timber and steel section

Problem 1007
A uniformly distributed load of 300 lb/ft (including the weight of the beam) is simply supported on a 20-ft span. The cross section of the beam is described in Problem 1005. If n = 20, determine the maximum stresses produced in the wood and the steel.
 

Problem 1006
Determine the width b of the 1/2-in. steel plate fastened to the bottom of the beam in Problem 1005 that will simultaneously stress the wood and the steel to their permissible limits of 1200 psi and 18 ksi, respectively.
 

Problem 1005
A timber beam 6 in. by 10 in. is reinforced only at the bottom by a steel plate as shown in Fig. P-1005. Determine the concentrated load that can be applied at the center of a simply supported span 18 ft long if n = 20, f_s ≤ 18 ksi and f_w ≤ 1200 psi. Show that the neutral axis is 7.1 in. below the top and that I_NA = 1160 in.⁴.
 

From assumption no. (3) in the previous page: The strains of any two adjacent materials at their junction point are equal.
$\epsilon_s = \epsilon_w$

$\dfrac{f_{bs}}{E_s} = \dfrac{f_{bw}}{E_w}$

$\dfrac{f_{bs}}{f_{bw}} = \dfrac{E_s}{E_w}$