Rise Of Arch In Three Hinged Circular Arch Calculator

Formula Used:

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

Radius of Arch (R):

Span of Arch (l):

Horizontal Distance from Support (x):

Ordinate of Point on Arch (y):

Rise of Arch (f):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Rise of Arch in Three-hinged Circular Arch?

The Rise of Arch is the vertical distance from the centerline to the arch's crown. It represents the highest point on the arch from the reference line and is a crucial parameter in arch design and structural analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( f \) — Rise of arch (m)
\( R \) — Radius of Arch (m)
\( l \) — Span of Arch (m)
\( x_{Arch} \) — Horizontal Distance from Support (m)
\( y_{Arch} \) — Ordinate of Point on Arch (m)

Explanation: This formula calculates the vertical rise of a three-hinged circular arch based on geometric relationships between the arch's radius, span, and specific point coordinates.

3. Importance of Rise Calculation

Details: Accurate rise calculation is essential for structural design, load distribution analysis, and ensuring proper arch geometry in construction projects. It helps determine the arch's stability and aesthetic proportions.

4. Using the Calculator

Tips: Enter all values in meters. Ensure radius and span are positive values, and horizontal distance should be within the arch span limits for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is a three-hinged arch?
A: A three-hinged arch is a structural arch with three hinges - two at the supports and one at the crown - which makes it statically determinate and allows for thermal expansion.

Q2: Why is the rise important in arch design?
A: The rise determines the arch's shape, affects load distribution, and influences the structural efficiency and aesthetic appearance of the arch.

Q3: What are typical values for arch parameters?
A: Values vary widely based on application, but radius typically ranges from 5-50m, span from 10-100m, and rise is usually 1/5 to 1/2 of the span.

Q4: Can this formula be used for parabolic arches?
A: No, this specific formula is designed for circular arches. Parabolic arches have different geometric relationships and require different equations.

Q5: What if I get a negative square root error?
A: This indicates invalid input where the horizontal distance exceeds the geometric constraints of the arch. Check that your input values are physically possible for a circular arch.