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

Arch Ordinate Formula:

\[ y = \left(\sqrt{R^2 - \left(\frac{l}{2} - x\right)^2}\right) \times R + f \]

Radius of Arch (R):

Span of Arch (l):

Horizontal Distance from Support (x):

Rise of Arch (f):

Ordinate of Point on Arch (y): m

1. What is the Ordinate of a Point on a Three-hinged Circular Arch?

Definition: The ordinate (y-coordinate) of any point along the central line of a three-hinged circular arch, measured from a reference line.

Purpose: This calculation helps structural engineers determine the exact position of points along the arch's curve for design and construction purposes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ y = \left(\sqrt{R^2 - \left(\frac{l}{2} - x\right)^2}\right) \times R + f \]

Where:

\( y \) — Ordinate of point on arch (meters)
\( R \) — Radius of arch (meters)
\( l \) — Span of arch (meters)
\( x \) — Horizontal distance from support (meters)
\( f \) — Rise of arch (meters)

Explanation: The formula calculates the vertical position of any point along a circular arch given its geometric parameters.

3. Importance of Arch Ordinate Calculation

Details: Accurate calculation of arch ordinates is crucial for proper load distribution, structural integrity, and aesthetic design of arched structures.

4. Using the Calculator

Tips: Enter all dimensions in meters. The ±5% indicates typical tolerance in construction measurements. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a three-hinged arch?
A: A three-hinged arch has hinges at both supports and at the crown, making it statically determinate.

Q2: Why is the rise important in arch calculations?
A: The rise determines the arch's height and affects its load-bearing capacity and aesthetic proportions.

Q3: How do I measure horizontal distance from support?
A: Measure horizontally from either support point to the vertical section where you want to find the ordinate.

Q4: Can this calculator be used for parabolic arches?
A: No, this formula is specific to circular arches. Parabolic arches have a different equation.

Q5: What does the ±5% tolerance mean?
A: It indicates that actual construction measurements may vary by up to 5% from design values.