· Normal and shear stress on
diagrams must
always cancel each
other out .
· [Fx = 0
,
[Fy = 0
,
[Fz = 0
Pressure radius
pR
·
Hoop Stress
, Oyy =
T thickness
·
longitudinal Stress
,
Our =PR Spherical Pressure Vessel A
Cylindrical Pressure Vessel
· For a spherical pressure
vessel , stresses in all directions are
equal due
to
symmetry .
, Summary
· Ear =P o
, Eyy
=
c ,
E22 =
i
· Volumetric strain
,
Evol =
Exc +
Eyy + Ezz
has Eas
· 2D
only and
Eyy
· Enr =
"Bright-Ukleft-due or
Eyy =
dya Local strain
· strain
only happens when there is a
change in shape .
deformation does not volume
· shear
change
dy shear strain if
angle at left and bottom top & right reduces
dun+ a
the
·
Vay = a+ B = -
ve shear strain if
angle at bottom and left increases
· If
angle becomes
larger , expect negative shear strain
· solid
body rotation has no shear because it is
just rotating ,
there
is no deformation .
translations have
·
Rigid body zero shear strain
=
Uky = dur d
+
· Can also be expressed as
Exy
2 like this positive
· Arrows
pointing is a shear