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Static Deflection at Distance x from End A given Length of Shaft Formula

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Static deflection at distance x from end A is the maximum displacement of a vibrating beam at a specific point from the fixed end. Check FAQs

y = (\frac{w}{24 \cdot E \cdot I shaft}) \cdot (x^{4} + {(L shaft \cdot x)}^{2} - 2 \cdot L shaft \cdot x^{3})

y - Static deflection at distance x from end A?w - Load per unit length?E - Young's Modulus?I_shaft - Moment of inertia of shaft?x - Distance of Small Section of Shaft from End A?L_shaft - Length of Shaft?

Static Deflection at Distance x from End A given Length of Shaft Example

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Here is how the Static Deflection at Distance x from End A given Length of Shaft equation looks like with Values.

Here is how the Static Deflection at Distance x from End A given Length of Shaft equation looks like with Units.

Here is how the Static Deflection at Distance x from End A given Length of Shaft equation looks like.

0.4318 = (\frac{3}{24 \cdot 15 \cdot 1.0855}) \cdot (5^{4} + {(3.5 \cdot 5)}^{2} - 2 \cdot 3.5 \cdot 5^{3})

0.4318m = (\frac{3}{24 \cdot 15N/m \cdot 1.0855kg·m²}) \cdot ({5m}^{4} + {(3.5m \cdot 5m)}^{2} - 2 \cdot 3.5m \cdot {5m}^{3})

0.4318 = (\frac{3}{24 \cdot 15 \cdot 1.0855}) \cdot (5^{4} + {(3.5 \cdot 5)}^{2} - 2 \cdot 3.5 \cdot 5^{3})

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Static Deflection at Distance x from End A given Length of Shaft Solution

Follow our step by step solution on how to calculate Static Deflection at Distance x from End A given Length of Shaft?

FIRST Step Consider the formula

y = (\frac{w}{24 \cdot E \cdot I shaft}) \cdot (x^{4} + {(L shaft \cdot x)}^{2} - 2 \cdot L shaft \cdot x^{3})

Next Step Substitute values of Variables

∴

y = (\frac{3}{24 \cdot 15N/m \cdot 1.0855kg·m²}) \cdot ({5m}^{4} + {(3.5m \cdot 5m)}^{2} - 2 \cdot 3.5m \cdot {5m}^{3})

Next Step Prepare to Evaluate

∴

y = (\frac{3}{24 \cdot 15 \cdot 1.0855}) \cdot (5^{4} + {(3.5 \cdot 5)}^{2} - 2 \cdot 3.5 \cdot 5^{3})

Next Step Evaluate

∴

y = 0.431819898629415m

LAST Step Rounding Answer

∴

y = 0.4318m

Static Deflection at Distance x from End A given Length of Shaft Formula Elements

Variables

Static deflection at distance x from end A

Static deflection at distance x from end A is the maximum displacement of a vibrating beam at a specific point from the fixed end.

Symbol: y

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Static deflection at distance x from end A

Load per unit length

Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit length

Young's Modulus

Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Moment of inertia of shaft

Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.

Symbol: I_shaft

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of inertia of shaft

Distance of Small Section of Shaft from End A

Distance of small section of shaft from end A is the length of a small section of shaft measured from end A in free transverse vibrations.

Symbol: x

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance of Small Section of Shaft from End A

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

Go Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

ω n = \frac{2 \cdot π \cdot 0.571}{\sqrt{δ}}

Go Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

δ = {(\frac{0.571}{f})}^{2}

Go Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

f = \frac{0.571}{\sqrt{δ}}

Go M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

I shaft = \frac{w \cdot {L shaft}^{4}}{384 \cdot E \cdot δ}

How to Evaluate Static Deflection at Distance x from End A given Length of Shaft?

Static Deflection at Distance x from End A given Length of Shaft evaluator uses Static deflection at distance x from end A = (Load per unit length/(24*Young's Modulus*Moment of inertia of shaft))*(Distance of Small Section of Shaft from End A^4+(Length of Shaft*Distance of Small Section of Shaft from End A)^2-2*Length of Shaft*Distance of Small Section of Shaft from End A^3) to evaluate the Static deflection at distance x from end A, Static Deflection at Distance x from End A given Length of Shaft formula is defined as a measure of the bending or displacement of a shaft at a specific point due to an applied load, providing insight into the shaft's structural integrity and potential for vibration or failure. Static deflection at distance x from end A is denoted by y symbol.

How to evaluate Static Deflection at Distance x from End A given Length of Shaft using this online evaluator? To use this online evaluator for Static Deflection at Distance x from End A given Length of Shaft, enter Load per unit length (w), Young's Modulus (E), Moment of inertia of shaft (I_shaft), Distance of Small Section of Shaft from End A (x) & Length of Shaft (L_shaft) and hit the calculate button.

FAQs on Static Deflection at Distance x from End A given Length of Shaft

What is the formula to find Static Deflection at Distance x from End A given Length of Shaft?

The formula of Static Deflection at Distance x from End A given Length of Shaft is expressed as Static deflection at distance x from end A = (Load per unit length/(24*Young's Modulus*Moment of inertia of shaft))*(Distance of Small Section of Shaft from End A^4+(Length of Shaft*Distance of Small Section of Shaft from End A)^2-2*Length of Shaft*Distance of Small Section of Shaft from End A^3). Here is an example- 0.43182 = (3/(24*15*1.085522))*(5^4+(3.5*5)^2-2*3.5*5^3).

How to calculate Static Deflection at Distance x from End A given Length of Shaft?

With Load per unit length (w), Young's Modulus (E), Moment of inertia of shaft (I_shaft), Distance of Small Section of Shaft from End A (x) & Length of Shaft (L_shaft) we can find Static Deflection at Distance x from End A given Length of Shaft using the formula - Static deflection at distance x from end A = (Load per unit length/(24*Young's Modulus*Moment of inertia of shaft))*(Distance of Small Section of Shaft from End A^4+(Length of Shaft*Distance of Small Section of Shaft from End A)^2-2*Length of Shaft*Distance of Small Section of Shaft from End A^3).

Can the Static Deflection at Distance x from End A given Length of Shaft be negative?

No, the Static Deflection at Distance x from End A given Length of Shaft, measured in Length cannot be negative.

Which unit is used to measure Static Deflection at Distance x from End A given Length of Shaft?

Static Deflection at Distance x from End A given Length of Shaft is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Static Deflection at Distance x from End A given Length of Shaft can be measured.

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Static Deflection at Distance x from End A given Length of Shaft Formula

Static Deflection at Distance x from End A given Length of Shaft Example

Static Deflection at Distance x from End A given Length of Shaft Solution

Static Deflection at Distance x from End A given Length of Shaft Formula Elements

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

How to Evaluate Static Deflection at Distance x from End A given Length of Shaft?

FAQs on Static Deflection at Distance x from End A given Length of Shaft

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