Please determine the change in diameter of the bar ass well as the change in lenght of the bar, if the bar is subjected to axial force of 160 KN
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![Consider the stress-strain diagram, shown in the figure, of a bar made from a composite material, The bar has a 53 mm diameter (d), a length (L) of 0.6 m, and a Poisson ratio (v) of
0.35.
(1) Determine the Young's modulus [elastic modulus] of the material.
800
700
600
500
400
300
200
100
0.0015
0.003
0.0045
0.006
0.0075
0.009
0.0105
E [mm/mm]
o [MPa]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba1d1496-0cc5-4770-9b07-e8ae54bd65a2%2Fe1babde0-d308-4f7c-b6b0-9562501f6a82%2Fopwyajg_processed.jpeg&w=3840&q=75)
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- From the stress-strain data for poly(methyl methacrylate) shown in figure below, determine the modulus of elasticity in the elastic linear region and the tensile strength at 40 °C (104 °F). Stress (MPa) 80 70 60 30 20 10 4°C (40°F) ,20°C (68°F) 30°C (86°F) .40°C (104°F) 0.1 Strain 50°C (122°F) 60°C (140°F) 0.2 To 1.30 The modulus of elasticity is 2.3 GPa and the tensile strength is 49 MPa O The modulus of elasticity is 38 MPa and the tensile strength is 3.3 GPa The modulus of elasticity is 1.2 GPa and the tensile strength is 52 MPa The modulus of elasticity is 1.2 GPa and the tensile strength is 38 MPa T 12 10 8 2 0.3 Stress (10³ psi)A polypropylene has the following tensile creep compliance measured at 40 °C: D(t) = 1.2 x t0.1 GPa-1 where t is expressed in seconds. It is subjected to the following tensile stress sequence at 40 °C. Find the tensile strain at 3200 sec. Stress (MPa) 1.5 1.0 0.5 1000 2000 3000 Time (s)A solid homogeneous truss tie-rod has a diameter of 9.52 mm and an original length of 1.75 m experiences a stress of 600 MPa when placed under tension. If the material used for the truss tie-rod has a Young's Modulus, E, of 5.8 x 1011 N/m?, calculate: (i) the tie-rod's extension in millimetres (mm); (ii) the strain energy (U) in Joules; and (ii) the strain energy per unit volume (U/V) in Joules per cubic metre (m³). Give your answers to two decimal places.
- 3. For a steel alloy, the stress-strain behaviour is shown below. Determine the modulus of elasticity, proportional limit, yield strength at 0.002 and maximum allowable load. 600 500E 400- 500 300 400- 300아 200 200- 100- 100E 0.000 0.002 0.004 0.006 Strain 0.00 0.04 0.08 0.12 0.16 0.20 Strain Stress (MPa) Stress (MPa)A tensile test is conducted on a mild steel bar. The following data was obtained from the test : diameter of the steel bar= 3cm, Gauge Length of the bar = 20cm, Load at Elastic limit= 250kN, Extension at a load of 150kN= 0.21 mm, Maximum Load = 380kN, Total Extension= 60mm, Diameter of the rod at failure=2.25cm, determine young's modulus?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:
- 124,000s o(2) 0 s85 0.03 (o in MPa) 1+ 300ɛ (a) Find the axial normal strain in the cable and its elongation due to the load W = 6.8 kN. (b) If the forces are removed, what is the permanent set of the cable? Hint: Start with constructing the stress-strain dia- gram and determine the modulus of elasticity, E, and the 0.2% offset yield stress. D 2 m A 1.5 m B 1.5 m E m--1 m- 0.75 m 0.25 m W = 6.8 kN1.4-7 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 FractureQuestion 4 Consider the same truss again here as shown below. Suppose that the cross-sectional area of the first element is A1=200 mm?, and all members are made from a same material with Young's modulus of E=55 GPa. Find the stiffness matrix of the first element in N/m. Work out the summation of all terms located on the main diagonal of this stiffness matrix. 100 mm (1) (2) (3) 3 4 150 mm 200 mm Your Answer: Answer Hide hint for Question 4 The summation of all terms located on the main diagonal of matrix т1 т2 M is m1 + m4. т3 т4 100 mm 2.
- Problem 4 The attached figure shows, for a gray cast iron, the tensile engineering stress-strain curve in the elastic region. Determine (a) the tangent modulus at 25 MPa and (b) the secant modulus taken to 35 MPa. Stress (MPa) 60 50 40 30 20 10 0.0002 0.0004 Strain 0.0006 T 8 6 ★ 2 0.0008 Stress (10³ psi)A solid bar of length L = 4 m and diameter 200 mm is heated from 20 to 320 degrees celsius and restrained between two solid immovable walls. Young's modulus of the material is 90 GPa and the coefficient of thermal expansion is 22 x 10-6/°C. →Calculate the thermal strain, e, in micro-strain correct to two decimal places. micro-strain. Calculate the thermal stress, o, in megapascals (MPa) correct to two decimal places. E: σ: MPa. Hence calculate the force exerted by the bar in meganewtons (MN) correct to two decimal places: F MN. L1.6-7 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?