Question

Two rods of different materials with coefficients of thermal expansion. Find out the displacement of the joint of the rods

Answer 1

 excellent question,

even i got messed up with that heating part

see the tolat length of the rod ie. fwom one wall to the other remains constant

now each rod will have two forces acting on it

Tensile force and the other due to the heating effect

each rod shall expand by:-

(a1l1T) - ((Fl1)/AY1))

where everything has its usual meaning

F is the thermal stress developed and A is cross section area

=> Tolat extension is:-

(a1l1T) - ((Fl1)/AY1)) + (a2l2T) - ((Fl2)/AY2))

now the summation for both the rods is zeroe (why?? read the 3rd line)

equate the expression to 0 and get the value of F!!

now the displace of the joint is given by :-

delta l  =  l1 + ((a1l1T) - ((Fl1)/AY1))  [ put the value of F here]!!

here you are

by my calculations the answer should be:-

 

(((l1l2(Y2a2 - Y1a1)T))) /((Y2l1 + Y1l2))

aM I RIGHt??