Rise of three-hinged Circular Arch Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rise of the arch = (Ordinate of a point on arch*(Span of the arch^2))/(4*(Span of the arch-(2*Horizontal distance from the support)))
f = (y*(l^2))/(4*(l-(2*x)))
This formula uses 4 Variables
Variables Used
Rise of the arch - (Measured in Meter) - The Rise of the 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.
Ordinate of a point on arch - (Measured in Meter) - Ordinate of a 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.
Span of the arch - (Measured in Meter) - Span of the arch is the horizontal distance between the two supporting members of an arch.
Horizontal distance from the support - (Measured in Meter) - Horizontal distance from the support represents the horizontal distance from any support of the arch to the section being considered.
STEP 1: Convert Input(s) to Base Unit
Ordinate of a point on arch: 1.5 Meter --> 1.5 Meter No Conversion Required
Span of the arch: 16 Meter --> 16 Meter No Conversion Required
Horizontal distance from the support: 2 Meter --> 2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
f = (y*(l^2))/(4*(l-(2*x))) --> (1.5*(16^2))/(4*(16-(2*2)))
Evaluating ... ...
f = 8
STEP 3: Convert Result to Output's Unit
8 Meter --> No Conversion Required
FINAL ANSWER
8 Meter <-- Rise of the arch
(Calculation completed in 00.031 seconds)

Credits

Created by Swarnima Singh
NIT Jaipur (mnitj), jaipur
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Verified by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
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4 Three -Hinged Arches Calculators

Rise of three-hinged Parabolic Arch
Rise of the arch = (Ordinate of a point on arch*(Span of the arch^2))/(4*Horizontal distance from the support*(Span of the arch-Horizontal distance from the support)) Go
Ordinate at any point along the central line of a three-hinged Parabolic arch
Ordinate of a point on arch = (4*Rise of the arch*Horizontal distance from the support/(Span of the arch^2))*(Span of the arch-Horizontal distance from the support) Go
Ordinate of any point along the central line of three-hinged circular arch
Ordinate of a point on arch = (((Radius of the arch^2)-((Span of the arch/2)-Horizontal distance from the support)^2)^(1/2))*(Radius of the arch+Rise of the arch) Go
Rise of three-hinged Circular Arch
Rise of the arch = (Ordinate of a point on arch*(Span of the arch^2))/(4*(Span of the arch-(2*Horizontal distance from the support))) Go

Rise of three-hinged Circular Arch Formula

Rise of the arch = (Ordinate of a point on arch*(Span of the arch^2))/(4*(Span of the arch-(2*Horizontal distance from the support)))
f = (y*(l^2))/(4*(l-(2*x)))

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 Rise of three-hinged Circular Arch?

Rise of three-hinged Circular Arch calculator uses Rise of the arch = (Ordinate of a point on arch*(Span of the arch^2))/(4*(Span of the arch-(2*Horizontal distance from the support))) to calculate the Rise of the arch, The Rise of three-hinged Circular Arch formula is used to calculate the clear vertical distance between the highest point on the intrados and the springing line. Rise of the arch is denoted by f symbol.

How to calculate Rise of three-hinged Circular Arch using this online calculator? To use this online calculator for Rise of three-hinged Circular Arch, enter Ordinate of a point on arch (y), Span of the arch (l) & Horizontal distance from the support (x) and hit the calculate button. Here is how the Rise of three-hinged Circular Arch calculation can be explained with given input values -> 8 = (1.5*(16^2))/(4*(16-(2*2))).

FAQ

What is Rise of three-hinged Circular Arch?
The Rise of three-hinged Circular Arch formula is used to calculate the clear vertical distance between the highest point on the intrados and the springing line and is represented as f = (y*(l^2))/(4*(l-(2*x))) or Rise of the arch = (Ordinate of a point on arch*(Span of the arch^2))/(4*(Span of the arch-(2*Horizontal distance from the support))). Ordinate of a 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, Span of the arch is the horizontal distance between the two supporting members of an arch & Horizontal distance from the support represents the horizontal distance from any support of the arch to the section being considered.
How to calculate Rise of three-hinged Circular Arch?
The Rise of three-hinged Circular Arch formula is used to calculate the clear vertical distance between the highest point on the intrados and the springing line is calculated using Rise of the arch = (Ordinate of a point on arch*(Span of the arch^2))/(4*(Span of the arch-(2*Horizontal distance from the support))). To calculate Rise of three-hinged Circular Arch, you need Ordinate of a point on arch (y), Span of the arch (l) & Horizontal distance from the support (x). With our tool, you need to enter the respective value for Ordinate of a point on arch, Span of the arch & Horizontal distance from the support 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 Rise of the arch?
In this formula, Rise of the arch uses Ordinate of a point on arch, Span of the arch & Horizontal distance from the support. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Rise of the arch = (Ordinate of a point on arch*(Span of the arch^2))/(4*Horizontal distance from the support*(Span of the arch-Horizontal distance from the support))
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