For the cantilever and simply-supported beams given below use Double Integration to determine the slope and displacement equations and graph both results versus positon along the beam. A 7 ft Pin A 2 kips/ft 3 kips/ft Bmm 10 ft 8 kips B 50 kip-ft

A two-span, continuous wood girder (E = 2,000 ksi) supports a roof patio structure (part (a) of the figure). A uniform load of intensity q acts on the girder, and each span is of length 8 ft. The girder is made up using two 2 x 8 wood members (part (b) of the figure). a q= 17.0 lb/ft -8 ft (a) B 8 ft 41 8 in. 2 in. 2 in. Section a-a (b) 000 8 in. Ignore the weight of the beam. Use the nominal dimensions of the beam in your calculations. (Solve by the method of superposition. The beam has constant flexural rigidity EI, unless otherwise stated.) (a) Find the reactions at A, B, and C. (Enter your answers in lb. Round your answer for Rg to at least one decimal place. Use the statics sign convention.) lb RA RB = lb RC lb

For the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at B and (b) the deflection of the beam at C. Assume a constant value of El = 27 x 106 lb-ft² for the beam; w₁ = 6200 lb/ft, LAB = 7.0 ft, Lgc = 15 ft. Lcd = 8 ft. Wo X LBC LCD LAB Answer: (a) 0g = (b) vc= B rad in. D

For the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at C (positive if counterclockwise and negative if clockwise). (b) the deflection of the beam at C. Assume LAB = 250 mm, LBC= 170 mm, LCD= 130 mm, LDE = 310 mm, Mp = 270 N-m, P = 1610 N and a constant value of EI = 590 × 106 N- mm2 for the beam. P MB B D LAB LBC LCD LDE Answers: (а) Ос 3 rad (b) vc = mm

sketch the deflected structure of this frame (just shape no exact values for how much deflection). This is linear analysis so only looking at the displacement of the nodes. Note that D is a hinge support, E is fixed and C is a roller

Problem Set 1: The stepped beam of length 4a carries a distributed load of intensity Wo over its middle half. The moments of inertia are 1.5l, for the middle half and Io for the rest of the beam. Find the displacement of the beam at its midspan. (Hint: Utilize symmetry and analyze the right half of the beam only). Use Double Integration A Wo mim 2a B. a D