200 Mechanics of Materials $9.1 Fig.9.2.Cross-section of a thin cylinder. Area of metal resisting this force ndt(approximately) force nd2/4 pd stress set up =卫X area 元dt4t i.e. Pd longitudinal stress o= (9.2) 4t 9.1.3.Changes in dimensions (a)Change in length The change in length of the cylinder may be determined from the longitudinal strain,i.e. neglecting the radial stress. Longitudinal strain-E[-vo and change in length longitudinal strain x original length 1 -EloL-vOm]L -是1-2 (9.3) (b)Change in diameter As above,the change in diameter may be determined from the strain on a diameter,i.e.the diametral strain. Diametral strain change in diameter original diameter Now the change in diameter may be found from a consideration of the circumferential change.The stress acting around a circumference is the hoop or circumferential stress o# giving rise to the circumferential strain Change in circumference strain x original circumference =eH×元d200 Mechanics of Materials 09.1 Fig. 9.2. Cross-section of a thin cylinder. Area of metal resisting this force = ltdt(approximate1y) .. i.e. force d2/4 pd stress set up = - = p x - = - area ndt 4t pd longitudinal stress uL = - 4t 9.1.3. Changes in dinrensions (a) Change in length The change in length of the cylinder may be determined from the longitudinal strain, i.e. neglecting the radial stress. 1 E Longitudinal strain = - [uL - vuH] and change in length = longitudinal strain x original length 1 E = -[uL-vuH]L pd =-[1-2v]L 4tE (b) Change in diameter (9.3) As above, the change in diameter may be determined from the strain on a diameter, i.e. the diametral strain. change in diameter original diameter Diametral strain = Now the change in diameter may be found from a consideration of the cipcumferential change. The stress acting around a circumference is the hoop or circumferential stress on giving rise to the circumferential strain cH. Change in circumference = strain x original circumference =EHXnd