Thread strength is judged against the proof strength $S_{p}$ , which is the stress at which permanent deformation begins to occur. This is typically close to, but lower than $S_{y}$ (yield strength).

Some relevant lengths to analyze stiffness of bolt and material:

Grip length $l = l_{s} + l_{t}$ , length under tension or material thickness under compression
Threaded section under tension $l_{t}$
Unthreaded (shank) section $l_{s}$
Total threaded section $l_{t h d}$

Deformation of Bolt and Material

Stiffness of the bolt: There are two sections, $l_{s}$ and $l_{t}$ . (Note that $l_{t} = l - l_{s}$ ). These two sections have different stiffness values connected in series.

Deflection of an elastic member under tension:

δ = \frac{F L}{A E}

Equivalent stiffness:

k = \frac{F}{δ} ⟹ k = \frac{A E}{L}

Stiffness of the unthreaded section:

k_{u t} = \frac{A _{b} E _{b}}{l _{s}} = \frac{A _{b} E _{b}}{l - l _{t}} (A_{b} = \frac{π d ^{2}}{4})

Stiffness of threaded section:

k_{t} = \frac{A _{t} E _{b}}{l _{t}} (A_{t} : tensile stress area)

Equivalent stiffness of the total grip $l$ :

\frac{1}{k _{b}} = \frac{1}{k _{t}} + \frac{1}{k _{u t}} = \frac{l _{t}}{A _{t} E _{b}} + \frac{l _{s}}{A _{b} E _{b}} ⟹ k_{b} = \frac{A _{t} A _{b}}{A _{b} l _{t} + A _{t} l _{s}} E_{b}

Stiffness of the material is given by an equivalent stiffness:

k_{m} = \frac{A _{m} E}{l}

where $A_{m} = \frac{π D _{eff}^{2}}{4} \approx \frac{π D _{w}^{2}}{4} - \frac{π d ^{2}}{4}$ . $D_{w}$ is an equivalent washer diameter.

Strengths of Standard Bolts

Examples

/notes/

Recent

LADR Exercises 3A

Discriminative vs. Generative Models

UDL Chapter 2 Problems

Screw Strength Analysis

Deformation of Bolt and Material

Strengths of Standard Bolts

Examples

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