Consider the brass alloy for which the stress-strain behavior is shown in the animated figure 7.12. a cylindrical specimen of this material 10.0 mm (0.3937 in.) in diameter and 100.6 mm (3.961 in.) long is pulled in tension with a force of 9970 n (2241 lbf). if it is known that this alloy has a value for poisson's ratio of 0.35, compute
(a) the specimen elongation,
(b) the reduction in specimen diameter.

because the diameter decreases, enter a minus sign in your answer.

(a) 0.1509 mm

(b) 0.00525 mm

Explanation:

Stress, is given by

where F is force and A is area and area is given by hence

where d is the diameter. Substituting 9970 N for F and 10mm=0.01 m for d hence

From the attached stress-strain diagram, the stress of 127 Mpa corresponds to strain of 0.0015 and since strain is given by

where is the strain, is elongation and l is original length and making elongation the subject

and substituting strain with 0.0015 and length l with 100.6 mm then

(b)

Lateral strain is given by

and substituting for where v is poisson ratio then

and making the subject then

and substituting 0.35 for v, 0.0015 for strain and 10 mm for d

and the negative sign indicates decrease in diameter

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answer:

look in settings

explanation: