Core Diameter of Screw Given Transverse Shear Stress in Screw Calculator

Formula Used:

\[ d_c = \frac{W_a}{\tau_s \cdot \pi \cdot t \cdot z} \]

Axial Load on Screw (W_a):

Transverse Shear Stress in Screw (τ_s):

Thread Thickness (t):

Number of Engaged Threads (z):

Core Diameter of Screw (d_c):

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1. What is Core Diameter of Screw?

Core diameter of screw is defined as the smallest diameter of the thread of the screw or nut. The term "minor diameter" replaces the term "core diameter" as applied to the thread of a screw. It's a critical parameter in mechanical design and strength calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_c = \frac{W_a}{\tau_s \cdot \pi \cdot t \cdot z} \]

Where:

\( d_c \) — Core diameter of screw (m)
\( W_a \) — Axial load on screw (N)
\( \tau_s \) — Transverse shear stress in screw (Pa)
\( \pi \) — Archimedes' constant (≈3.1416)
\( t \) — Thread thickness (m)
\( z \) — Number of engaged threads

Explanation: This formula calculates the minimum core diameter required to withstand the given axial load without exceeding the allowable transverse shear stress, considering the number of engaged threads and thread thickness.

3. Importance of Core Diameter Calculation

Details: Accurate core diameter calculation is crucial for ensuring screw strength, preventing shear failure, and maintaining structural integrity in mechanical assemblies and fastening systems.

4. Using the Calculator

Tips: Enter axial load in newtons, transverse shear stress in pascals, thread thickness in meters, and number of engaged threads. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is core diameter important in screw design?
A: Core diameter determines the screw's strength against shear forces and is critical for calculating the screw's load-bearing capacity.

Q2: What is transverse shear stress in screws?
A: Transverse shear stress is the resistance force developed per unit cross-sectional area by the screw to avoid transverse deformation under load.

Q3: How does thread engagement affect the calculation?
A: More engaged threads distribute the load over a larger area, reducing the stress on individual threads and allowing for a smaller core diameter.

Q4: What are typical values for transverse shear stress?
A: Allowable transverse shear stress varies by material, typically ranging from 0.5-0.8 times the material's tensile yield strength for ductile materials.

Q5: When should this calculation be used?
A: This calculation is essential during screw design phase to ensure the screw can withstand expected loads without shearing failure.