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Static Deflection at Distance x from End A 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 \cdot (x^{4} - 2 \cdot L shaft \cdot x + {L shaft}^{3} \cdot x)}{24 \cdot E \cdot I shaft}

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

Static Deflection at Distance x from End A Example

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

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

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

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

6.175m = \frac{3 \cdot ({5m}^{4} - 2 \cdot 3.5m \cdot 5m + {3.5m}^{3} \cdot 5m)}{24 \cdot 15N/m \cdot 1.0855kg·m²}

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

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Static Deflection at Distance x from End A Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

y = 6.17502455040064m

LAST Step Rounding Answer

∴

y = 6.175m

Static Deflection at Distance x from End A 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

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

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

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

Go Circular Frequency given Static Deflection

ω n = 2 \cdot π \cdot \frac{0.5615}{\sqrt{δ}}

Go Natural Frequency given Static Deflection

f = \frac{0.5615}{\sqrt{δ}}

Go Uniformly Distributed Load Unit Length given Static Deflection

w = \frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot {L shaft}^{4}}

Go Length of Shaft given Static Deflection

L shaft = {(\frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot w})}^{\frac{1}{4}}

How to Evaluate Static Deflection at Distance x from End A?

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

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

FAQs on Static Deflection at Distance x from End A

What is the formula to find Static Deflection at Distance x from End A?

The formula of Static Deflection at Distance x from End A is expressed as Static deflection at distance x from end A = (Load per unit length*(Distance of Small Section of Shaft from End A^4-2*Length of Shaft*Distance of Small Section of Shaft from End A+Length of Shaft^3*Distance of Small Section of Shaft from End A))/(24*Young's Modulus*Moment of inertia of shaft). Here is an example- 6.175025 = (3*(5^4-2*3.5*5+3.5^3*5))/(24*15*1.085522).

How to calculate Static Deflection at Distance x from End A?

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

Can the Static Deflection at Distance x from End A be negative?

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

Which unit is used to measure Static Deflection at Distance x from End A?

Static Deflection at Distance x from End A 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 can be measured.

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Static Deflection at Distance x from End A Formula

Static Deflection at Distance x from End A Example

Static Deflection at Distance x from End A Solution

Static Deflection at Distance x from End A Formula Elements

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

How to Evaluate Static Deflection at Distance x from End A?

FAQs on Static Deflection at Distance x from End A

Variable Name