Span of Arch in Three-hinged Circular Arch Calculator

Formula Used:

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

Radius of Arch (R):

Ordinate of Point on Arch (y_Arch):

Rise of Arch (f):

Horizontal Distance from Support (x_Arch):

Span of Arch (l):

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

The span of an arch refers to the horizontal distance between the two supporting members of a three-hinged circular arch structure. It is a critical parameter in arch design and structural analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the total span of a three-hinged circular arch based on its geometric properties and the position of a point along the arch.

3. Importance of Span Calculation

Details: Accurate span calculation is essential for structural design, load distribution analysis, and ensuring the stability and integrity of arch structures in civil engineering projects.

4. Using the Calculator

Tips: Enter all values in meters. Radius must be positive. Ensure consistent units for all inputs.

5. Frequently Asked Questions (FAQ)

Q1: What is a three-hinged arch?
A: A three-hinged arch is a structural element with three hinges - two at the supports and one at the crown - that allows for better distribution of loads and thermal expansion.

Q2: Why is the span calculation important?
A: The span determines the overall dimensions of the structure and affects load-bearing capacity, deflection characteristics, and overall stability.

Q3: What units should be used for input?
A: All inputs should be in consistent units (preferably meters) for accurate results.

Q4: Are there limitations to this formula?
A: This formula applies specifically to circular arches and assumes ideal geometric conditions. Real-world applications may require additional considerations for material properties and loading conditions.

Q5: Can this calculator be used for arch design?
A: This calculator provides basic span calculation but should be used in conjunction with proper engineering analysis and design principles for actual structural projects.