1.Design a rectangular section for a cantilever beam that spans 12 feet out and has a dead weight of 2 kip/ft and a live load of 12 kips at the end of the beam. Assume concrete weighs 150 lb/ft^3, fy=60000 psi, f'c=4000psi and roe=(1/2)roe balanced. Roe is the ratio of nonprestressed reinforcement in a section, and roe balanced is the ratio of tensile reinforcing producing balanced strain condition. Show cross sections, including bar sizes, arrangements, and spacing.
2.Determine the magnitude of the average force acting on a highway bumper when a 5000-lb car traveling at 60 mph crashes against it. The time interval during which the car is brought to rest is 0.3 s. Assume the car is coasting when it strikes the bumper, the bumper does not move and the car does not bounce back.