Wood beams cantilever out from a house to form an elevated deck. The owners wanted a bigger deck, so they extended the beams and added columns at the far ends.The addition was not engineered, so the...

Wood beams cantilever out from a house to form an elevated deck. The owners wanted a bigger deck, so they extended the beams and added columns at the far ends.The addition was not engineered, so the owners have no idea whether the deck is safe. Now that they want to sell the house, they have hired our firm to evaluate the capacity of the deck in its current condition. Although this is not a strength issue, the senior engineer on the team wants us to determine the peak vertical deflection of the extended beam due to a lateral load on the handrai1.The handrails are rigidly connected to the ends of some beams rather than connecting to the columns. Each beam is 50 x 300 lumber (I = 9.63x 10~ mm4, E = 10 GPa = 10 kN/mm2 ) .Because there is only a couple moment acting on the extended beam, the Conjugate Beam Method is probably more efficient than the Double Integration Method.

a. Guess the location of the peak vertical displacement (e.g., middle of span AB, near C).

b. Estimate the peak vertical displacement considering the original configuration of the deck: a couple moment at the end of cantilevered segment AB. Will this provide an upper bound, a lower bound, or just an approximation for the actual peak vertical displacement? Justify your answer.

c. Construct the moment diagram for the deck beam as currentlyconstructed. Identify at least three features of the moment diagram that suggest you have a reasonable answer. d. Determine the location and value of the peak vertical displacement for the beam. Homework Problems 283 e. Evaluate the displacement prediction using your results from part (b). f. Comment on why your guess in part (a) was or was not close to the solution in part (d).