Question

To estimate the long-term settlement of a footing, a geotechnical engineer uses the total load on the footing calculated by summing the dead load of the structure and the live load (loads imposed by furniture and occupancy). Because each is the sum of many relatively small weights, the engineer assumes that the dead load (X) and the live load (Y) are normally distributed. He collected data from numerous buildings of a similar type and found that the mean and the standard deviation of X are 100 kips and 10 kips, respectively, and the mean and the standard deviation of Y are 40 kips and 10 kips, respectively. Assuming that the design load is the total load for which the exceeding probability is 5%. Determine the design load.

Answer 1

The linear combination of the sum of 2 normal variables is also a normal variable. We have here:

Therefore, the distribution for total load here is given as:

From standard normal tables, we have here:
P(Z > 1.645) = 0.05

Therefore the design load here is computed as:
= Mean + 1.645*Std Dev

therefore 163.2638 kips is the design load here.