Solution to Problem 506 | Flexure Formula

$(\rho - 1)^2 + 20^2 = \rho^2$

$\rho^2 - 2\rho + 1 + 400 = \rho^2$

$2\rho = 401$

$\rho = 200.5 \, \text{in}$
 

$M = \dfrac{EI}{\rho}$

$f_b = \dfrac{Mc}{I} = \dfrac{(EI/\rho)c}{I}$

$f_b = \dfrac{Ec}{\rho} = \dfrac{(29 \times 10^6)(1/8)}{200.5}$

$f_b = 18\,079.8 \, \text{psi}$

$f_b = 18.1 \, \text{ksi}$           answer
 

$M = \dfrac{EI}{\rho} = \dfrac{(29 \times 10^6)\dfrac{1(1/4)^3}{12}}{200.5}$

$M = 188.3 \, \text{ lb}\cdot\text{in}$           answer