Fig. 3.13 (a) shows a copper tube of length Lc having cross sectional area Ac is placed between two very rigid caps made of invar. Four bolts each of dia ‘d’ are symmetrically arranged parallel to the axis of the tube and lightly tightened. If the temperature of the assembly is raised by ‘ Δt ‘, the stresses that will be developed in copper and steel materials are as follows :
As acu >ast, the thermal elongation of copper is δtc and δtc is the thermal elongation of steel. As the copper and steel members are rigidly capped by invar materials, there will be compromise between copper and steel expansion and the final level will be say X-X line (Fig. 3.13(b)).
So steel bolts will be pulled up to XX by increasing δs more whereas the copper will be shortened by o,. So we can write
δ tc = δc + δs +δ
Lac Δt = PC LC / AC EC + PS LS / AS ES + LaS ΔT
4PS = PC
There are two unknowns P5 and P, which can be solved from equations (3.3) and (3.4).
We can take Ls = Lc.