Length of Span given Deflection due to Prestressing for Doubly Harped Tendon Calculator

Span Length Formula:

\[ L = \left( \frac{\delta \times 48 \times E \times I_p}{a \times (4 - 3a^2) \times F_t} \right)^{1/3} \]

Deflection due to Moments:

Young's Modulus:

Moment of Inertia:

kg·m²

Part of Span Length:

Thrust Force:

Span Length (m):

1. What is Span Length given Deflection Calculator?

Definition: This calculator determines the span length of a doubly harped tendon based on deflection, material properties, and applied forces.

Purpose: It helps structural engineers calculate appropriate span lengths while considering prestressing effects and deflection limitations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \left( \frac{\delta \times 48 \times E \times I_p}{a \times (4 - 3a^2) \times F_t} \right)^{1/3} \]

Where:

\( L \) — Span Length (meters)
\( \delta \) — Deflection due to moments (meters)
\( E \) — Young's Modulus (Pascals)
\( I_p \) — Moment of Inertia in Prestress (kg·m²)
\( a \) — Part of Span Length (dimensionless, typically 0.8±5%)
\( F_t \) — Thrust Force (Newtons)

Explanation: The formula calculates the maximum span length that will keep deflection within acceptable limits for a doubly harped tendon configuration.

3. Importance of Span Length Calculation

Details: Proper span length calculation ensures structural integrity, controls deflection, and maintains serviceability of prestressed concrete members.

4. Using the Calculator

Tips: Enter deflection, material properties (Young's Modulus and Moment of Inertia), part of span length (default 0.8±5%), and thrust force. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a doubly harped tendon?
A: A tendon that is deviated at two points along its length, creating a three-segment profile.

Q2: Why is part of span length typically 0.8±5%?
A: This represents the common proportioning of harped tendon geometry in practice, with 5% tolerance.

Q3: How does deflection affect span length?
A: Greater allowed deflection permits longer spans, while stricter deflection limits require shorter spans.

Q4: What's a typical Young's Modulus for prestressed concrete?
A: Typically 28-35 GPa (28,000-35,000 MPa) for normal strength concrete.

Q5: How does thrust force impact the calculation?
A: Higher thrust forces allow for longer spans as they counteract deflection more effectively.