To use a stress-strain diagram to determine the ultimate stress of a material and to determine the minimum diameters of posts supporting a beam under static loading. As shown, beam ABC is subjected to a load at A that has mass W = 850 kN. The cylindrical posts BD and CE are made of the same material, whose properties are shown in the stress- strain diagram provided. Let a = 9.0 m, b = 5.5 m, r = 5.0 m, and 8 = 7.5 m. A W D b B C E S (MPa) a more realistic curve 1200 800 400 0.10 0.20 0.30 0.40 3 To understand how the modulus of resilience and modulus of toughness are related to the stress-strain curve and strain hardening. Forces and displacements are important in engineering design. Sometimes, however, the total energy of an interaction also is a key design factor. For example, when designing an impact absorber, the material must be able to handle all the kinetic energy of the impacting object. There are two material properties that provide a measure of a material's ability to handle energy. The total energy that a material can handle depends on the absolute dimensions. The corresponding material property is the strain energy density, which is a measurement of the energy per unit volume. The modulus of resilience is the maximum strain energy density a material can absorb without any plastic deformation. The modulus of toughness is the maximum strain energy density a material can tolerate before fracturing.