The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is made from a homogeneous material. The length (L) of the rod is 1.75 m and Young’s Modulus for the material (E) is 250 GPa. When the rod is placed under tension it experiences deformation and a stress (?) of 650 MPa. Calculate the following:

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.6.15P

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Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

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The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is
made from a homogeneous material. The length (L) of the rod is 1.75 m and
Young’s Modulus for the material (E) is 250 GPa. When the rod is placed under
tension it experiences deformation and a stress (?) of 650 MPa. Calculate the
following:
(i) Strain energy (U) to 2 decimal places in Joules.
(ii) Strain energy per unit volume (U/V) in J/m3
.
(iii) The change in length ∆L to 2 decimal places in mm.
(iv) The strain (?) due to deformation to 2 significant figures

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