Shear Flow in Built$-$up Beams

A beam is made from three boards nailed together. The nails connecting the three boards are spaced every $200$ mm and $V=1\mathrm{.}58kN.I_x=322\mathrm{.}8({10}^5)m{m}^4,I_y=899\mathrm{.}1({10}^6)m{m}^4$

Calculate $Q$ the first moment of area, of the board that is to be connected to the vertical boards. $(3$ pts$)$

a$.1\mathrm{.}41({10}^6)m{m}^3$

b$.1\mathrm{.}36({10}^5)m{m}^3$

c$.1\mathrm{.}31({10}^6)m{m}^3$

d$.1\mathrm{.}26({10}^5)m{m}^3$

view or the cross$-$section

Calculate $q,$ the shear flow, in the built$-$up beam as constructed. $(3$ pts$)$

a$.6\mathrm{.}37\frac{N}{mm}$

b$.6\mathrm{.}91\frac{N}{mm}$

c$.7\mathrm{.}18\frac{N}{mm}$

d$.6\mathrm{.}64\frac{N}{mm}$

view or the top or the beam

Calculate the shear force resisted by each nail. $(4$ pts$)$

Shear Force per Nail$=$