If for a given material, E = 2G (E is the modulus of elasticity, G is the shear modulus), then the bulk modulus K will be E E (a) (b) 2 3 (c) E 4 (d)
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- Q.2) A brass bar 500 mm long and 100 mm × 100 mm in cross-section is subjected to an axial pull in the direction of its length. If the increase in volume of the bar is 50 mm³, then the magnitude of the pull (kN) will be (Take E = 100 GPa and µ = 0.25) (A) 20 (С) 25 (В) 30 (D) 15A wire 2 m long and 2 mm in diameter, when stretched by weight of 8 kg has its length increased by 0.24 mm. Find the stress, strain and Young’s modulus of the material of the wire. (Note: g = 9.8 m/s2). Answers: (2.5 x 107 N/m2, 1.2 x 10-4 m/m, 2.08 x 1011 N/m2)The ratio of Young's modulus of elasticity . to modulus of rigidity for a material having Poisson's ratio 0.2 is 12 (a) 5. (b) 12 14 (c) T4 (d) 5
- A very thick structure is subjected to certain traction boundary conditions on its surface. The cross-section and the applied load do not vary with the z-coordinate. The following stress function is proposed for this problem: -y p(x,y) = Sin (x) (A x²e + B e") (i) use the biharmonic equation to find restrictions, if any, on values of A and B (ii) calculate all stress components (iii) calculate all strain components in terms of A, B, and C as well as the Young modulus and Poisson's ratio E and y, respectively. (iv) check that the equilibrium equations are satisfied (v) determine the traction boundary conditions at x =± a and y=+b100KN A force of 100 KN is applied on a column as shown. The column is made from two materials. [The top one is a functionally graded material with a linearly varying modulus and densities. Its length is 2 meter. The density and elastic modulus of the top material at point A are 2700 А kg m3 and 72 Gpa, respectively. The density and modulus of kg the top material at point B are 3000 and 100 Gpa. The m 3 В kg bottom material is made from steel (density =7800 and m2 modulus=200GPA). The length of the bottom material is 1m. The cross-sections of both materials comprising the column are cylindrical with a diameter of 0.5 m. C ID (oijj + bị = 0) and considering the weight and the applied force determine: Using equilibrium while The stress distribution in both members1.6-7 A wire of length L = 2.5 m and diameter d = 1.6 mm is stretched by tensile forces P = 600 N. The wire is made of a copper alloy having a stress- strain relationship that may be described mathemat- ically by 124,020ɛ 0 s8s 0.03 (o = MPa) 1+ 300ɛ in which e is nondimensional and o has units of MPa. (a) Construct a stress-strain diagram for the material. (b) Determine the elongation of the wire due to the forces P. (c) If the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
- The figure shows the stress-strain curve for a rectangular steel test piece in tension. The test piece is loaded up to point B and then released. If the test piece was originally 58.9 mm long, estimate its new length (in mm) after it is released? State your answer in mm without including the units. Stress (MPа) Elastic Inclastic strain strain 473 - В 408 - 340 272 - Unload 204 - Reload 136 - Plastic Elastic 68 - deformation recovery 0.0020 0.0060 0.0100 0.0000 0.0040 0.0080 0.0120 Strain (mm/mm) Answer:A 75-cm-long cylindrical rod of cross-sectional area A, = 0.5 cm² is placed inside a tube of the same length and of cross-sectional area A, = 0.65 cm2. The ends of the rod and tube are attached to a rigid support on one side, and to a rigid plate on the other. The rod is pure elastic, but the tube is elastoplastic. The rod has modulus of elasticity E, = 250 GPa. The tube has modulus of elasticity E, = 120 GPa and yield strength (ot)y = 320 MPa. If the load P applied to the rod-tube assembly is increased from zero to 70 kN and decreased back to zero, determine the permanent set (Sp) of the rod-tube assembly after the load P has been completely removed. - Tube Plate Rod 75 cm(b) Consider a square element in the x-y plane with side length of 3 cm. The thickness of the element is 7 mm. The element has modulus of elasticity of 200 GPa and Poison's ratio of 0.33. If the element is subjected to forces in the x and y directions of 3 KN and 1.5 KN, respectively, find the dimensions of the loaded element.
- Same problem is considered here again using three equal length elements. Suppose that the Young's modules is E=19GPa, and the applied force is P=35KN. Find the strain energy of element 1 in N.m if the element area of this element is A₁-30 mm². (Hint: round your answer to 4 digits after decimal point). -. 10 cm (1) 2 15 cm (2) (3) - 4 cm1.4-7 The data shown in the table below were obtained from a tensile test of high-strength steel. The test specimen had a diameter of 13 mm and a gage length of 50 mm (see figure for Prob. 1.4-3). At fracture, the elongation between the gage marks was 3.0 mm and the minimum diameter was 10.7 mm. Plot the conventional stress-strain curve for the steefor the steel and determine the proportional limit, modulus of elastics of elastic- ity (i.e., the slope of the initial part of the stress-strain,tress-strain curve), yield stress at 0.1% offset, ultimate stress, percent, elongation in 50 mm, and percent reduction in area. 'ess, percent area. TENSILE-TEST DATA FOR PROB. 1.4-7 Elongation (mm) 0.005 0.015 0.048 Load (kN) 5 10 30 50 0.084 60 0.099 64.5 0.109 67.0 0.119 68.0 0.137 69.0 0.160 70.0 0.229 72.0 0.259 76.0 0.330 84.0 0.584 92.0 0.853 100.0 1.288 112.0 2.814 113.0 FractureQ1) Bar (1) of length 2.8 m and bar (2) of length 0.73 m are fixed at ends A and C. There is a A = 3.5 mm gap between bar (2) and the rigid plate at B. Load P is applied to plate B and as a result of that, bar (1) elongates and bar (2) get compressed. If the normal strain in bar (1) is 2429 um/m, find the normal strain in bar (2). (1) P, (2) A P 2.8 m 0.73 m