505 Steel Band Saw

Problem 505
A high strength steel band saw, 20 mm wide by 0.80 mm thick, runs over pulleys 600 mm in diameter. What maximum flexural stress is developed? What minimum diameter pulleys can be used without exceeding a flexural stress of 400 MPa? Assume E = 200 GPa.

Solution 505

Flexural stress developed:
$M = \dfrac{EI}{\rho}$

$f_b = \dfrac{Mc}{I}$
$f_b = \dfrac{(EI / \rho)c}{I}$
$f_b = \dfrac{Ec}{\rho}$
$f_b = \dfrac{200000(0.80/2)}{300}$
$f_b = 266.67 \, \text{MPa}$

Minimum diameter of pulley:
$f_b = \dfrac{Ec}{\rho}$
$400 = \dfrac{200\,000(0.80/2)}{\rho}$
$\rho = 200 \, \text{mm}$

diameter, $d = 400 \, \text{mm}$