Variation of Eccentricity of Tendon B Calculator

Eccentricity Variation Formula:

\[ EB(x) = eB1 + \left(\frac{4 \times \Delta eB \times x}{L}\right) \times \left(1 - \frac{x}{L}\right) \]

Eccentricity at End for B:

Change in Eccentricity B (±5%):

Distance from Left End (±5%):

Length of Beam in Prestress (±5%):

Eccentricity Variation of Tendon B: m

1. What is Variation of Eccentricity of Tendon B?

Definition: This calculator computes the eccentricity variation of tendon B at any point along the length of a prestressed beam.

Purpose: It helps structural engineers determine the position of tendons at different sections of prestressed concrete beams.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ EB(x) = eB1 + \left(\frac{4 \times \Delta eB \times x}{L}\right) \times \left(1 - \frac{x}{L}\right) \]

Where:

\( EB(x) \) — Eccentricity variation of tendon B at distance x (meters)
\( eB1 \) — Eccentricity at end for B (meters)
\( \Delta eB \) — Change in eccentricity B (meters)
\( x \) — Distance from left end (meters)
\( L \) — Length of beam in prestress (meters)

Explanation: The formula calculates the parabolic variation of tendon eccentricity along the beam length.

3. Importance of Eccentricity Calculation

Details: Proper eccentricity calculation ensures correct prestress force application and beam performance under loads.

4. Using the Calculator

Tips: Enter all values in meters. The ±5% tolerance accounts for construction variations. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is tendon eccentricity?
A: It's the distance between the tendon's centroid and the beam's centroid at a given section.

Q2: Why does eccentricity vary along the beam?
A: To optimize prestress moment distribution and counteract expected loading conditions.

Q3: What's the significance of the ±5% tolerance?
A: It accounts for allowable construction tolerances in tendon placement.

Q4: How is change in eccentricity (ΔeB) determined?
A: It's typically half the difference between midspan and end eccentricities.

Q5: Can this formula be used for all prestressed beams?
A: It works for simply supported beams with parabolic tendon profiles. Other profiles require different formulas.