Page 226 - Introduction to Continuum Mechanics

Stress 211

where a and ft are constants.
(a) Determine and sketch the distribution of the stress vector acting on the square in thex\ = 0 plane
with vertices located at (0,1,1), (0,-1,1), (0,1,-1), (0,-1,-1).
(b) Find the total resultant force and moment about the origin of the stress vectors acting on
the square of part (a).
4.8, Do the previous problem if the stress distribution is given by

and all other 7)y = 0.

4.9. Do problem 4.7 for the stress distribution

and all other TJy = 0.
4.10. Consider the following stress distribution for a circular cylindrical bar

(a) What is the distribution of the stress vector on the surfaces defined by
X2 + *3 = 4, *! = 0 and *i = / ?
(b) Find the total resultant force and moment on the end face*i= /.

2 2
4.11. An elliptical bar with lateral surface defined by jef + 2*3 = 1 has the following stress
distribution

(a) Show that the stress vector any point^j^^s) ° n tne lateral surface is zero.
(b) Find the resultant force and resultant moment about the origin O of the stress vector on
the left end face x\ ~ 0.

4.12. For any stress state T., we define the deviatoric stress S to be