Prestress Force at Stressing End using Taylor Series Expansion Calculator

Prestress Force Formula:

\[ P_{End} = \frac{P_x}{1 - (\mu \cdot \alpha) - (k \cdot x)} \]

Prestress Force at a Distance (P_x):

Prestress Friction Coefficient (μ):

Cumulative Angle (α):

rad

Wobble Coefficient (k):

Distance from Left End (x):

End Prestress Force (P_End):

1. What is Prestress Force at Stressing End?

Definition: This calculator determines the initial prestressing force at the jacking end of a tendon using Taylor series expansion approximation.

Purpose: It helps engineers calculate the required jacking force considering friction losses along the tendon.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_{End} = \frac{P_x}{1 - (\mu \cdot \alpha) - (k \cdot x)} \]

Where:

\( P_{End} \) — Prestress force at jacking end (N)
\( P_x \) — Prestress force at distance x from jacking end (N)
\( \mu \) — Prestress friction coefficient (±5%)
\( \alpha \) — Cumulative angle through which tendon profile turns (rad ±5%)
\( k \) — Wobble coefficient (±5%)
\( x \) — Distance from jacking end (m ±5%)

Explanation: The formula accounts for both curvature friction (μ·α) and wobble friction (k·x) losses.

3. Importance of Prestress Force Calculation

Details: Accurate calculation ensures proper stress transfer to concrete and accounts for friction losses in post-tensioned members.

4. Using the Calculator

Tips: Enter all required values with appropriate units. The calculator provides ±5% tolerance for friction-related parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for friction coefficient (μ)?
A: Usually between 0.05 to 0.30 for steel tendons, depending on tendon type and sheath material.

Q2: How is the wobble coefficient determined?
A: Typically 0.0015 to 0.01 per meter, depending on workmanship and duct alignment.

Q3: Why use Taylor series approximation?
A: It simplifies the exponential function in the exact solution while maintaining reasonable accuracy for small losses.

Q4: When is this approximation not valid?
A: When friction losses exceed about 20% of initial prestress force, the exact exponential solution should be used.

Q5: How to measure cumulative angle (α)?
A: Sum all angular changes (in radians) along the tendon profile from jacking end to point x.