Factor for Multiplying Stresses and Deflections under Existing Loads Calculator

✖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.ⓘ Weight on Roof [W]			+10% -10%
✖Beam span is the effective span of the beam.ⓘ Beam Span [l]			+10% -10%
✖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.ⓘ Modulus of Elasticity [E]			+10% -10%
✖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.ⓘ Moment of Inertia [I]			+10% -10%

✖Multiplying Factor is the factor used for multiplying stresses and deflections under existing loads to determine stresses and deflections under existing loads plus ponding.ⓘ Factor for Multiplying Stresses and Deflections under Existing Loads [C_p]

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Factor for Multiplying Stresses and Deflections under Existing Loads

Formula

`"C"_{"p"} = 1/(1-(("W"*"l"^3)/(pi^4*"E"*"I")))`

Example

`"1.51235"=1/(1-(("55N"*("3000mm")^3)/(pi^4*"50MPa"*"900000mm⁴")))`

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Factor for Multiplying Stresses and Deflections under Existing Loads Solution

STEP 0: Pre-Calculation Summary

Formula Used

Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia)))
C_p = 1/(1-((W*l^3)/(pi^4*E*I)))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Weight on Roof - (Measured in Newton) - 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.
Beam Span - (Measured in Meter) - Beam span is the effective span of the beam.
Modulus of Elasticity - (Measured in Pascal) - 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.
Moment of Inertia - (Measured in Meter⁴) - 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.

STEP 1: Convert Input(s) to Base Unit

Weight on Roof: 55 Newton --> 55 Newton No Conversion Required
Beam Span: 3000 Millimeter --> 3 Meter (Check conversion here)
Modulus of Elasticity: 50 Megapascal --> 50000000 Pascal (Check conversion here)
Moment of Inertia: 900000 Millimeter⁴ --> 9E-07 Meter⁴ (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_p = 1/(1-((W*l^3)/(pi^4*E*I))) --> 1/(1-((55*3^3)/(pi^4*50000000*9E-07)))

Evaluating ... ...

C_p = 1.51235003429219

STEP 3: Convert Result to Output's Unit

1.51235003429219 --> No Conversion Required

FINAL ANSWER

1.51235003429219 ≈ 1.51235 <-- Multiplying Factor

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Timber Engineering » Laboratory Recommendations, Roof Slope and Oblique Plane » Roof Slope to Prevent Ponding » Factor for Multiplying Stresses and Deflections under Existing Loads

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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Factor for Multiplying Stresses and Deflections under Existing Loads

Go Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia)))

Factor for Multiplying Stresses and Deflections under Existing Loads Formula

Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia)))
C_p = 1/(1-((W*l^3)/(pi^4*E*I)))

What is Roof Load?

All buildings must be constructed so that the beams, walls, and anything else structural are up to bearing the weight of the roof and anything on it. Dead load is the weight of the roof itself and other loads acting on the roof are wind loads, snow loads, earthquake loads, Special loads.

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

Factor for Multiplying Stresses and Deflections under Existing Loads calculator uses Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia))) to calculate 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 calculate Factor for Multiplying Stresses and Deflections under Existing Loads using this online calculator? To use this online calculator 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. Here is how the Factor for Multiplying Stresses and Deflections under Existing Loads calculation can be explained with given input values -> 1.51235 = 1/(1-((55*3^3)/(pi^4*50000000*9E-07))).

FAQ

What is Factor for Multiplying Stresses and Deflections under Existing Loads?

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 and is represented as C_p = 1/(1-((W*l^3)/(pi^4*E*I))) or Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia))). 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, Beam span is the effective span of the beam, 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 & 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.

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

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 is calculated using Multiplying Factor = 1/(1-((Weight on Roof*Beam Span^3)/(pi^4*Modulus of Elasticity*Moment of Inertia))). To calculate Factor for Multiplying Stresses and Deflections under Existing Loads, you need Weight on Roof (W), Beam Span (l), Modulus of Elasticity (E) & Moment of Inertia (I). With our tool, you need to enter the respective value for Weight on Roof, Beam Span, Modulus of Elasticity & Moment of Inertia and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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