q = PIL D. C A. p.

A pontoon bridge (see figure) is constructedof two longitudinal wood beams, known as balks,that span between adjacent pontoons and supportthe transverse floor beams, which are called chesses.For purposes of design, assume that a uniform floorload of 7.5 kPa acts over the chesses. (This loadincludes an allowance for the weights of the chessesand balks.) Also, assume that the chesses are 2.5 m long and that the balks are simply supported with aspan of 3.0 m. The allowable bending stress in thewood is 15 MPa.(a) If the balks have a square cross section, what istheir minimum required width bmin?(b) Repeat part (a) if the balk width is 1.5 b andthe balk depth is b; compare the cross-sectionalareas of the two designs.

A cantilever beam AB supports a distributed load of peak intensity g, acting over one-half of the length (see figure). (The beam has constant flexural rigidity EI. Use the second-order differential equation of the deflection curve. Enter the magnitudes.) ly 90 A C В L/2- L/2 Derive the equations of the deflection curve for the beam. (Use the following as necessary: qo, L, E, I, x.) Osxs v(x) = sxsL vx) = Also, obtain formulas for the deflections 8, and 8. at points B and C, respectively. (Use the following as necessary: 9,, L, E, I.) 7 160 E·I 11 %0 L3 192 E·I

2kN/ m y = kx? vertex 3 m A 1 m 3 m 2kN/ m A cantilever beam (fixed at A) is acted upon by a cubic distributed load as shown in the figure. Calculate the support reactions at point A. FBD is mandatory.