Chapter 1, Problem 20P

A beam subjected to axial loading will experience an axial stress, σ_a. If in addition, the beam is subjected to a bending load, a bending stress, σ_b, will also occur at the outer fibers of the beam. The maximum stress at the outer fibers of the beam will be σ_max = σ_a + σ_b. Assume that σ_a and σ_b are independent and $\bar{\sigma }\text{ = 90 MPa, }{\hat{\sigma }}_{{\sigma }_a}\text{ = 8}\text{.4 MPa}$, $\bar{\sigma }\text{ = 383 MPa, }{\hat{\sigma }}_{{\sigma }_b}\text{ = 22}\text{.3 MPa}$. The rod is made of a steel with $\overline{S_y}\text{ = 553 MPa}$ and ${\hat{\sigma }}_{S_y}\text{ = 42}\text{.7 MPa}$. Assuming the strength and load have normal distributions, determine the design factor and the reliability guarding against yielding.