Specified Compressive Strength of Concrete given Total Horizontal Shear Calculator

Formula:

\[ f_c = \frac{2 \times V_h}{0.85 \times A_c} \]

28-Day Compressive Strength (f_c):

With Tolerance (±5%):

1. What is Specified Compressive Strength of Concrete?

Definition: The 28-Day Compressive Strength of Concrete is a measure of the concrete's ability to withstand axial loads, determined by testing concrete specimens after 28 days of curing.

Purpose: This calculator determines the required compressive strength based on horizontal shear forces and effective concrete flange area in composite beam construction.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ f_c = \frac{2 \times V_h}{0.85 \times A_c} \]

Where:

\( f_c \) — 28-Day Compressive Strength of Concrete (Pa)
\( V_h \) — Total Horizontal Shear (N)
\( A_c \) — Actual Area of Effective Concrete Flange (m²)

Explanation: The formula calculates the minimum required concrete strength to resist the horizontal shear forces in composite beam construction.

3. Importance of Compressive Strength Calculation

Details: Proper calculation ensures structural integrity, prevents shear failure in composite beams, and helps in material specification.

4. Using the Calculator

Tips: Enter the total horizontal shear in Newtons, effective concrete flange area in square meters, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical tolerance for compressive strength?
A: The default ±5% is common, but project specifications may require different values.

Q2: How is horizontal shear (V_h) determined?
A: It's calculated from structural analysis of the composite beam system.

Q3: What affects the effective concrete flange area?
A: Beam spacing, slab thickness, and connection details influence A_c.

Q4: Why 28-day strength specifically?
A: Concrete gains most of its strength in 28 days, making this a standard testing period.

Q5: How does this relate to concrete mix design?
A: The calculated f_c helps specify the required concrete mix proportions.