Rise of Three-Hinged Arch for Angle between Horizontal and Arch Calculator

Rise of Arch Formula:

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

Rise of Arch (m):

1. What is Rise of Three-Hinged Arch Calculator?

Definition: This calculator determines the vertical rise of a three-hinged arch based on the angle between horizontal and arch, span length, and horizontal distance from support.

Purpose: It helps structural engineers and architects calculate the arch geometry needed for bridge and architectural designs.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( f \) — Rise of arch (meters)
\( y' \) — Angle between horizontal and arch (%) ±5%
\( l \) — Span of arch (meters)
\( x \) — Horizontal distance from support (meters)

Explanation: The formula calculates the vertical rise at the crown of a three-hinged arch based on geometric relationships.

3. Importance of Arch Rise Calculation

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

4. Using the Calculator

Tips: Enter the angle (as percentage ±5%), span length in meters, and horizontal distance from support in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle input as a percentage?
A: The angle is expressed as a percentage slope (rise/run × 100) with ±5% tolerance for practical construction purposes.

Q2: What's a typical span range for three-hinged arches?
A: Three-hinged arches are commonly used for spans between 20m to 100m in bridge construction.

Q3: How does horizontal distance affect the rise?
A: Greater horizontal distances from the support result in higher rise calculations for the same span and angle.

Q4: What are common applications of three-hinged arches?
A: They're used in bridges, roof structures, and architectural features where movement accommodation is needed.

Q5: Does this calculator account for material properties?
A: No, this calculates geometric properties only. Material properties should be considered in structural analysis.