Show that the octahedral shear stress τ0 (the magnitude of the tangential component of the traction vector on the octahedral plane, that is, a plane whose normal makes equal angles with the three principal directions) is given by τ0 = q 2 3 IIs, where IIs is the second invariant of the stress deviator.

Ahouse has the following electrical appliance usage (1) single 40w lamp used for 4 hours per day (2) single 60w fan used for 12 hours per day (3) single 200w refrigerator that runs 24 hours per day with compressor run 12 hours and off 12 hours find the solar power inverter size in watt with correction factor of 1.25.

Determine whether or not it is possible to compress air adiabatically from k to 140 kpa and 400 k. what is the entropy change during this process?

Ajournal bearing has a journal diameter of 3.250 in with a unilateral tolerance of 20.003 in. the bushing bore has a diameter of 3.256 in and a unilateral tolerance of 0.004 in. the bushing is 2.8 in long and supports a 700-lbf load. the journal speed is 900 rev/min. find the minimum oil film thickness and the maximum film pressure for both sae 20 and sae 20w-30 lubricants, for the tightest assembly if the operating film temperature is 160°f. a computer code is appropriate for solving this problem.