Page 230 - Introduction to Continuum Mechanics

Stress 215

(a) Find the value of C.
(b) The boundary plane x\ - x.^ = 0 for the body is free of stress. Determine the values of A
and B.
4.31. In the absence of body forces, do the stress components

satisfy the equations of equilibrium?
432. Repeat the previous problem for the stress distribution

433. Suppose that the stress distribution has the form (called plane stress)

(a) What are the equilibrium equations in this special case?
sucri
(b) If we introduce a function <p(x\^C2) that

will this stress distribution be in equilibrium with zero body force?
434. In cylindrical coordinates (r,0,z), consider a differential volume of material bounded by
the three pairs of faces r = r 0> r = r 0 + dr, B- 0 0> 6 = 6 0 + dO and z = z 0^ z - z 0 + dz.
Derive the equations of motion in cylindrical coordinates and compare the equations with
those given in Section 4.8.
435. Verify that the stress field of Example 4.8.1 satisfies the z-equation of equilibrium in the
absence of body forces.
436. Given the following stress field in cylindrical coordinates

Verify that the state of stress satisfies the equations of equilibrium in the absence of body force.