solve this problem using lognormal assumption of the load. The magnitude of a lo

ID: 3205384 • Letter: S

Question

solve this problem using lognormal assumption of the load.

The magnitude of a load acting in a structure can be modeled by a normal distribution with a mean of 100 kip and a standard deviation of 20kip.

(a) If the design load is considered to be the 90th percentile value, determine the design load.

(b) If the design load is considered to be the mean +2 standard deviation value, what is the probability that it will be exceeded?

(c) A load of magnitude less than zero is physically illogical; calculate its probability. Is a normal distribution appropriate to model the load?

a) here for 90th percentile from normal value table ; z =1.2815

hence design load =mean +z*std deviation =125.63

b) probabilty that design load exceed +2 std deviation =P(Z>2) =1-P(Z<2) =1-0.97725 =0.02275

c) probabilty of load less then 0=P(X<0) =P(Z<(0-100)/20) =P(Z<-5)=2.866*10-7

as probabilty of load less then 0 is approximately 0, but not exactly ), hence in this case it is not appropriate.

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.