Moment of inertia
I=200(2503)12−150(2003)12=160416666.7 mm4
Maximum Shear
Vmax=23P
Value of P based on the strength of nails
R=2(1300)=2600 N
Q=150(25)(112.5)=421875 mm3
s=RIVQ
125=2600(160416666.7)23P(421875)
P=11.86 kN
Value of P based on shear strength of wood
Q=200(125)(62.5)−150(100)(50)=812500 mm3
Fv=VQIb
0.827=23P(812500)160416666.7(50)
P=12.25 kN
For safe value of P, use P = 11.86 kN answer for part (1)
Maximum Flexural Stress
Maximum Moment
Mmax=1.2(23P)=0.8(11.86)
Mmax=9.488 kN⋅m
fb=McI
fb=9.488(125)(10002)160416666.7
fb=7.39 MPa answer for part (2)