Answer:
Largest longitudinal spacing = 60mm
Step-by-step explanation:
If we can find the shear stress and allowable load in one nail, then we can compute the needed spacing of the nails.
Now, moment of Inertial of rectangular section is given as;
I = bh³/12
Since nailed together, the effective total height will be 150mm
Thus, I = (100 x 150³)/12 = 28.125 x 10^6 mm⁴ = 28.125 x 10^(-6) m⁴
Also, the area of the section = 100 x 50 = 5000 mm²
Now, from the centre of the 150mm length to the centre of the 50mm joined part, the centroid is calculated as 50mm.
Thus, centroid ȳ1 = 50mm
So moment of area = 5000mm² x 50mm = 250,000 mm³ or 250 x 10^(-6) m³
Formula of shear stress(q) = VQ/I
q = (1500 x 250 x 10^(-6))/(28.125 x 10^(-6)) = 13.333 x 10³ N/m
For the required spacing, we'll use the formula;
qs = (Shearing force in each nail) x 2
Where q = shear stress and s = spacing
Thus;s = (400 x 2)/13.333 x 10³ = 60 x 10^(-3)m = 60mm