Question

Data As x + tid: 5464389_1&course_id - 86783 1 3a. The bar shown is made from a material for which yold = 22 ksi, E=25x10 psi, and 0.28. The bar has a circular cross section with initial diameter d-2 inand initial length L = 36 in 13 kips 13 kips Under the application of the 13 kip load, determine the following: 1. The strain in the bar's longitudinal direction, i.e., its axial strain, 2. the strain in the transverse direction, 3. the bar's axial deformation (its change in length), 4. the change in the bar's volume, 5. the strain energy density stored in the bar, and 6. the total strain energy stored in the bar. Assume linear elastic behavior. Neglect localized effects in proximity to the loading points. 3b. The bar shown is made from a material for which = 212 MPa, E-191GPa. and v 0.31. The cross-section of the bar is a rectangle with initial dimensions 20 mm x 40 mm. The bar has an initial length of 1200 mm. 22 kN 22 kN 40 mm 20 mm Cross-Section Under the application of the 22 kN load, determine the following: 1. The strain in the bar's longitudinal direction, ie, its axial strain. 2. the strain in the transverse directions, 3. the bar's axial deformation (its change in length). 4. the change in the bar's volume, 5. the strain energy density stored in the bar, and 6. the total strain energy stored in the bar. Assume linear elastic behavior. Neglect localized effects in proximity to the loading points.

Answer 1

30) 13 kips-P 13 kipe L=36in yield 22KS E2250106 psi 4= 0.28 de 2 in 0 - - p AE = 13x103 I x(2)? x 25x106 -0.0001655 (Compreson) 2 Ed --W En (as odintater =o) - - 0.28 * 0.0001655 --0.0000463 = 0.0000463 (Tensile) ③ ul Euxi- 0.0001655 x 36 = 0.005958 (Part 4 solved later ). 6 Shrain energy density E = 1/2 x 62 Doa P- 13x103 = 4138-028 (212 E. 1 (4138028) = 0.342465 PS 25x106

6 total Stain energy tored in the bar. - energy Stored x vol Vol 0.342.465 x x (2)?x36 - 38-73 lb in 7 Change in volo (Ent 2 Ed) x Vol intrial Ex Eut2 Ed Here we took Comp tve Tension a ve Ev Eu= 0.0001655 Ed=-0.0000463. Ev=0.000/655- 2x0.0000463 Ex=0.0000729 Change in vol = 0.0000729 x 7 x (2) ²x 36 - 0.00824479 in (Reduction)

212 Mpa - 10 x 103 mpa a=0. 31 - 1200 mm P: 22 10 22 x 10 = 0.0001439 --03170-000139 --0-000046335 09-. 0.0001439x1200 Tensile (yue) Compo 0.172 mm 0-000046355 ③ AV=Vev Ev = Eu+ y + Ez 0-0001439-2 = 0.000054633 AV = 0.000054633 x Hox20x1200 = 52.44768 mm (expansion) ③ Stear energy/vol - 235 frey Powel +3820001979 )

energy Stored energy stored vol x vol -0.001979 x 40 x 20 x 1200 = 1900:52 N mm