Average Strain under Tension Calculator

Average Strain Formula:

\[ \varepsilon_m = \varepsilon_1 - \frac{W_{cr} \times (h_{Crack} - x) \times (D_{CC} - x)}{3 \times E_s \times A_s \times (L_{eff} - x)} \]

Strain at Selected Level:

Crack Width:

mm (±5%)

Height of Crack:

mm (±5%)

Depth of Neutral Axis:

mm (±5%)

Distance from Compression to Crack Width:

mm (±5%)

Modulus of Elasticity of Steel Reinforcement:

MPa (±5%)

Area of Reinforcement:

mm² (±5%)

Effective Length:

mm (±5%)

Average Strain: %

1. What is Average Strain under Tension?

Definition: Average strain describes the response of a solid to the application of a normal force induced at the selected level under tension conditions.

Purpose: This calculation helps structural engineers assess crack behavior and deformation in reinforced concrete elements.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \varepsilon_m = \varepsilon_1 - \frac{W_{cr} \times (h_{Crack} - x) \times (D_{CC} - x)}{3 \times E_s \times A_s \times (L_{eff} - x)} \]

Where:

\( \varepsilon_m \) — Average strain (%)
\( \varepsilon_1 \) — Strain at selected level (%)
\( W_{cr} \) — Crack width (mm)
\( h_{Crack} \) — Height of crack (mm)
\( x \) — Depth of neutral axis (mm)
\( D_{CC} \) — Distance from compression to crack width (mm)
\( E_s \) — Modulus of elasticity of steel reinforcement (MPa)
\( A_s \) — Area of reinforcement (mm²)
\( L_{eff} \) — Effective length (mm)

3. Importance of Average Strain Calculation

Details: Accurate strain calculation helps predict structural behavior, serviceability, and potential failure modes in concrete elements under tension.

4. Using the Calculator

Tips: Enter all required parameters. The ±5% indicates typical measurement tolerances. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical modulus of elasticity for steel reinforcement?
A: Typically 200 GPa (200,000 MPa) for structural steel reinforcement.

Q2: How do I determine the depth of the neutral axis?
A: This requires section analysis considering material properties and loading conditions.

Q3: Why is crack width important in strain calculation?
A: Crack width directly affects the strain distribution in the tension zone.

Q4: What units should I use for inputs?
A: Use millimeters for all length dimensions, MPa for modulus, and mm² for area.

Q5: How accurate is this calculation?
A: The calculation provides theoretical values; actual conditions may vary by ±5% or more.