In a harbor structure exposed to the sea, cracks form along the length of tension members in the reinforced-concrete trusses. Crack occurrence along the length of the member follows a (spatial) Poisson process with mean rate of 2/ft. The members are 20 ft long. A crack exposes the reinforcing steel to corrosion at that point. At any point in time the amount of corrosion and hence the strength loss at any crack is approximately exponentially distributed. At present the mean loss is 1 kip. The remaining strength of any member is its initial strength, 100 kips, minus the largest strength loss along the member.
(a) Find the distribution of the remaining strength of any member.
(b) What is the probability that any particular member will fail when subjected to an applied force of 90 kips?
(c) What is the distribution of the strength of a (statically determinate) truss that will fail if any of 10 such (independent) tension members fail? (Neglect the possibility that failure of the truss will be caused by anything other than failure of one of these 10 members.) A unit load causes a unit force in each member.