Page 356 - Introduction to Continuum Mechanics

340 The Elastic Solid

(c) Evaluate the effective modulus for Poisson's ratio equal to 1/3 and 1/2.
5.44. Let the state of stress in a tension specimen be given by TH = o, all other 7} ; - = 0.

(a) Find the components of the deviatoric stress T° = T — — T^l.

(b) Find the scalar invariants of T°
5.45. Three identical steel rods support the load P, as shown in Fig.P5.2. How much load does
each rod carry? Neglect the weights of the rod and the rigid bar.

Fig. P5.2

5.46. Solve the previous problem if the cross-sectional area of the middle bar is twice that of
the left- and right-hand bars.
5.47. Let the axis of a cylindrical bar be vertical and initially coincide with the j^ axis. If
KI — 0 corresponds to the lower face, then the body force is given by pB = -p gej. Assume
that the stress distribution induced by the body force alone is of the form

and all other 7^ = 0.

(a) Show that the stress tensor is a possible state of stress in the presence of the body force
mentioned above.
(b) If this possible state of stress is the actual distribution of stress in the cylindrical bar, what
surface tractions should act on the lateral face and the pair of end faces in order to produce
this state of stress.

5.48. A circular steel shaft is subjected to twisting couples of 2700 N • m. The allowable tensile
stress is 0.124 GPa. If the allowable shearing stress is 0.6 times the allowable tensile stress,
what is the minimum allowable diameter?