Lezione 7: Strength limited design

Question 1

Talk about the yielding of columns and ties

Answer 1

A tie is a rod loaded in tension while a column is loaded in compression.
The state of stress within them is uniform and the material remains elastic at stresses below the yield strength (σ < σy)

Question 2

Talk about yielding in beams in bending

Answer 2

In bending, the maximum longitudinal stress on a
beam or panel is σmax = Mym/I = M/Ze
If σmax exceeds σy then the component is no
longer elastic. At a moment well beyond the yield strength, a component will collapse by rotating about its plastic hinge.

Question 3

What parameters help us understand the plasticity of the section?

Answer 3

Zp is the plastic section modulus, represents the full plasticity of the section.
Ze is the elastic section modulus
Both of them are functions of shape that help define the failure of a beam in bending. Zp/Ze is the safety margin, close to 1 for efficient section shapes.

Question 4

Talk about yielding of shafts and helical springs

Answer 4

For a shaft loaded in torsion, failure occurs when the maximum surface stress exceeds the yield strength of the material, tau max = TR/K. Failure in shear happens when tau max = σy/2. The max torque applicable to the shaft is when tau = k

Question 5

Talk about yielding in contact stresses

Answer 5

Yielding at contacts is closely linked to failure by wear and fatigue – when surfaces are placed in contact they touch at a few discrete points – if the surfaces are loaded, the contacts flatten elastically and the contact areas grow. For a round sphere in contact with a flat surface: tau max = F/2πa^2 (where a is the radius of the contact area. If this exceeds the shear yield strength k=σy/2, a plastic zone appears beneath the center of the contact at a depth a/2)

Question 6

Talk about stress concentrations

Answer 6

Holes, slots, threads, and changes in section concentrate stress locally – yielding will start at these places but the initial yielding is not usually catastrophic