Question

3.- At the ambient temperature of 20 ° C, there is a 1.5 mm gap between the ends of the rods shown below when the temperature reaches 140 ° C. Find:

a) the normal stress on the aluminum rod,

b) changing length of aluminum rod.

Make the free body diagram and explain step by step

1.5 mm 325 mm 225 mm A B Aluminum A = 2000 mm E = 75 CPA a = 23 x 10-6/C Stainless steel Acero inoxidable A= 500 mm E = 190 CPa a = 173 x 10-60 Fig. 3

Answer 1

The temperature difference is Woritter aq 140°C -20c AT AT 120c = Now foree thermal expansion is expressed ag 67 Laca ATT Lg Lg AT &T (325*23x160x120 ) + (225*17.3x106x120) & 1.3641 mm Now shortening due to 'p" constraint is given aq 8p = (1.3641– 1.5)mm 8p 0.1359 mm P P. op = pla Aa Ea + plg Ag Eg 225 + 3) P Ep = (-325 and ② 2000 x 75x10 800x190x103 bp = (3.6469x106) P Equate ① 0.1359 3.64698100 p P =-37264.5N p = - 37.2645 KN

by ба = The normal stress on the aluminums nod i8 givers 오 Aa са (-37264.5)N 2000 mm "а 18.632 MPa changing length of aluminum nod is Written as Pla Sa = Lada AT- Aata 325 da = 325x23x156x120 - (-37264.5 2000x 75 x103 &a 0.9779 moms - da =0.977 mm