Question

stress analysis please answer ASAP

Show that Airy's stress function D = Cre sine satisfies the biharmonic equation. Also determine the stresses in polar co-ordinate system. 2 A 10-in. length of steel tubing (with properties of E 30 X 106 psi, v = 0.3 and a 7X10-5 F) having a cross-sectional area of 1 square in is installed with fixed ends so that it is stress- free at 80°F measurements indicate that the fixed ends separate by 0.008 in. What loads are exerted on the ends of the tube, what are the resultant stresses and strains? 3 Careful In operation, the tube is heated throughout to a uniform 480°F.

Answer 1

Tube thof dueto 9ncrease in king 10х 7X x (480-9) O.028 inch But fixed end Separates by O.O0& in hence actual deformahion O o 28 o.oo 8 o o 20 inch. O 00inch PL AE deformed posihon. actual pasitio РX /o 0 o2 oF Fixed end 2 Wx 30 x/06 Р- 60 Kido pound

stress = P 60 60KSI chamge in lengt 4n = o.02 inch X - 3 2-8XIinch cross Secon shape hence chage helec it But this wiM So -4 O O 20 O.0 020 -0-3 o.0029) Ez=
since we have to stop the bar to expand by 0.02 inch hence strain is compressive in x direction while tensile in other two directions.