Pre-Analysis & Start-Up — Lesson 2

Pre-Analysis

It is recommended that you make some back-of-the-envelope estimates of expected results before launching into your computer solution. Here are the dimensions you need:

$h = 3 \, \text{in}, \quad r = 1 \, \text{in}, \quad D = 8 \, \text{in}, \quad \frac{h}{r} = 3, \quad \frac{2h}{D} = \frac{3}{4} = 0.75
$

The following formula for the axial stress concentration factor, K, holds (see Roark’s Formulas for Stress and Strain, Warren C. Young and Richard G. Budynas, 2002):

$K = C_1 + C_2 \frac{2h}{D} + C_3 \left( \frac{2h}{D} \right)^2 + C_4 \left( \frac{2h}{D} \right)^3$

$C_1 = 1.225 + 0.831 \sqrt{\frac{h}{r}} - 0.010 \left( \frac{h}{r} \right) = 2.634$

$C_2 = -1.831 - 0.318 \sqrt{\frac{h}{r}} - 0.049 \left( \frac{h}{r} \right) = -2.529$

$C_3 = 2.236 - 0.5220 \sqrt{\frac{h}{r}} + 0.176 \left( \frac{h}{r} \right) = 1.8599$

$C_4 = -0.63 + 0.009 \sqrt{\frac{h}{r}} - 0.117 \left( \frac{h}{r} \right) = -0.965411543$

$\Rightarrow K = C_1 + C_2 \frac{2h}{D} + C_3 \left( \frac{2h}{D} \right)^2 + C_4 \left( \frac{2h}{D} \right)^3 = 1.3766$

where

$\sigma_{MAX} = K \sigma_{NOM} = K \frac{P}{A_{MIN}} = K \frac{4P}{\pi (D - 2h)^2} = 1376 \, \text{psi}$

We'll compare the above axial stress concentration factor to the value obtained from Ansys.

Start-Up

Launch Ansys Workbench and start a "Static Structural" analysis on the project page as shown in the video below.