6三向应力状态( Three-Dimensional State of Stress): 三个主应力都不为零的应力状态。 G二向应力状态( Plane state of stress): 一个主应力为零的应力状态。 单向应力状态( Unidirectional state of stress): 个主应力不为零的应力状态。 Ox B
单向应力状态（Unidirectional State of Stress）： 一个主应力不为零的应力状态。 二向应力状态（Plane State of Stress）： 一个主应力为零的应力状态。 三向应力状态（ Three—Dimensional State of Stress）： 三个主应力都不为零的应力状态。 A s sx x tzx s sx x B t xz
ANALYSIS OFSTRESSAND STRAIN 87-2 ANALYSIS OF THE STATE OF PLANE STRESS ANALYTICAL METHOD y equivalent x 2 O
§7–2 ANALYSIS OF THE STATE OF PLANE STRESS — ANALYTICAL METHOD equivalent sx txy sy x y z x y sx txy sy O
§7-2平面应力状态分析—解析法 y 等价 xy x 2 O
§7–2 平面应力状态分析——解析法 等价 sx txy sy x y z x y sx txy sy O
ANALYSIS OFSTRESSAND STRAIN I Stresses acting in arbitrary inclined plane Stipulate: O oais positive if its direction is the same with one of the external normal line of the section;2 tois positive if it make the element rotate clockwise; 3 A countclockwise angle a O Fig is considered to be positive Assume that area of the inclined section is s According to the equilibrium of the free body we get y xn∑=0 O S-O Scos a+t Scosasina O x Fig2 -O Ssin att ssin acos=0
Stipulate：s is positive if its direction is the same with one of the external normal line of the section；t is positive if it make the element rotate clockwise； A countclockwise angle is considered to be positive. Fig.1 Assume that area of the inclined section is S. According to the equilibrium of the free body we get： Fn =0 sin sin cos 0 cos cos sin 2 2 − + = − + s t s s t S S S S S y yx x xy 1、Stresses acting in arbitrary inclined plane x y sx txy sy O sy t yx sx s t x y O t n Fig.2
任意斜截面上的应力 规定:◎σ,截面外法线同向为正 2τ绕研究对象顺时针转为正; 6a逆时针为正。 O 图1 设:斜截面面积为S,由分离体平衡得: ∑ F=0 y X o s-o Scos a+T Scosasina -o Ssin a+r Ssinacosd-0 O x 图2
规定：s 截面外法线同向为正； t 绕研究对象顺时针转为正； 逆时针为正。 图1 设：斜截面面积为S，由分离体平衡得： Fn =0 sin sin cos 0 cos cos sin 2 2 − + = − + s t s s t S S S S S y yx x xy 一、任意斜截面上的应力 x y sx txy sy O sy t yx sx s t x y O t n 图2