Determine the load and strength variability

Question

Solve the following problem:

Redesign the box-beam of Example 1 and 2 to make better use of the material; i.e., changing the geometry of the cross-section in such a way that the serviceability (deflection) requirement is met without over dimensioning for strength as much as it is done in Example 2. Perform the new design for a reliability of 99.5% assuming the load and strength variability are represented by C_σ = 0.2, C_F = 0.3.

Example 1:

Design a box section to be used as a cantilever beam of length L = 2 m subject to a tip load P = 1000 N. Limit the tip deflection δ to 1/300 of the span L of the beam.

Example 2:

Verify that the box-beam (Figure ) designed in Example 1 is sufficiently strong, for a reliability of 99.5%, assuming the load and strength variability are represented by C_σ = 0.2, CF = 0.3.