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

Strength Theorymi@se.er.cn

Strength Theory mi@seu.edu.cn

Contents·Strength Condition for Simple Stress States（简单应力状态的强度理论回顾·FractureCriteriaforBrittleMaterials（脆性材料强度理论)·YieldCriteriaforDuctileMaterials（塑性材料强度理论)·Summary ofFour StrengthTheories（四大强度理论）·Remarks on StrengthTheory（强度理论补充说明）·Measurement of Strain &StrainRosettes（应变计与应变花）2

• Strength Condition for Simple Stress States（简单应 力状态的强度理论回顾） • Fracture Criteria for Brittle Materials（脆性材料强度 理论） • Yield Criteria for Ductile Materials（塑性材料强度理 论） • Summary of Four Strength Theories（四大强度理论） • Remarks on Strength Theory（强度理论补充说明） • Measurement of Strain & Strain Rosettes（应变计与 应变花） Contents 2

Strength Condition for Simple Stress States.Tensile/compressivestress:. Torsional shearing stressFNT≤[]a≤[]代maxAmaxWmaxmax. Bending shearing stress: Bending normal stressM,FsS2≤[]≤[α]TOmaxmax1.bWmaxmax: Strength condition at locations under complicated stress state:→FdiCStrength theory: Preliminary: find the three principal stress components a, O, and o.3

• Tensile/compressive stress: • Bending normal stress: • Torsional shearing stress: • Bending shearing stress: • Strength condition at locations under complicated stress state: Strength theory x y z dx dz dy F F • Preliminary: find the three principal stress components σa , σb and σc . 3 Strength Condition for Simple Stress States max   max FN A           max   P max T W             * S max max Z z F S I b           max   max Z z M W          

Fracture Criteria for Brittle Materials: Brittle materials fail suddenly in tensile tests. The failure condition ischaracterized by the ultimate strength ou1. Maximum tensile stress criteria2.Maximum tensile strain criteriaFailure criteria: , = SuFailure criteria: O, =OuStrength condition:Strength condition: Oi ≤Ou0102 +0)≤8u61EA· Accurate for materials=9, -v(α2 +0,)≤0uprimarily under tensile stressstate.: Only applicable to linearly: No influences from 02, 0, areelastic brittle materials (untiltaken into considerationfailure)· O, must be tensile stress: Only accurate for few brittlematerials4

1. Maximum tensile stress criteria • Brittle materials fail suddenly in tensile tests. The failure condition is characterized by the ultimate strength σU . Failure criteria:   1  U Strength condition:   1  U • Accurate for materials primarily under tensile stress state. • No influences from σ2 , σ3 are taken into consideration. • σ1 must be tensile stress. 2. Maximum tensile strain criteria 1 U Failure criteria:    Strength condition:     1 1 2 3 1 2 3 U U E E                    • Only applicable to linearly elastic brittle materials (until failure) • Only accurate for few brittle materials 4 Fracture Criteria for Brittle Materials

Yield Criteria for Ductile Materials3. Maximum shearing stress (Tresca) criteriaOb1D at yielding : Tmax = Ty = Oy /2+y2D(o, ±0,0, ±0,0。=0)For o, and o, with the same signda+y-yOao; max(lo.l/o,)≤0yTmax=max2922For o, and o, with opposite signs,? Conservative criteria and0.-0b; a-0,<0Twidely adoptedmax22No influences from , is3D(α。+0,0, + 0,0±0)taken into consideration0i-03; 0,-0,≤0yTmax225

3. Maximum shearing stress (Tresca) criteria max 1D at yielding : 2 Y Y      For σa and σb with the same sign, max max , ; max ,   2 2 2 a b Y a b Y                 For σa and σb with opposite signs, max ; 2 2 a b Y a b Y             • Conservative criteria and widely adopted. • No influences from σ2 is taken into consideration.   1 3 max 1 3 ; 3 0, 0, 0 2 2 : Y a c Y D  b                  5 Yield Criteria for Ductile Materials 2 0, 0, 0 : D   a b c    