东南大学：《建筑力学 Architectural Mechanics》课程教学课件（英文讲稿）A17 Strength Theory

Yield Criteria for Ductile Materials4. Maximum distortion energy (von Mises)OUcriteria:+YA(1+vC(g。-0,)+(c,-0)+(o。-0a)a6E-OYOGa+OY1D at yielding(, =0y,0, = 0, = 0) (1+v)Da=uyQYB3E2D(o。±0,0, ±0,0。=0)Economic criteria(1+v-0,0,+o?=ud3E· All three principal0-0,0,+0,=0,stress components areua=uytaken into3D(g。± 0,, ±0,0。+0))二Ua=uyconsiderationF[(0。-0,) +(0, -0.) +(0。-0.)]<0y6

4. Maximum distortion energy (von Mises) criteria:                         2 2 2 2 2 2 2 2 2 2 2 2 1D at yieldi 1 3 1 3 1 ng , 0 : 2 0, 0, 0 : 3 0, 0, 2 : 1 6 0 Y Y d a a Y b d a b b c c a a b b d Y a b c a c a b c a b b Y d Y a b b c c a u E D D u E u E u u u u                                                                                   Y    • Economic criteria. • All three principal stress components are taken into consideration. 6 Yield Criteria for Ductile Materials

Summary of Four Strength TheoriesAll of the four types of strength theory can be written in a universalform, in terms of an effective stress o,:1. Maximum tensile stress criteria: Ori = O, ≤[α]2. Maximum tensile strain criteria: ,2 = , -v(α2 +0,) ≤[α]3. Maximum shearing stress: Or3 = , -O, ≤[α]4. Maximum distortion energy criteria:[(0。-0,) +(0, -0.) +(0。-.) ]≤[0]ONote: the limit stress has been replaced by the allowable stress7

1. Maximum tensile stress criteria:  r1 1     2. Maximum tensile strain criteria:       r2 1 2 3     ( )   3. Maximum shearing stress：     r3 1 3      4. Maximum distortion energy criteria:         2 2 2 4 1 2         r a b b c c a            All of the four types of strength theory can be written in a universal form, in terms of an effective stress σr : 7 Summary of Four Strength Theories Note: the limit stress has been replaced by the allowable stress