Span of Arch in Three-hinged Circular Arch Calculator

✖Radius of Arch is the radius of the circular arch's curvature.ⓘ Radius of Arch [R]			+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 Point on Arch [y_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%
✖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 in Three-hinged Circular Arch [l]

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Formula

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Span of Arch in Three-hinged Circular Arch

Formula

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

Example

`"15.98814m"=2*((sqrt((("6m")^2)-(("1.4m"-"3m")/"6m")^2))+"2m")`

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Span of Arch in Three-hinged Circular Arch Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Span of Arch - (Measured in Meter) - Span of Arch is the horizontal distance between the two supporting members of an arch.
Radius of Arch - (Measured in Meter) - Radius of Arch is the radius of the circular arch's curvature.
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.

STEP 1: Convert Input(s) to Base Unit

Radius of Arch: 6 Meter --> 6 Meter No Conversion Required
Ordinate of Point on Arch: 1.4 Meter --> 1.4 Meter No Conversion Required
Rise of arch: 3 Meter --> 3 Meter No Conversion Required
Horizontal Distance from Support: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = 2*((sqrt((R^2)-((y_Arch-f)/R)^2))+x_Arch) --> 2*((sqrt((6^2)-((1.4-3)/6)^2))+2)

Evaluating ... ...

l = 15.9881422895941

STEP 3: Convert Result to Output's Unit

15.9881422895941 Meter --> No Conversion Required

FINAL ANSWER

15.9881422895941 ≈ 15.98814 Meter <-- Span of Arch

(Calculation completed in 00.004 seconds)

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Created by Rachana B V

The National Institute of Engineering (NIE), Mysuru

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Gautam Buddha University (GBU), Greater Noida

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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)

Span of Arch in Three-hinged Circular Arch Formula

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)
l = 2*((sqrt((R^2)-((y_Arch-f)/R)^2))+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.

How to Calculate Span of Arch in Three-hinged Circular Arch?

Span of Arch in Three-hinged Circular Arch calculator uses 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) to calculate the Span of Arch, The Span of Arch in Three-hinged Circular Arch formula is defined as the distance between the two support points on the arch's curve. Span of Arch is denoted by l symbol.

How to calculate Span of Arch in Three-hinged Circular Arch using this online calculator? To use this online calculator for Span of Arch in Three-hinged Circular Arch, enter Radius of Arch (R), Ordinate of Point on Arch (y_Arch), Rise of arch (f) & Horizontal Distance from Support (x_Arch) and hit the calculate button. Here is how the Span of Arch in Three-hinged Circular Arch calculation can be explained with given input values -> 15.98958 = 2*((sqrt((6^2)-((1.4-3)/6)^2))+2).

FAQ

What is Span of Arch in Three-hinged Circular Arch?

The Span of Arch in Three-hinged Circular Arch formula is defined as the distance between the two support points on the arch's curve and is represented as l = 2*((sqrt((R^2)-((y_Arch-f)/R)^2))+x_Arch) or 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). Radius of Arch is the radius of the circular arch's curvature, 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, 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.

How to calculate Span of Arch in Three-hinged Circular Arch?

The Span of Arch in Three-hinged Circular Arch formula is defined as the distance between the two support points on the arch's curve is calculated using 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). To calculate Span of Arch in Three-hinged Circular Arch, you need Radius of Arch (R), Ordinate of Point on Arch (y_Arch), Rise of arch (f) & Horizontal Distance from Support (x_Arch). With our tool, you need to enter the respective value for Radius of Arch, Ordinate of Point on Arch, Rise of arch & Horizontal Distance from Support and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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