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

Arch Ordinate Formula:

\[ y = \frac{4fx}{l^2} \times (l - x) \]

Ordinate of Point on Arch (y): m

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

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

Purpose: This calculation helps structural engineers determine the exact shape and position of points along a parabolic arch.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ y = \frac{4fx}{l^2} \times (l - x) \]

Where:

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

Explanation: The formula calculates the vertical position (y-coordinate) of any point along a parabolic arch given its horizontal position.

3. Importance of Arch Ordinate Calculation

Details: Accurate calculation of arch ordinates is crucial for structural analysis, construction planning, and ensuring the arch maintains its designed parabolic shape.

4. Using the Calculator

Tips: Enter the rise of arch, horizontal distance from support, and span of arch. All values must be positive numbers. The ±5% indicates typical tolerance in measurements.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the arch shape parabolic?
A: A parabolic shape is often used because under uniform vertical loading, it produces pure compression with no bending moments.

Q3: What does the ±5% tolerance mean?
A: This indicates that measurements typically have a 5% margin of error, which should be accounted for in construction.

Q4: How is the rise (f) determined?
A: The rise is typically determined by architectural design and structural requirements, often between 1/5 to 1/10 of the span.

Q5: Can this be used for non-parabolic arches?
A: No, this calculator is specifically for parabolic arches. Other arch shapes require different equations.