Question

The disk in Fig. 4.2-7 of Sec. 4.2.6 is sometimes used as a calibration specimen when using the experimental technique involving photoelastic fringes (see Chap. 8). The fringes depend on the difference in the principal stresses $\sigma_1-\sigma_2$. Owing to symmetry, $\tau_{x y}=0$ along the $x$ axis. Thus $\sigma_x$ and $\sigma_y$ are the principal stresses along the $x$ axis. (a) Using Eqs. (4.2-37) with $y=0$, reduce $\sigma_x-\sigma_y$ to the simplest form. (b) With $P=1.0 \mathrm{kN}, R=50 \mathrm{~mm}$, and $t=6 \mathrm{~mm}$ plot $\sigma_x-\sigma_y$, for $y=0$, as functions of $x$.

   The disk in Fig. 4.2-7 of Sec. 4.2.6 is sometimes used as a calibration specimen when using the experimental technique involving photoelastic fringes (see Chap. 8). The fringes depend on the difference in the principal stresses $\sigma_1-\sigma_2$. Owing to symmetry, $\tau_{x y}=0$ along the $x$ axis. Thus $\sigma_x$ and $\sigma_y$ are the principal stresses along the $x$ axis.
(a) Using Eqs. (4.2-37) with $y=0$, reduce $\sigma_x-\sigma_y$ to the simplest form.
(b) With $P=1.0 \mathrm{kN}, R=50 \mathrm{~mm}$, and $t=6 \mathrm{~mm}$ plot $\sigma_x-\sigma_y$, for $y=0$, as functions of $x$.

Advanced strength and Applied Stress Analysis

Richard Budynas 2nd Edition

Chapter 4, Problem 14

Instant Answer

Step 1

2-37) which relates the difference in principal stresses to the displacement in the y-direction: $\sigma_x - \sigma_y = \frac{P}{\pi R^2} \left(1 - \frac{r^2}{R^2}\right)$ Show more…

Show all steps

Thanks for your feedback!

The disk in Fig. 4.2-7 of Sec. 4.2.6 is sometimes used as a calibration specimen when using the experimental technique involving photoelastic fringes (see Chap. 8). The fringes depend on the difference in the principal stresses $\sigma_1-\sigma_2$. Owing to symmetry, $\tau_{x y}=0$ along the $x$ axis. Thus $\sigma_x$ and $\sigma_y$ are the principal stresses along the $x$ axis. (a) Using Eqs. (4.2-37) with $y=0$, reduce $\sigma_x-\sigma_y$ to the simplest form. (b) With $P=1.0 \mathrm{kN}, R=50 \mathrm{~mm}$, and $t=6 \mathrm{~mm}$ plot $\sigma_x-\sigma_y$, for $y=0$, as functions of $x$.

Play audio

Feedback

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later

Please give Ace some feedback