东南大学：《弹性力学》课程教学课件（英文讲稿）04 Stress and Equilibrium

Sign Convention: Normal stress: tension positive / compression negative: Shear stress: product of the surface normal (the firstsubscript) and the stress direction (the second subscript): All stress components shown in the figure are positive.TVtyztxyTzyZXtxza6

6 Sign Convention • Normal stress: tension positive / compression negative • Shear stress: product of the surface normal (the first subscript) and the stress direction (the second subscript) • All stress components shown in the figure are positive

Traction on an Obligue Plane - 2Df0-ZFn[0=ZF,TiT"A= o,AAcos0+twAsin0AATnAA = t..AAcosO+o.Asin0=o.n.+tn.yxXXyx"trn.+o.n>{T" T"}vxTnoBa2D Cauchy's relation=n·o7

    0 0 cos sin cos sin x y x x yx y xy y x x x yx y y xy x y y x xy x y x y yx y F F T A A A T A A A T n n T n n T T n n T n                                                                n n n n n n n n T = n σ 7 Traction on an Oblique Plane - 2D 2D Cauchy’s relation n t A  x  y yx  xy  n T 

Traction on an Obligue Plane - 3D. The state of stress at a point is defined by?nzOx,Ty,TxTyx,Oy,Tye,T-xTay,O,o2 Consider the tetrahedron with unit normal nTxyftxz(nn·ei620cos(n,e,n,fnne,Wzy0 =ZF，00=ZF, 0=ZFtozT"A=o,AAn,+tuAAn,+tAnT"A= txAn,+o,AAn,+t,AAnT"A=t.AAn, +tAn, +o.AAn=n,o3D Cauchy's relationT=n.o8

  Tx n   Ty n   Tz n • The state of stress at a point is defined by: , , , , , , , ,          x xy xz yx y yz zx zy z • Consider the tetrahedron with unit normal n cos ,   0 , 0 , 0 i i i i x y z x x x yx y zx z y xy x y y zy z z xz z yz y z z i j ji n F F F T A An An An T A An An An T A An An An T n                                                  n n n n n n e n e n e T = n σ 3D Cauchy’s relation 8 Traction on an Oblique Plane - 3D