Problem 2: A metal bar of square cross section (precisely 6 cm cross sectional e

Question

Problem 2: A metal bar of square cross section (precisely 6 cm cross sectional edge, 60cm long) is used to apply loads to small samples in a high-precision dilatometer (a length-measuring device). The modulus of elasticity is 220 GPa and the Poisson's ratio is 0.3. (34 points) a) Calculate the resulting dimensions (length and cross section dimensions) if the crystal is subjected to a 1000 KN axial compression load. b) If the yield stress if the metal is 200MPa, will the bar plastically deform under the applied load? If yes, what is the maximum cross section dimension required so that the bar remains elastic under the applied force of 1000KN? Recall Pa=N/m/m

Explanation / Answer

a) F = 1000,000 N

l0 = 60 cm

A0 = 36 cm2

E = 220 GPa

= 0.3

lf = lo ( 1+ F/A0E)

= 0.6[1+ 1000,000/ 0.0036 * (220*109)]

= 60.076 cm

= 0.3 = -( dA/A0)/(dl/l0)

= - dA*60/36*0.076

dA = -0.014 cm2

Af = 36-0.014 = 35.986 cm2

b. y = 200MPa

Fy = y * A0 = (200*106 N/m2) * 0.0036 m2

= 720000 N < 100,000 N

So, answer is yes.

Maximum length , lmax = l0 ( 1+ F/A0E)

= 0.6[1+ 720,000/ 0.0036 * (220*109)]

= 60.054 cm

= 0.3 = -( dA/A0)/(dl/l0)

dA = - 0.3*36*0.054/60

= 0.00972

Amax = 36-0.00972 = 35.99 cm2

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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