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Ordinate of any point along Central Line of Three-hinged Circular Arch Formula

GoOrdinate at any point along Central Line of Three-hinged Parabolic Arch Formula

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Ordinate of Point on Arch is the ordinate of any point along the central line of the arch. It basically gives the Equation for a three-hinged Parabolic arch. Check FAQs

y Arch = ({((R^{2}) - {((\frac{l}{2}) - x Arch)}^{2})}^{\frac{1}{2}}) \cdot R + f

y_Arch - Ordinate of Point on Arch?R - Radius of Arch?l - Span of Arch?x_Arch - Horizontal Distance from Support?f - Rise of arch?

Ordinate of any point along Central Line of Three-hinged Circular Arch Example

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Here is how the Ordinate of any point along Central Line of Three-hinged Circular Arch equation looks like with Values.

Here is how the Ordinate of any point along Central Line of Three-hinged Circular Arch equation looks like with Units.

Here is how the Ordinate of any point along Central Line of Three-hinged Circular Arch equation looks like.

3 = ({((6^{2}) - {((\frac{16}{2}) - 2)}^{2})}^{\frac{1}{2}}) \cdot 6 + 3

3m = ({(({6m}^{2}) - {((\frac{16m}{2}) - 2m)}^{2})}^{\frac{1}{2}}) \cdot 6m + 3m

3 = ({((6^{2}) - {((\frac{16}{2}) - 2)}^{2})}^{\frac{1}{2}}) \cdot 6 + 3

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Ordinate of any point along Central Line of Three-hinged Circular Arch Solution

Follow our step by step solution on how to calculate Ordinate of any point along Central Line of Three-hinged Circular Arch?

FIRST Step Consider the formula

y Arch = ({((R^{2}) - {((\frac{l}{2}) - x Arch)}^{2})}^{\frac{1}{2}}) \cdot R + f

Next Step Substitute values of Variables

∴

y Arch = ({(({6m}^{2}) - {((\frac{16m}{2}) - 2m)}^{2})}^{\frac{1}{2}}) \cdot 6m + 3m

Next Step Prepare to Evaluate

∴

y Arch = ({((6^{2}) - {((\frac{16}{2}) - 2)}^{2})}^{\frac{1}{2}}) \cdot 6 + 3

LAST Step Evaluate

∴

y Arch = 3m

Ordinate of any point along Central Line of Three-hinged Circular Arch Formula Elements

Variables

Ordinate of Point on Arch

Ordinate of Point on Arch is the ordinate of any point along the central line of the arch. It basically gives the Equation for a three-hinged Parabolic arch.

Symbol: y_Arch

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Ordinate of Point on Arch

Radius of Arch

Radius of Arch is the radius of the circular arch's curvature.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Arch

Span of Arch

Span of Arch is the horizontal distance between the two supporting members of an arch.

Symbol: l

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Span of Arch

Horizontal Distance from Support

Horizontal Distance from Support represents the horizontal distance from any support of the arch to the section being considered.

Symbol: x_Arch

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Horizontal Distance from Support

Rise of arch

The Rise of arch is the vertical distance from the centerline to the arch’s crown. It is the highest point on the arch from the reference line.

Symbol: f

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Rise of arch

Other Formulas to find Ordinate of Point on Arch

Go Ordinate at any point along Central Line of Three-hinged Parabolic Arch

y Arch = (4 \cdot f \cdot \frac{x Arch}{l^{2}}) \cdot (l - x Arch)

Other formulas in Three Hinged Arches category

Go Rise of Three-Hinged Arch for Angle between Horizontal and Arch

f = \frac{y' \cdot (l^{2})}{4 \cdot (l - (2 \cdot x Arch))}

Go Rise of three-hinged Parabolic Arch

f = \frac{y Arch \cdot (l^{2})}{4 \cdot x Arch \cdot (l - x Arch)}

Go Angle between Horizontal and Arch

y' = f \cdot 4 \cdot \frac{l - (2 \cdot x Arch)}{l^{2}}

Go Horizontal Distance from Support to Section for Angle between Horizontal and Arch

x Arch = (\frac{l}{2}) - (\frac{y' \cdot l^{2}}{8 \cdot f})

How to Evaluate Ordinate of any point along Central Line of Three-hinged Circular Arch?

Ordinate of any point along Central Line of Three-hinged Circular Arch evaluator uses Ordinate of Point on Arch = (((Radius of Arch^2)-((Span of Arch/2)-Horizontal Distance from Support)^2)^(1/2))*Radius of Arch+Rise of arch to evaluate the Ordinate of Point on Arch, The Ordinate of any point along Central Line of Three-hinged Circular Arch is defined as the circular arch. The ordinate of any point on the arch is calculated using the values of radius, rise, span, and abscissa. Ordinate of Point on Arch is denoted by y_Arch symbol.

How to evaluate Ordinate of any point along Central Line of Three-hinged Circular Arch using this online evaluator? To use this online evaluator for Ordinate of any point along Central Line of Three-hinged Circular Arch, enter Radius of Arch (R), Span of Arch (l), Horizontal Distance from Support (x_Arch) & Rise of arch (f) and hit the calculate button.

FAQs on Ordinate of any point along Central Line of Three-hinged Circular Arch

What is the formula to find Ordinate of any point along Central Line of Three-hinged Circular Arch?

The formula of Ordinate of any point along Central Line of Three-hinged Circular Arch is expressed as Ordinate of Point on Arch = (((Radius of Arch^2)-((Span of Arch/2)-Horizontal Distance from Support)^2)^(1/2))*Radius of Arch+Rise of arch. Here is an example- 3 = (((6^2)-((16/2)-2)^2)^(1/2))*6+3.

How to calculate Ordinate of any point along Central Line of Three-hinged Circular Arch?

With Radius of Arch (R), Span of Arch (l), Horizontal Distance from Support (x_Arch) & Rise of arch (f) we can find Ordinate of any point along Central Line of Three-hinged Circular Arch using the formula - Ordinate of Point on Arch = (((Radius of Arch^2)-((Span of Arch/2)-Horizontal Distance from Support)^2)^(1/2))*Radius of Arch+Rise of arch.

What are the other ways to Calculate Ordinate of Point on Arch?

Here are the different ways to Calculate Ordinate of Point on Arch-

Ordinate of Point on Arch=(4*Rise of arch*Horizontal Distance from Support/(Span of Arch^2))*(Span of Arch-Horizontal Distance from Support)

Can the Ordinate of any point along Central Line of Three-hinged Circular Arch be negative?

No, the Ordinate of any point along Central Line of Three-hinged Circular Arch, measured in Length cannot be negative.

Which unit is used to measure Ordinate of any point along Central Line of Three-hinged Circular Arch?

Ordinate of any point along Central Line of Three-hinged Circular Arch is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Ordinate of any point along Central Line of Three-hinged Circular Arch can be measured.

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Ordinate of any point along Central Line of Three-hinged Circular Arch Formula

​GoOrdinate at any point along Central Line of Three-hinged Parabolic Arch Formula

Ordinate of any point along Central Line of Three-hinged Circular Arch Example

Ordinate of any point along Central Line of Three-hinged Circular Arch Solution

Ordinate of any point along Central Line of Three-hinged Circular Arch Formula Elements

Other Formulas to find Ordinate of Point on Arch

Other formulas in Three Hinged Arches category

How to Evaluate Ordinate of any point along Central Line of Three-hinged Circular Arch?

FAQs on Ordinate of any point along Central Line of Three-hinged Circular Arch

Variable Name

GoOrdinate at any point along Central Line of Three-hinged Parabolic Arch Formula