In this picture the copper length of Lc has the cross sectional area AC. This tube is placed in between the two very rigid invar cap.There are four different bolts having diameter ‘d’. These are arranged properly in the direction which is completely parallel to the axis. Now, in case of raising temperature Δt, the stress will get developed in steel as well as in copper material.
In case of acu >ast
The thermal elongation of Copper is δtc
The thermal elongation of steel is δts
Compromise of steel and copper materials can be seen and their ultimate change can be noticed as X-X line as
So bolt of steel is pulled up increased by δs and copper is decreased by o
Thus, δ tc = δc + δs +δ
Lac Δt = PC LC / AC EC + PS LS / AS ES + LaS ΔT
4PS = PC
The two unknowns are here as Ps and Pc and this can be solved easily by knowing
Ls = Lc.