The basic procedure followed to generate sample data for the stress problem outlined in the problem statement is as follows:

• 1,000 random numbers were generated for each variable using the RAND( ) function in Microsoft Excel.

• The random numbers were then converted to random variables by inverse transformation.

• The variables c and I are normally distributed and were transformed by the following equation: , where m_i is given by the problem statement, s = m *COV, where COV is given in the problem statement, and f^-1 is determined by the NORMSINV() function in Excel.

• The variables M and f_y are lognormally distributed and were transformed by the following equation: ,where s_y² = ln[1 + (s_x/m_x)²], s_x and m_x are the same as above, m_y = ln(m_x) – 0.5s_y², and f^-1 is again determined by NORMSINV( ).

• The mean, standard deviation, COV, maximum, minimum, and sample size were determined for each random variable and then compared with the problem specifications.

• s was then calculated for each random variable by the following equation: to determine beam failure. If s > f_y, then failure occurred, otherwise it was a non-failure case.

To view the tables of random variables click on the links below.

Random variable c

Random variable M

Random variable I

Random variable fy