Rise of three-hinged Parabolic Arch Calculator

Rise of Arch Formula:

\[ f = \frac{y_{Arch} \times l^2}{4 \times x_{Arch} \times (l - x_{Arch})} \]

Rise of Arch (m):

1. What is Rise of three-hinged Parabolic Arch?

Definition: The rise of an 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.

Purpose: This calculation is essential in structural engineering for designing parabolic arches that can support specific loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ f = \frac{y_{Arch} \times l^2}{4 \times x_{Arch} \times (l - x_{Arch})} \]

Where:

\( f \) — Rise of arch (meters)
\( y_{Arch} \) — Ordinate of point on arch (meters)
\( l \) — Span of arch (meters)
\( x_{Arch} \) — Horizontal distance from support (meters ±5%)

Explanation: The formula calculates the vertical rise at any point along a three-hinged parabolic arch based on its geometry.

3. Importance of Rise Calculation

Details: Accurate rise calculation ensures structural stability, proper load distribution, and aesthetic proportions in arch design.

4. Using the Calculator

Tips: Enter the ordinate of point on arch, span of arch, and horizontal distance from support (with ±5% tolerance). All values must be positive and horizontal distance must be less than span.

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 horizontal distance input marked ±5%?
A: This accounts for measurement tolerances in field applications where exact distances may vary slightly.

Q3: What's the typical range for arch rise?
A: The rise typically ranges between 1/4 to 1/2 of the span, depending on structural and aesthetic requirements.

Q4: How does rise affect arch performance?
A: Higher rises generally reduce horizontal thrust but increase material usage and construction complexity.

Q5: Can this calculator be used for other arch types?
A: No, this formula is specific to three-hinged parabolic arches. Other arch types require different calculations.