\frac{520}{2.9E+7 \cdot 81}})}) \cdot 81

960.2793lbs = (\frac{32000lbf/in²}{1 + 0.25 \cdot \sec (0.375 \cdot 120in \cdot \sqrt{\frac{520kN}{2.9E+7lbf/in² \cdot 81in²}})}) \cdot 81in²

960.2793 = (\frac{32000}{1 + 0.25 \cdot \sec (0.375 \cdot 120 \cdot \sqrt{\frac{520}{2.9E+7 \cdot 81}})}) \cdot 81

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Ultimate Unit Load for Bridges using Structural Carbon Steel Solution

Follow our step by step solution on how to calculate Ultimate Unit Load for Bridges using Structural Carbon Steel?

FIRST Step Consider the formula

P u = (\frac{S y}{1 + 0.25 \cdot \sec (0.375 \cdot l \cdot \sqrt{\frac{P cs}{ε \cdot A}})}) \cdot A

Next Step Substitute values of Variables

∴

P u = (\frac{32000lbf/in²}{1 + 0.25 \cdot \sec (0.375 \cdot 120in \cdot \sqrt{\frac{520kN}{2.9E+7lbf/in² \cdot 81in²}})}) \cdot 81in²

Next Step Convert Units

∴

P u = (\frac{32000lbf/in²}{1 + 0.25 \cdot \sec (0.375 \cdot 120in \cdot \sqrt{\frac{520000N}{2.9E+7lbf/in² \cdot 0.0523m²}})}) \cdot 0.0523m²

Next Step Prepare to Evaluate

∴

P u = (\frac{32000}{1 + 0.25 \cdot \sec (0.375 \cdot 120 \cdot \sqrt{\frac{520000}{2.9E+7 \cdot 0.0523}})}) \cdot 0.0523

Next Step Evaluate

∴

P u = 435.575366048289kg

Next Step Convert to Output's Unit

∴

P u = 960.279305488873lbs

LAST Step Rounding Answer

∴

P u = 960.2793lbs

Ultimate Unit Load for Bridges using Structural Carbon Steel Formula Elements

Variables

Functions

Ultimate Load

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.

Symbol: P_u

Measurement: WeightUnit: lbs

Note: Value can be positive or negative.

Formulas to find Ultimate Load

Yield Point of Material

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.

Symbol: S_y

Measurement: StressUnit: lbf/in²

Note: Value can be positive or negative.

Formulas to find Yield Point of Material

Column Length

Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l

Measurement: LengthUnit: in

Note: Value should be greater than 0.

Formulas to find Column Length

Ultimate Crushing Load for Columns

The Ultimate Crushing Load for Columns is the ultimate load that column can bear before failure.

Symbol: P_cs

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Ultimate Crushing Load for Columns

Modulus of Elasticity of Material

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.

Symbol: ε

Measurement: StressUnit: lbf/in²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Material

Section Area of Column

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.

Symbol: A

Measurement: AreaUnit: in²

Note: Value can be positive or negative.

Formulas to find Section Area of Column

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.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Ultimate Load

Go Ultimate Load for Bridges using Structural Carbon Steel

P u = (26500 - 0.425 \cdot {L|r}^{2}) \cdot A

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

P u = (25600 - 0.566 \cdot {L|r}^{2}) \cdot A

Other formulas in Additional Bridge Column Formulas category

Go Allowable Unit Load for Bridges using Structural Carbon Steel

Q = \frac{\frac{S y}{f s}}{1 + (0.25 \cdot \sec (0.375 \cdot L|r) \cdot \sqrt{\frac{f s \cdot P}{ε \cdot A}})} \cdot A

Go Allowable Load for Bridges using Structural Carbon Steel

Q = (15000 - (\frac{1}{4}) \cdot {L|r}^{2}) \cdot A

Go Allowable Load for Bridges using Structural Carbon Steel when Column Ends are Pinned

Q = (15000 - (\frac{1}{3}) \cdot {L|r}^{2}) \cdot A

How to Evaluate Ultimate Unit Load for Bridges using Structural Carbon Steel?

Ultimate Unit Load for Bridges using Structural Carbon Steel evaluator 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 evaluate 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 evaluate Ultimate Unit Load for Bridges using Structural Carbon Steel using this online evaluator? To use this online evaluator 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.

FAQs on Ultimate Unit Load for Bridges using Structural Carbon Steel

What is the formula to find Ultimate Unit Load for Bridges using Structural Carbon Steel?

The formula of Ultimate Unit Load for Bridges using Structural Carbon Steel is expressed as 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. Here is an example- 2117.053 = (220632233.379338/(1+0.25*sec(0.375*3.04800000001219*sqrt(520000/(199947961500.025*0.0522579600004181)))))*0.0522579600004181.

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

With 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) we can find Ultimate Unit Load for Bridges using Structural Carbon Steel using the formula - 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. This formula also uses Secant (sec), Square Root (sqrt) function(s).

What are the other ways to Calculate Ultimate Load?

Here are the different ways to Calculate Ultimate Load-

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

Can the Ultimate Unit Load for Bridges using Structural Carbon Steel be negative?

Yes, the Ultimate Unit Load for Bridges using Structural Carbon Steel, measured in Weight can be negative.

Which unit is used to measure Ultimate Unit Load for Bridges using Structural Carbon Steel?

Ultimate Unit Load for Bridges using Structural Carbon Steel is usually measured using the Pound[lbs] for Weight. Kilogram[lbs], Gram[lbs], Milligram[lbs] are the few other units in which Ultimate Unit Load for Bridges using Structural Carbon Steel can be measured.

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Ultimate Unit Load for Bridges using Structural Carbon Steel Formula

​GoUltimate Load for Bridges using Structural Carbon Steel Formula

​GoUltimate Load for Bridges using Structural Carbon Steel when Columns are Pinned Formula

Ultimate Unit Load for Bridges using Structural Carbon Steel Example

Ultimate Unit Load for Bridges using Structural Carbon Steel Solution

Ultimate Unit Load for Bridges using Structural Carbon Steel Formula Elements

Other Formulas to find Ultimate Load

Other formulas in Additional Bridge Column Formulas category

How to Evaluate Ultimate Unit Load for Bridges using Structural Carbon Steel?

FAQs on Ultimate Unit Load for Bridges using Structural Carbon Steel

Variable Name

GoUltimate Load for Bridges using Structural Carbon Steel Formula

GoUltimate Load for Bridges using Structural Carbon Steel when Columns are Pinned Formula