Fastener Standards and Parameters

Thread Parameters

• Major diameter
• Minor diameter
• Pitch diameter
• Pitch $p$

Thread Callouts for Fasteners

• Inch (UNS – Unified National Standard) threads
  • Smaller than 1/4” screws are specified by numbers, #0 ~ #12
  • #6 - 32 UNC 2B means $d=0.138\text{ in}$

• Metric (ISO) threads

Thread Standards

Basic profile and standard formula:

• Pitch $p$ and height $H$:

$$H=\frac{1}{\tan 30°}\cdot p=\frac{\sqrt{3}}{2}\cdot p\approx 0.866025\cdot p$$

• Formula for $d_p$:

$$d_p=d-\frac{5\sqrt{3}}{8}p=d-0.649519\cdot p=d-0.649519/N$$

• Formula for $d_r$:

$$\begin{array}{rl}\text{UNS threads:}& d_r=d-1.299038/N\left(=d-\frac{3\sqrt{3}}{4}p\right)\\ \text{ISO threads:}& d_r=d-1.226869\cdot p\end{array}$$

Parameters for strength analysis:

• For tensile stress analysis, use the mean area of $d_p$ and $d_r$

$$A_t=\frac{\pi }{4}{\left(\frac{d_p+d_r}{2}\right)}^2⟶{\sigma }_t=\frac{F}{A_t}$$

• For torsional shear stress, use the minimum area (given by $d_r$)

$$J=\frac{\pi r^4}{2}=\frac{\pi d_r^4}{32}⟶\tau =\frac{Tr}{J}=\frac{16T}{\pi d_r^3}$$

Standard Thread Dimensions