A cylindrical specimen of brass that has a diameter of 20 mm, a tensile modulus of 110 gpa, and a poissons ratio of 0.35 is pulled in tension with force of 40,000 n. If the deformation is totally elastic, what is the strain experienced by the specimen?
Answers
Explanation:
6.2FEA cylindrical specimen of brass that has a diameter of 20 mm, a tensile modulus of 110 GPa, and a Poisson’s ratio of 0.35 is pulled in tension with force of 40,000 N. If the deformation is totally elastic, what is the strain experienced by the specimen? (A) 0.00116 (C) 0.00463 (B) 0.00029 (D) 0.01350 Solution This problem calls for us to calculate the elastic strain that results for a brass specimen stressed in tension. The cross-sectional area A0is equal to A0=πd02⎛⎝⎜⎞⎠⎟2=π20 ×10−3m2⎛⎝⎜⎞⎠⎟2=3.14 ×10−4mHere d0is the original cross-sectional diameter. Also, the elastic modulus for brass is given in the problem statement as 110 GPa (or 110 ×109N/m2). Combining Equations 6.1 and 6.5 and solving for the strain yields ε=σE=FA0ENow incorporating values for stress, cross-sectional area, and modulus of elasticity into this expression leads to the following value of strain: ε= 40,000 N(3.14 ×10−m2)(110 ×109N/m2)=1.16 ×−3=0.00116which is answer A.