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Factor for Multiplying Stresses and Deflections under Existing Loads Formula

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Multiplying Factor is the factor used for multiplying stresses and deflections under existing loads to determine stresses and deflections under existing loads plus ponding. Check FAQs

C p = \frac{1}{1 - (\frac{W \cdot l^{3}}{π^{4} \cdot E \cdot I})}

C_p - Multiplying Factor?W - Weight on Roof?l - Beam Span?E - Modulus of Elasticity?I - Moment of Inertia?π - Archimedes' constant?

Factor for Multiplying Stresses and Deflections under Existing Loads Example

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Here is how the Factor for Multiplying Stresses and Deflections under Existing Loads equation looks like with Values.

Here is how the Factor for Multiplying Stresses and Deflections under Existing Loads equation looks like with Units.

Here is how the Factor for Multiplying Stresses and Deflections under Existing Loads equation looks like.

1.5124 = \frac{1}{1 - (\frac{55 \cdot 3000^{3}}{{3.1416}^{4} \cdot 50 \cdot 900000})}

1.5124 = \frac{1}{1 - (\frac{55N \cdot {3000mm}^{3}}{{3.1416}^{4} \cdot 50MPa \cdot 900000mm⁴})}

1.5124 = \frac{1}{1 - (\frac{55 \cdot 3000^{3}}{{3.1416}^{4} \cdot 50 \cdot 900000})}

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Factor for Multiplying Stresses and Deflections under Existing Loads Solution

Follow our step by step solution on how to calculate Factor for Multiplying Stresses and Deflections under Existing Loads?

FIRST Step Consider the formula

C p = \frac{1}{1 - (\frac{W \cdot l^{3}}{π^{4} \cdot E \cdot I})}

Next Step Substitute values of Variables

∴

C p = \frac{1}{1 - (\frac{55N \cdot {3000mm}^{3}}{π^{4} \cdot 50MPa \cdot 900000mm⁴})}

Next Step Substitute values of Constants

∴

C p = \frac{1}{1 - (\frac{55N \cdot {3000mm}^{3}}{{3.1416}^{4} \cdot 50MPa \cdot 900000mm⁴})}

Next Step Convert Units

∴

C p = \frac{1}{1 - (\frac{55N \cdot {3m}^{3}}{{3.1416}^{4} \cdot 5E+7Pa \cdot 9E-7m⁴})}

Next Step Prepare to Evaluate

∴

C p = \frac{1}{1 - (\frac{55 \cdot 3^{3}}{{3.1416}^{4} \cdot 5E+7 \cdot 9E-7})}

Next Step Evaluate

∴

C p = 1.51235003429219

LAST Step Rounding Answer

∴

C p = 1.5124

Factor for Multiplying Stresses and Deflections under Existing Loads Formula Elements

Variables

Constants

Multiplying Factor

Multiplying Factor is the factor used for multiplying stresses and deflections under existing loads to determine stresses and deflections under existing loads plus ponding.

Symbol: C_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Multiplying Factor

Weight on Roof

Weight on Roof is the weight used to find the multiplying factor which is considered as the weight of 1 in water (25.4 mm) on roof area supported by the beam.

Symbol: W

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Weight on Roof

Beam Span

Beam span is the effective span of the beam.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Beam Span

Modulus of Elasticity

The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.

Symbol: E

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Moment of Inertia

Moment of Inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or second moment of inertia.

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

How to Evaluate Factor for Multiplying Stresses and Deflections under Existing Loads?

Factor for Multiplying Stresses and Deflections under Existing Loads evaluator uses Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia))) to evaluate the Multiplying Factor, The Factor for Multiplying Stresses and Deflections under Existing Loads formula is defined as a multiplying factor for improvising or for magnifying the ponding, snow loads, or water trapped by gravel stops, parapet walls, or ice dams. Multiplying Factor is denoted by C_p symbol.

How to evaluate Factor for Multiplying Stresses and Deflections under Existing Loads using this online evaluator? To use this online evaluator for Factor for Multiplying Stresses and Deflections under Existing Loads, enter Weight on Roof (W), Beam Span (l), Modulus of Elasticity (E) & Moment of Inertia (I) and hit the calculate button.

FAQs on Factor for Multiplying Stresses and Deflections under Existing Loads

What is the formula to find Factor for Multiplying Stresses and Deflections under Existing Loads?

The formula of Factor for Multiplying Stresses and Deflections under Existing Loads is expressed as Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia))). Here is an example- 1.51235 = 1/(1-((55*3^3)/(pi^4*50000000*9E-07))).

How to calculate Factor for Multiplying Stresses and Deflections under Existing Loads?

With Weight on Roof (W), Beam Span (l), Modulus of Elasticity (E) & Moment of Inertia (I) we can find Factor for Multiplying Stresses and Deflections under Existing Loads using the formula - Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia))). This formula also uses Archimedes' constant .

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Factor for Multiplying Stresses and Deflections under Existing Loads Formula

Factor for Multiplying Stresses and Deflections under Existing Loads Example

Factor for Multiplying Stresses and Deflections under Existing Loads Solution

Factor for Multiplying Stresses and Deflections under Existing Loads Formula Elements

How to Evaluate Factor for Multiplying Stresses and Deflections under Existing Loads?

FAQs on Factor for Multiplying Stresses and Deflections under Existing Loads

Variable Name