A 25 ft. reinforced concrete beam is being designed to support a uniformly distributed load. This load has an average value of 1.4 kip/ft with a standard deviation of 0.3 kip/ft. The average flexural resistance of the beam is 230 ft-kip with a standard deviation of 15 ft-kip, and the average shear resistance of the beam is 45 kip with a standard deviation of 7 kip.
1) Find the global safety factor in both flexure and shear (note: safety factor = resistance/load effect)
2) Find the safety index in both flexure and shear
3) If the average flexural resistance is increased to 270 ft-kip with the same standard deviation of 15 ft-kip, find the new safety index in flexure
4) If the standard deviation of the shear resistance is decreased to 5 kip with the same shear resistance, find the new safety index in shear
5) Comment on your results
