Question

A cantilever beam with a square cross section is subjected to a bending stress due to a weight placed on its unsupported end. The bending stress for this loading condition is found using σ = 6FL / h^3 , where F is the force on the tip of the beam, L is the length of the beam, and h is the height of the beam cross section. The beam is made of 6061-T6 aluminum, which has a yield stress of 276 MP a. Due to manufacturing tolerances and uncertainty about the true mass and placement of the object at the end of the beam, your design team has provided the following uncertainties along with the nominal dimensions: h = 15mm ± 0.1mm; L = 30cm ± 1.0cm; F = 250N ± 25N; σyield = 276 MPa

Answer the following questions: a) What is the factor of safety for the beam considering the nominal bending stress? b) What is the factor of safety considering the maximum possible bending stress? Use a three standard deviation confidence interval to predict the stress (i.e. σmax = σnom + 3U (σ))?

Answer 1