Core Diameter of Screw Given Direct Compressive Stress Calculator

Core Diameter of Screw Formula:

\[ d_c = \sqrt{\frac{4 \times W_a}{\pi \times \sigma_c}} \]

Core Diameter of Screw (d꜀):

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1. What is Core Diameter of Screw?

The core diameter of a screw is defined as the smallest diameter of the thread of the screw or nut. It is a critical parameter in mechanical engineering that determines the screw's strength and load-bearing capacity under compressive stress.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_c = \sqrt{\frac{4 \times W_a}{\pi \times \sigma_c}} \]

Where:

\( d_c \) — Core diameter of screw (m)
\( W_a \) — Axial load on screw (N)
\( \sigma_c \) — Compressive stress in screw (Pa)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: This formula calculates the minimum core diameter required to withstand a given axial load without exceeding the material's compressive stress limit.

3. Importance of Core Diameter Calculation

Details: Accurate calculation of core diameter is crucial for designing screws that can safely carry intended loads without failure. It ensures structural integrity and prevents mechanical failures in various applications.

4. Using the Calculator

Tips: Enter axial load in Newtons (N) and compressive stress in Pascals (Pa). Both values must be positive numbers. The calculator will compute the required core diameter in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between core diameter and major diameter?
A: Core diameter is the smallest diameter of the screw thread, while major diameter is the largest diameter measured across the thread crests.

Q2: Why is core diameter important in screw design?
A: Core diameter determines the screw's cross-sectional area, which directly affects its strength and ability to withstand tensile and compressive loads.

Q3: What factors affect compressive stress in screws?
A: Material properties, thread design, manufacturing quality, and applied load all influence the compressive stress a screw can withstand.

Q4: Can this formula be used for all screw materials?
A: Yes, but the compressive stress value must be appropriate for the specific material being used.

Q5: How does axial load affect core diameter requirements?
A: Higher axial loads require larger core diameters to maintain the same stress level, following the square root relationship in the formula.