Answer to Question #257322 in Mechanics | Relativity for Hemanth

Question

Two wooden box beams (A and B) have the same outside dimensions (bh) and the same thickness t throughout, as shown in the figure. Both beams are formed by nailing. with each nail having an allowable shear load of f ball The beams are designed for a shear force of V. The magnitudes of the different parameters are: b=190 mm h=320 mm.t=24 mm f nall =250 N and V = 3kN

Answer 1

$I=\frac 1{12}(bh^3-b_1h_1^3)=340.69\cdot 10^6~mm^4,$

$\frac{2F}s=\frac{VQ}I,\implies s_{max}=\frac{2FI}{VQ},$

a)

$Q=A_pd_p=bt\frac{h-t}2=680\cdot 10^3~mm^3,$

$s_A=78.3~mm,$

b)

$Q=A_fd_f=(b-2t)t\frac{h-t}2=544\cdot 10^3~mm^3,$

$s_B=97.9~mm,$

c)

$s_B>s_A$ beam B is more efficient.