(Solved): A wooden beam is fabricated from one 210 and two 210 dimension lumber boards to form the double ...

A wooden beam is fabricated from one $$2\times 10$$ and two $$2\times 10$$ dimension lumber boards to form the double-tee cross section shown. The beam flange is fastened to the stem with nails. Each nail can safely transmit a force of $$182\mathrm{lb}$$ in direct shear. The allowable shear stress of the wood is $$74\mathrm{psi}$$. Assume $$b_1=10$$ in., $$b_2=2$$ in., $$d_1=2$$ in. $$d_2=10$$ in. (a) If the nails are uniformly spaced at an interval of $$s=3.3$$ in. along the span, what is the maximum internal shear force $$V$$ that can be supported by the double-tee cross section? (b) What nail spacing s would be necessary to develop the full strength of the double-tee shape in shear? (Full strength means that the maximum horizontal shear stress in the double-tee shape equals the allowable shear stress of the wood.) Answers: (a) $$V=$$ lb. (b) $$5=$$ in.