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Ordinate at any point along the central line of a three-hinged Parabolic arch Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
y = (4*f*x/(l^2))*(l-x)
This formula uses 3 Variables
Variables Used
Rise of the arch - 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. (Measured in Meter)
Horizontal distance from the support - Horizontal distance from the support represents the horizontal distance from any support of the arch to the section being considered. (Measured in Meter)
Span of the arch - Span of the arch is the horizontal distance between the two supporting members of an arch. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Rise of the arch: 3 Meter --> 3 Meter No Conversion Required
Horizontal distance from the support: 2 Meter --> 2 Meter No Conversion Required
Span of the arch: 16 Meter --> 16 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
y = (4*f*x/(l^2))*(l-x) --> (4*3*2/(16^2))*(16-2)
Evaluating ... ...
y = 1.3125
STEP 3: Convert Result to Output's Unit
1.3125 Meter --> No Conversion Required
FINAL ANSWER
1.3125 Meter <-- Ordinate of a point on arch
(Calculation completed in 00.016 seconds)

3 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

Ordinate at any point along the central line of a three-hinged Parabolic arch Formula

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)
y = (4*f*x/(l^2))*(l-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 Ordinate at any point along the central line of a three-hinged Parabolic arch?

Ordinate at any point along the central line of a three-hinged Parabolic arch calculator uses 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) to calculate the Ordinate of a point on arch, The Ordinate at any point along the central line of a three-hinged Parabolic arch gives the equation of a parabolic arch in terms of the rise of the arch and it's horizontal span. Ordinate of a point on arch is denoted by y symbol.

How to calculate Ordinate at any point along the central line of a three-hinged Parabolic arch using this online calculator? To use this online calculator for Ordinate at any point along the central line of a three-hinged Parabolic arch, enter Rise of the arch (f), Horizontal distance from the support (x) & Span of the arch (l) and hit the calculate button. Here is how the Ordinate at any point along the central line of a 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 the central line of a three-hinged Parabolic arch?
The Ordinate at any point along the central line of a three-hinged Parabolic arch gives the equation of a parabolic arch in terms of the rise of the arch and it's horizontal span and is represented as y = (4*f*x/(l^2))*(l-x) or 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). 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, Horizontal distance from the support represents the horizontal distance from any support of the arch to the section being considered & Span of the arch is the horizontal distance between the two supporting members of an arch.
How to calculate Ordinate at any point along the central line of a three-hinged Parabolic arch?
The Ordinate at any point along the central line of a three-hinged Parabolic arch gives the equation of a parabolic arch in terms of the rise of the arch and it's horizontal span is calculated using 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). To calculate Ordinate at any point along the central line of a three-hinged Parabolic arch, you need Rise of the arch (f), Horizontal distance from the support (x) & Span of the arch (l). With our tool, you need to enter the respective value for Rise of the arch, Horizontal distance from the support & Span of the 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 a point on arch?
In this formula, Ordinate of a point on arch uses Rise of the arch, Horizontal distance from the support & Span of the arch. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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)
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