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# Cylindrical rod

Cylindrical rod is loaded by tensile forces.

Problem type:
Axisymmetric problem of stress analysis.

Geometry:

Given:
Rod's length L=3000 mm, cross-section diameter d = 30 mm;
Young's modulus of the aluminum alloy E = 70 GPa;
Poisson's coefficient of the aluminum alloy ν = 1/3;
Force P = 85 kN.

Calculate bar elongation, the decrease in diameter and the increase in volume.

Solution:
One of the rod's ends is fixed. The other end is loaded by the tensile force fz = P / S,
where S= 786·10-6 [m2] - is the rod cross-section area.

Volume change can be calculated by the length dL and width dr increments:
dV = (L+dL)·π·(r+dr)2 - L·π·r2.

Results: Volume change dV = (3000+5.1536)·π·(15-0.008589)2 - 3000·π·152 = 1210.91 mm3.

 Elongation dL, mm Decrease in diameter 2·dr, mm Increase in volume dV, mm3 QuickField 5.1536 0.017178 1210.9 Theory* 5.1557 0.017186 1214.8 Error 0.04% 0.05% 0.3%

* James M. Gere, Stephen P. Timoshenko "Mechanics of materials", Third edition (1990), pp.26-27. ISBN:0-534-92174-4.

• Video: Cylindrical bar