Resultant of Vertical Reaction from Concrete on Tendon Calculator

Vertical Resultant Formula:

\[ N = 2 \times P_x \times \sin\left(\frac{\theta}{2}\right) \]

Vertical Resultant (N):

1. What is Vertical Reaction Resultant?

Definition: The vertical resultant is the resultant of vertical reaction from concrete to tendons due to curvature of the tendon.

Purpose: This calculation is essential in prestressed concrete design to determine the vertical forces exerted on the concrete by curved tendons.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N = 2 \times P_x \times \sin\left(\frac{\theta}{2}\right) \]

Where:

\( N \) — Vertical resultant force (kN)
\( P_x \) — Prestress force at a distance (kN)
\( \theta \) — Subtended angle (degrees)

Explanation: The formula calculates the vertical component of the prestress force at a curved section of the tendon.

3. Importance of Vertical Reaction Calculation

Details: Proper calculation ensures structural integrity by accounting for vertical forces that affect shear capacity and load distribution in prestressed concrete members.

4. Using the Calculator

Tips: Enter the prestress force in kN, the subtended angle in degrees, and the tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for subtended angles?
A: In most applications, angles range from 5° to 30°, depending on tendon curvature.

Q2: Why include a tolerance percentage?
A: The tolerance accounts for variations in material properties, construction tolerances, and design assumptions.

Q3: How is prestress force at a distance determined?
A: It's calculated considering initial prestress force minus losses due to friction, elastic shortening, creep, and relaxation.

Q4: Does this calculation consider friction losses?
A: No, friction losses should be calculated separately and applied to the prestress force before using this formula.

Q5: What units should be used?
A: The calculator uses kN for force and degrees for angles. Convert units if necessary before input.