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

✖Radius of Arch is the radius of the circular arch's curvature.ⓘ Radius of Arch [R]			+10% -10%
✖Span of Arch is the horizontal distance between the two supporting members of an arch.ⓘ Span of Arch [l]			+10% -10%
✖Horizontal Distance from Support represents the horizontal distance from any support of the arch to the section being considered.ⓘ Horizontal Distance from Support [x_Arch]			+10% -10%
✖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.ⓘ Rise of arch [f]			+10% -10%

✖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.ⓘ Ordinate of any point along Central Line of Three-hinged Circular Arch [y_Arch]

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

STEP 0: Pre-Calculation Summary

Formula Used

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
y_Arch = (((R^2)-((l/2)-x_Arch)^2)^(1/2))*R+f
This formula uses 5 Variables

Variables Used

Ordinate of Point on Arch - (Measured in Meter) - 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.
Radius of Arch - (Measured in Meter) - Radius of Arch is the radius of the circular arch's curvature.
Span of Arch - (Measured in Meter) - Span of Arch is the horizontal distance between the two supporting members of an arch.
Horizontal Distance from Support - (Measured in Meter) - Horizontal Distance from Support represents the horizontal distance from any support of the arch to the section being considered.
Rise of arch - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Radius of Arch: 6 Meter --> 6 Meter No Conversion Required
Span of Arch: 16 Meter --> 16 Meter No Conversion Required
Horizontal Distance from Support: 2 Meter --> 2 Meter No Conversion Required
Rise of arch: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y_Arch = (((R^2)-((l/2)-x_Arch)^2)^(1/2))*R+f --> (((6^2)-((16/2)-2)^2)^(1/2))*6+3

Evaluating ... ...

y_Arch = 3

STEP 3: Convert Result to Output's Unit

3 Meter --> No Conversion Required

FINAL ANSWER

3 Meter <-- Ordinate of Point on Arch

(Calculation completed in 00.004 seconds)

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Created by Swarnima Singh

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< Three Hinged Arches Calculators

Rise of three-hinged Parabolic Arch

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

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

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

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

LaTeX Go 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

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

LaTeX Go Rise of arch = (Angle between Horizontal and Arch*(Span of Arch^2))/(4*(Span of Arch-(2*Horizontal Distance from Support)))

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

LaTeX Go

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
y_Arch = (((R^2)-((l/2)-x_Arch)^2)^(1/2))*R+f

What is a Three-Hinged Arch?

A three-hinged arch is a geometrically stable and statically determinate structure. It consists of two curved members connected by an internal hinge at the crown and is supported by two hinges at its base. Sometimes, a tie is provided at the support level or at an elevated position in the arch to increase the stability of the structure.

What makes Arches different from Other Structures?

One of the main distinguishing features of an arch is the development of horizontal thrusts at the supports as well as the vertical reactions, even in the absence of a horizontal load. The internal forces at any section of an arch include axial compression, shearing force, and bending moment.

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

Ordinate of any point along Central Line of Three-hinged Circular Arch calculator 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 calculate 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 calculate Ordinate of any point along Central Line of Three-hinged Circular Arch using this online calculator? To use this online calculator 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. Here is how the Ordinate of any point along Central Line of Three-hinged Circular Arch calculation can be explained with given input values -> 3 = (((6^2)-((16/2)-2)^2)^(1/2))*6+3.

FAQ

What is Ordinate of any point along Central Line of Three-hinged Circular 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 and is represented as y_Arch = (((R^2)-((l/2)-x_Arch)^2)^(1/2))*R+f or 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. Radius of Arch is the radius of the circular arch's curvature, Span of Arch is the horizontal distance between the two supporting members of an arch, Horizontal Distance from Support represents the horizontal distance from any support of the arch to the section being considered & 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.

How to calculate Ordinate of any point along Central Line of Three-hinged Circular 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 is calculated using 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 calculate Ordinate of any point along Central Line of Three-hinged Circular Arch, you need Radius of Arch (R), Span of Arch (l), Horizontal Distance from Support (x_Arch) & Rise of arch (f). With our tool, you need to enter the respective value for Radius of Arch, Span of Arch, Horizontal Distance from Support & Rise of arch and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Ordinate of Point on Arch?

In this formula, Ordinate of Point on Arch uses Radius of Arch, Span of Arch, Horizontal Distance from Support & Rise of arch. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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