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Allowable Unit Load for Bridges using Structural Carbon Steel Formula

GoAllowable Load for Bridges using Structural Carbon Steel Formula

GoAllowable Load for Bridges using Structural Carbon Steel when Column Ends are Pinned Formula

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The allowable load is the load which induces the maximum permissible unit stress at a critical section of a structural member. Check FAQs

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

Q - Allowable Load?S_y - Yield Point of Material?f_s - Factor of Safety for Bridge Column?L|r - Critical Slenderness Ratio?P - Total Allowable Load for Bridges?ε - Modulus of Elasticity of Material?A - Section Area of Column?

Allowable Unit Load for Bridges using Structural Carbon Steel Example

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

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

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

592.0573 = \frac{\frac{32000}{3}}{1 + (0.25 \cdot \sec (0.375 \cdot 140) \cdot \sqrt{\frac{3 \cdot 10.5}{2.9E+7 \cdot 81}})} \cdot 81

592.0573lbs = \frac{\frac{32000lbf/in²}{3}}{1 + (0.25 \cdot \sec (0.375 \cdot 140) \cdot \sqrt{\frac{3 \cdot 10.5kN}{2.9E+7lbf/in² \cdot 81in²}})} \cdot 81in²

592.0573 = \frac{\frac{32000}{3}}{1 + (0.25 \cdot \sec (0.375 \cdot 140) \cdot \sqrt{\frac{3 \cdot 10.5}{2.9E+7 \cdot 81}})} \cdot 81

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Allowable Unit Load for Bridges using Structural Carbon Steel Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Q = \frac{\frac{32000lbf/in²}{3}}{1 + (0.25 \cdot \sec (0.375 \cdot 140) \cdot \sqrt{\frac{3 \cdot 10.5kN}{2.9E+7lbf/in² \cdot 81in²}})} \cdot 81in²

Next Step Convert Units

∴

Q = \frac{\frac{32000lbf/in²}{3}}{1 + (0.25 \cdot \sec (0.375 \cdot 140) \cdot \sqrt{\frac{3 \cdot 10500N}{2.9E+7lbf/in² \cdot 0.0523m²}})} \cdot 0.0523m²

Next Step Prepare to Evaluate

∴

Q = \frac{\frac{32000}{3}}{1 + (0.25 \cdot \sec (0.375 \cdot 140) \cdot \sqrt{\frac{3 \cdot 10500}{2.9E+7 \cdot 0.0523}})} \cdot 0.0523

Next Step Evaluate

∴

Q = 268.552677622674kg

Next Step Convert to Output's Unit

∴

Q = 592.057308231909lbs

LAST Step Rounding Answer

∴

Q = 592.0573lbs

Allowable Unit Load for Bridges using Structural Carbon Steel Formula Elements

Variables

Functions

Allowable Load

The allowable load is the load which induces the maximum permissible unit stress at a critical section of a structural member.

Symbol: Q

Measurement: WeightUnit: lbs

Note: Value can be positive or negative.

Formulas to find Allowable 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

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.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety for Bridge Column

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.

Symbol: L|r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Critical Slenderness Ratio

Total Allowable Load for Bridges

Total allowable load for bridges is the capacity or can say the maximum load allowed.

Symbol: P

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Total Allowable Load for Bridges

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 Allowable Load

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

Other formulas in Additional Bridge Column Formulas category

Go Ultimate Unit Load for Bridges using Structural Carbon Steel

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

Go Ultimate Load for Bridges using Structural Carbon Steel

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

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

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

FAQs on Allowable Unit Load for Bridges using Structural Carbon Steel

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

The formula of Allowable Unit Load for Bridges using Structural Carbon Steel is expressed as 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. Here is an example- 1305.263 = (220632233.379338/3)/(1+(0.25*sec(0.375*140)*sqrt((3*10500)/(199947961500.025*0.0522579600004181))))*0.0522579600004181.

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

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

What are the other ways to Calculate Allowable Load?

Here are the different ways to Calculate Allowable Load-

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

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

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

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

Allowable 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 Allowable Unit Load for Bridges using Structural Carbon Steel can be measured.

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Allowable Unit Load for Bridges using Structural Carbon Steel Formula

​GoAllowable Load for Bridges using Structural Carbon Steel Formula

​GoAllowable Load for Bridges using Structural Carbon Steel when Column Ends are Pinned Formula

Allowable Unit Load for Bridges using Structural Carbon Steel Example

Allowable Unit Load for Bridges using Structural Carbon Steel Solution

Allowable Unit Load for Bridges using Structural Carbon Steel Formula Elements

Other Formulas to find Allowable Load

Other formulas in Additional Bridge Column Formulas category

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

FAQs on Allowable Unit Load for Bridges using Structural Carbon Steel

Variable Name

GoAllowable Load for Bridges using Structural Carbon Steel Formula

GoAllowable Load for Bridges using Structural Carbon Steel when Column Ends are Pinned Formula