146 CHAPTER 5 Energy Methods
Due to the temperature rise, the increase in length of the member BC is 3× 103 × 30 ×
7 × 10 −^6 =0.63mm. The truss has a degree of internal statical indeterminacy equal to 1 (by inspec-
tion).WethereforereleasethetrussbycuttingthememberBC,whichhasexperiencedthetemperature
rise,asshowninFig.5.22(b);weshallsupposethattheforceinBCisX 1 .Sincetherearenoexternal
loadsonthetruss, (^) BCiszeroandthecompatibilityconditionbecomes
a 11 X 1 =−0.63mm (i)
inwhich,asbefore
a 11 =
∑n
j= 1
F1,^2 jLj
AE
NotethattheextensionofBCisnegative,sinceitisoppositeindirectiontoX 1 .Thesolutionisnow
completedinTable5.8.Hence,
a 11 =
48000
200 × 200000
=1.2× 10 −^3
Fig.5.22
Self-straining due to a temperature change.
Table 5.8
Member Lj(mm) F1,j F^2 1,jLj Fa,j(N)
AB 4000 1.33 7111.1 − 700
BC 3000 1.0 3000.0 − 525
CD 4000 1.33 7111.1 − 700
DA 3000 1.0 3000.0 − 525
AC 5000 −1.67 13888.9 875
DB 5000 −1.67 13888.9 875
=48000.0