Consider the brass alloy for which the stress-strain behavior is shown in the An

Question

Consider the brass alloy for which the stress-strain behavior is shown in the Animated Figure 6.12. A cylindrical specimen of this material 9.8 mm (0.3858 in.) in diameter and 100.8 mm (3.969 in.) long is pulled in tension with a force of 9580 N (2154 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. Note: because the diameter decreases, enter a minus sign in your answer.

answers are both in mm

Explanation / Answer

(a) This portion of the problem asks that we compute the elongation of the brass specimen. The first calculation necessary is that of the applied stress using

sigma = F/ Ao = F / [ pi(do^2) / 4] = 9580/ [pi*(9.8x10^-3)^2 / 4] = 127 MPa

From the stress-strain plot, stress corresponds to a strain of about 1.5 x 10-3. From the definition of strain,
l = * lo = (1.5 × 10^-3)(100.8 mm) = 0.1512 mm

In order to determine the reduction in diameter d, it is necessary to the definition of lateral strain (i.e., x = d/d0 ) as
d = do* x = do **z = (9.8 mm)(0.35)(1.5 × 10^-3)

= = –5.145 × 10^-3 mm

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.