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

✖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%
✖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%
✖Span of Arch is the horizontal distance between the two supporting members of an arch.ⓘ Span of Arch [l]			+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 at any point along Central Line of Three-hinged Parabolic Arch [y_Arch]

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Formula

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

Formula

`"y"_{"Arch"} = (4*"f"*"x"_{"Arch"}/("l"^2))*("l"-"x"_{"Arch"})`

Example

`"1.3125m"=(4*"3m"*"2m"/(("16m")^2))*("16m"-"2m")`

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Download Unsymmetrical Bending and Three Hinged Arches Formulas PDF

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

STEP 0: Pre-Calculation Summary

Formula Used

Ordinate of Point on Arch = (4*Rise of arch*Horizontal Distance from Support/(Span of Arch^2))*(Span of Arch-Horizontal Distance from Support)
y_Arch = (4*f*x_Arch/(l^2))*(l-x_Arch)
This formula uses 4 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.
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.
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.
Span of Arch - (Measured in Meter) - Span of Arch is the horizontal distance between the two supporting members of an arch.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y_Arch = (4*f*x_Arch/(l^2))*(l-x_Arch) --> (4*3*2/(16^2))*(16-2)

Evaluating ... ...

y_Arch = 1.3125

STEP 3: Convert Result to Output's Unit

1.3125 Meter --> No Conversion Required

FINAL ANSWER

1.3125 Meter <-- Ordinate of Point on Arch

(Calculation completed in 00.004 seconds)

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Created by Swarnima Singh

NIT Jaipur (mnitj), jaipur

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< 8 Three Hinged Arches Calculators

Span of Arch in Three-hinged Circular Arch

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

Rise of three-hinged Parabolic Arch

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

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

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 Arch in Three-hinged Circular Arch

Go Rise of arch = (((Radius of Arch^2)-((Span of Arch/2)-Horizontal Distance from Support)^2)^(1/2))*Radius of Arch+Ordinate of Point on Arch

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

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

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

Go Horizontal Distance from Support = (Span of Arch/2)-((Angle between Horizontal and Arch*Span of Arch^2)/(8*Rise of arch))

Angle between Horizontal and Arch

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

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

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

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

Ordinate at any point along Central Line of Three-hinged Parabolic Arch calculator uses Ordinate of Point on Arch = (4*Rise of arch*Horizontal Distance from Support/(Span of Arch^2))*(Span of Arch-Horizontal Distance from Support) to calculate the Ordinate of Point on Arch, The Ordinate at any point along Central Line of Three-hinged Parabolic Arch is defined as a parabolic arch in terms of the rise of the arch and its horizontal span. Ordinate of Point on Arch is denoted by y_Arch symbol.

How to calculate Ordinate at any point along Central Line of Three-hinged Parabolic Arch using this online calculator? To use this online calculator for Ordinate at any point along Central Line of Three-hinged Parabolic Arch, enter Rise of arch (f), Horizontal Distance from Support (x_Arch) & Span of Arch (l) and hit the calculate button. Here is how the Ordinate at any point along Central Line of Three-hinged Parabolic Arch calculation can be explained with given input values -> 1.3125 = (4*3*2/(16^2))*(16-2).

FAQ

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

The Ordinate at any point along Central Line of Three-hinged Parabolic Arch is defined as a parabolic arch in terms of the rise of the arch and its horizontal span and is represented as y_Arch = (4*f*x_Arch/(l^2))*(l-x_Arch) or Ordinate of Point on Arch = (4*Rise of arch*Horizontal Distance from Support/(Span of Arch^2))*(Span of Arch-Horizontal Distance from Support). 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, Horizontal Distance from Support represents the horizontal distance from any support of the arch to the section being considered & Span of Arch is the horizontal distance between the two supporting members of an arch.

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

The Ordinate at any point along Central Line of Three-hinged Parabolic Arch is defined as a parabolic arch in terms of the rise of the arch and its horizontal span is calculated using Ordinate of Point on Arch = (4*Rise of arch*Horizontal Distance from Support/(Span of Arch^2))*(Span of Arch-Horizontal Distance from Support). To calculate Ordinate at any point along Central Line of Three-hinged Parabolic Arch, you need Rise of arch (f), Horizontal Distance from Support (x_Arch) & Span of Arch (l). With our tool, you need to enter the respective value for Rise of arch, Horizontal Distance from Support & Span 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 Rise of arch, Horizontal Distance from Support & Span of Arch. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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