Page 225 - Introduction to Continuum Mechanics

210 Problems

Problems

4.1. The state of stress at certain point of a body is given by

- —i
On each of the coordinate planes (normals ej, 62, 63) (a) what is the normal stress and (b)
what is the total shearing stress.

4.2. The state of stress at a certain point of a body is given by

(a) Find the stress vector at a point on the plane whose normal is in the direction
2 Cl + 2e 2 + e 3 .
(b) Determine the magnitude of the normal and shearing stresses on this plane.

4.3. Do the previous problem for a plane passing through the point and parallel to the plane
K\ - 2X2 + 3*3 = 4.
4.4. The stress distribution in a certain body is given by

Find the stress vector acting on a plane which passes through the point (1/2, V3~/2,3) and
2 2
is tangent to the circular cylindrical surface *i + x^ = I at that point.
4.5. Given T\\ = 1 Mpa, TII = — IMpa and all other TJy = 0 at a point in a continuum.
(a) Show that the only plane on which the stress vector is zero is the plane with normal in the
63-direction.

(b) Give three planes on which there is no normal stress acting.
4.6. For the following state of stress

1
findTn' and T ^' where e x' is in the direction of ej + 2e 2 + 3e 3 and 63'is in the direction
of e 1 4-e 2 ~e 3 .
4.7. Consider the following stress distribution