If Poisson's ratio of a material is 0.3, then the ratio of Young's Modulus to bulk modulus is (a) 0.6 (c) 1.2 (b) 0.8 (d) 1.4
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- A 20-mm-wide block is firmly bonded to rigid plates at its top and bottom. When the force P is applied the block deforms into the shape shown by the dashed line. (Figure 1) Part A Determine the magnitude of P. The block's material has a modulus of rigidity of G= 24 GPa .Assume that the material does not yield and use sma angle analysis. Express your answer to three significant figures and include the appropriate units. Figure µA ? Value kN P = 150 mm- You have already submitted this answer. Enter a new answer. No credit lost. Try again. 0.5 mm -- Submit Previous Answers Request Answer 150 mm Provide Feedback Next >The stress-strain relationship shown in Figure P1.13 was obtained during the tensile test of an aluminum alloy specimen. Determine the following: a. Young's modulus within the linear portion b. Tangent modulus at a stress of 310 MPa c. Yield stress using an offset of 0.002 strain d. If the yield stress in part c is considered failure stress, what is the maximum working stress to be applied to this material if a factor of safety of 1.5 is used? 450 300 150 0.002 0.004 0.006 0.008 Strain, m/m FIGURE P1.13 Stress, MPaTHERMAL STRESS 3. A rigid bar is supported by two copper rods and the gap between the aluminum rod and the bar is 1.50 mm. If the temperature for all materials is increased by 40 degrees Celsius, will the aluminum rod touch the rigid bar or not? Prove your answer. For each copper bar, A = 500 mm^2, E = 120 GPa and a = 16.8 um/(m C). For the aluminum bar, A = 400 mm^2, E = 70 GPa , and a = 23.1 um/(m C).
- Time len A material has the stress-strain behavior shown in the Figure below. Calculate the toughness (T) of this material. given that S1=195 Mpa; S2=243.75 Mpa; El=0.19; E2=0.38 E1 Strain E2 Stress - Strain diagram of a metal alloy OA.T= 18.52 Mpa O B.T= 92.62 Mpa O C.T= 37.05 Mpa O D.T= 60.21 Mpa Stress (Mpa) 3A piece of 50 mm x 30 mm material experiences a homogenous deformation as shown in the figure below. The deformed shape in x-y plane is illustrated by the solid lines. If E = 3.9 GPa and the Poisson's Ratio is 0.35, what is the associated shear stress? provide your answer in MPa with precision to two decimal points. Answer: 0.014 30 0.010 y 0.009 0.012 50o (ksi) e (in./in.) 33.2 0.0006 45.5 0.0010 49.4 0.0014 51.5 0.0018 53.4 0.0022 Data taken from a stress-strain test for a ceramic are given in the table. The curve is linear between the origin and the first point. Determine the modulus of elasticity and the modulus of resilience.
- A tri-metallic bar is uniformly compressed by an axial force P = 40 kN applied through a rigid end plate (see figure). The bar consists of a circular steel core surrounded by a brass and copper tubes. The steel core has a diameter of 30 mm, the brass tube has outer diameter of 45 mm, and the copper tube has outer diameter of 60 mm. the corresponding moduli of elasticity are E, = 210 GPa, E, = 100 GPa, and E. = 120 GPa. Copper tube Brass tube P= 40 kN Steel core 30 mm 45 mm 60 mm Calculate the compressive stress in the steel core in MPa due to the force P. A. 25.1 1. В. 28.3 С. 22.4 D. 21.8 2. Calculate the compressive stress in the brass tube in MPa. A. 7.9 Calculate the compressive stress in the copper tube in MPa. A. 12.5 В. 8.2 С. 9.8 D. 10.4 3. В. 14.2 С. 16.4 D. 17.8A tri-metallic bar is uniformly compressed by an axial force P = 40 kN applied through a rigid end plate (see figure). The bar consists of a circular steel core surrounded by a brass and copper tubes. The steel core has a diameter of 30 mm, the brass tube has outer diameter of 45 mm, and the copper tube has outer diameter of 60 mm. the corresponding moduli of elasticity are E, = 210 GPa, E, = 100 GPa, and E, = 120 GPa. P= 40 kN Copper tube Brass tube Steel core 30 mm 45 mm 60 mm 1. Calculate the compressive stress in the steel core in MPa due to the force P. А. 25.1 В. 28.3 С. 22.4 D. 21.8 2. Calculate the compressive stress in the brass tube in MPa. C. 9.8 В. 8.2 Calculate the compressive stress in the copper tube in MPa. В. 14.2 А. 7.9 D. 10.4 3. A. 12.5 С. 16,4 D. 17,8 O 1A O 18 O 10 O 10 O 2A O 28 O 20 O 20 O 3A O 38 O 30 O 3D1500 KN 800 mm 70 mm 100 mm 1500 KN A bar has a length of 800 mm, width 100 mm, and thickness 70 mm, and is being subjected to 1500 KN of tension as shown. As a result, the length of the bar as increased to 802.5 mm and its width has decreased to 99.906 mm. Assume elastic behavior. a) Determine the Young's modulus (E) of the material b) Determine the Poisson's ratio (v) of the material c) Determine the Shear modulus (G) of the material d) Determine the new thickness of the bar in mm e) Determine the percentage change in the total volume of the bar
- 3. An aluminum material element experiences a state of plane stress with the magnitudes and directions of the stress components given in the figure. Please calculate the change in volume per unit volume this material element would experience when subjected to the stress state given in the image below and a temperature increase of 80°C. (Note that the dotted horizontal line and 15 degree angle are irrelevant to this problem). Aluminum Properties: Thermal Coefficient of Expansion = 24 x 10-6 mm/mm/°C, Elastic Modulus = 69 GPa, Poisson Ratio = 0.35 250 MPa 60 MPa 15° 150 MPa1.16 The stress-strain relationship shown in Figure P1.16 was obtained during the tensile test of an aluminum alloy specimen. 60,000 H Stress, psi 40,000 20,000 0 Figure P1.16 0.002 0.004 0.006 0.008 Strain, in./in. Determine the following: a. Young's modulus within the linear portion. b. Tangent modulus at a stress of 45,000 psi c. Yield stress using an offset of 0.002 strain d. If the yield stress in part c is considered failure stress, what is the maximum working stress to be applied to this material if a factor of safety of 1.5 is used? 4M A cylinder of outer radius R2=100 mm is fitted on another cylinder of outside radius R₁=85 mm with thickness t=30 mm, as depicted below. If the (tensile) maximum hoop stress at the interface between the two cylinder is 90 MPa, solve the following questions (E=105 MPa and v=0.15). === R₁ What is the radial stress between the cylinders? What is the shrinkage allowance at the interface? ( M R₂ )