Question

If the core diameter of threads equal to the diameter of unthreaded portion of the bolt, then it is known as

• A. Bolt of uniform strength
• B. Bolt of fatigue strength
• C. Bolt of tensile strength
• D. Bolt of compressive strength

Hint:

A bolt of uniform strength can be manufactured using two methods: 1. Turning down the unthreaded shank diameter until it matches the core thread root diameter ($d_{\text{shank}} = d_c$). 2. Drilling an axial longitudinal hole through the center of the shank to reduce its net cross-sectional area to match the core area.

Answer 1

The Correct Option is A

Concept: When an ordinary standard bolt with a uniform shank diameter equal to its nominal major diameter (\(d\)) is subjected to an axial impact or shock force, the stress distribution along its length is highly non-uniform. Let us examine why this variation happens across the different sections of the bolt:
• Unthreaded Shank Section: The cross-sectional area available to resist loads is \(A_{\text{shank}} = \frac{\pi}{4}d^2\).
• Threaded Section: The cross-sectional area is determined by the smaller core (or root) diameter (\(d_c\)), given by \(A_{\text{core}} = \frac{\pi}{4}d_c^2\). Since \(d_c < d\), the cross-sectional area at the threads is significantly smaller than that of the unthreaded shank. When an axial force \(F\) acts on the bolt, the stress induced is inversely proportional to the cross-sectional area (\(\sigma = \frac{F}{A}\)). Consequently, the stress at the threaded root is much higher than the stress in the shank body: \[ \sigma_{\text{threaded}} = \frac{F}{\frac{\pi}{4}d_c^2} \gg \sigma_{\text{shank}} = \frac{F}{\frac{\pi}{4}d^2} \]

Step 1: Analyzing the strain energy capacity of a standard bolt.
The total capacity of a component to absorb impact energy without permanent deformation is determined by its resilience, which depends directly on the volume of material subjected to high stress: \[ U = \int \frac{\sigma^2}{2E} dV \] In a standard bolt, only the narrow threaded region experiences peak stress, meaning the large shank region remains under-stressed and contributes little to absorbing impact energy. Failure occurs prematurely at the threads due to this localized strain concentration.

Step 2: Defining the design modifications for a bolt of uniform strength.
To maximize the impact energy absorption capacity, the bolt must experience uniform stress throughout its entire length. This state of equal structural resistance is achieved when the cross-sectional area of the unthreaded shank equals the cross-sectional area of the threaded section. Mathematically, this requires: \[ A_{\text{shank}} = A_{\text{core}} \quad \Rightarrow \quad \frac{\pi}{4}d_{\text{shank}}^2 = \frac{\pi}{4}d_c^2 \quad \Rightarrow \quad d_{\text{shank}} = d_c \] When the diameter of the unthreaded portion is reduced to match the core thread diameter, the bolt can deform uniformly along its full length, maximizing its energy absorption capacity. This specialized design configuration is called a bolt of uniform strength, which corresponds to Option (1).