Prestress Drop given Strain due to Bending and Compression in Two Parabolic Tendons Calculator

Prestress Drop Formula:

\[ \Delta f_p = E_s \times (\varepsilon_{c1} + \varepsilon_{c2}) \]

Modulus of Elasticity of Steel Reinforcement:

MPa

Strain due to Compression:

Strain due to Bending:

Prestress Drop (MPa):

1. What is Prestress Drop?

Definition: Prestress Drop is the reduction in applied prestress force due to strain in tendons caused by compression and bending effects.

Purpose: This calculation helps engineers determine the actual prestress force available after accounting for strain losses in parabolic tendons.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Delta f_p = E_s \times (\varepsilon_{c1} + \varepsilon_{c2}) \]

Where:

\( \Delta f_p \) — Prestress drop (MPa)
\( E_s \) — Modulus of elasticity of steel reinforcement (MPa)
\( \varepsilon_{c1} \) — Strain due to compression (%)
\( \varepsilon_{c2} \) — Strain due to bending (%)

Explanation: The total strain (compression + bending) multiplied by the steel modulus gives the prestress loss.

3. Importance of Prestress Drop Calculation

Details: Accurate calculation ensures structural safety by accounting for prestress losses in design, preventing overestimation of available prestress force.

4. Using the Calculator

Tips: Enter the modulus of elasticity (default 200,000 MPa for steel), strain due to compression (%), and strain due to bending (%). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: Why are strains entered as percentages?
A: Strain values are typically small, so entering as percentages (e.g., 0.5% instead of 0.005) makes input more intuitive.

Q2: What's a typical modulus for prestressing steel?
A: Most prestressing steel has modulus around 195,000-200,000 MPa, but check material specifications for exact values.

Q3: How do I determine the strain values?
A: Strain due to compression comes from axial load analysis, while bending strain comes from moment-curvature relationships.

Q4: Does this account for all prestress losses?
A: No, this only calculates losses from elastic shortening. Other losses (creep, shrinkage, relaxation) need separate consideration.

Q5: Why two parabolic tendons?
A: Parabolic tendon profiles are common in beams, and having two tendons creates balanced forces that reduce eccentricity effects.