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- 4. Given: Structure shown below (The material has a constant density.) Find: Mass moment of inertia with respect to z axis 200 mm 600 mm 400 mm ni 800 mm lySelect all statements that describe the mechanical properties of materials correctly (Hint: there are three right answers). Elastic materials can reveal a nonlinear stress-strain relationship. The Poisson's ratio can reach 1.5 in most engineering materials. The Hooke's law can describe the stress-strain relationship for any linear elastic materials. A secant (modulus) method can be used to approximately obtain the Modulus of Elasticity from nonlinear stress-strain curves. A nonlinear elastic response shows that a loading path should be different from the unloading path in the stress-strain curve.Question 3 - Strain Transformation The state of strain at a point in a rectangular block of material using an x-y coordinate system is given by: • €xx = 51×10-4 €yy = 18 ×10-4 Yxy=-4x10-4 ● ● Part One a) Which element below best represents the deformed element due to the state of strain in the x-y plane? 6 2 B) D) D) F) Hint: Consider the relative magnitude and sign of each component of strain
- 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 MPa2) Consider the given graph of the force-distance (F-r) curves for two different materials. Which of the two materials will have a higher modulus of elasticity (E)? Justify jour answer. Material A Material B Interatomic spacing, r ForceQ4 The beam shown below is made of an alloy of titanium that has a stress-strain diagram that can in part be approximated by two straight lines. If the material behaviour is the same in both tension and compression, determine the bending moment that can be applied to the beam that will cause the material at the top and bottom of the beam to be subjected to a strain of 0.050 mm/mm 3 cm 2 cm σ(MPa) 1330 1050 σ = 105(10¹) € σ= 7000€ +980 0.010 gaizu 201 0.050 € (mm/mm)
- A 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 50Question 6 An internal stress (temperature stress) will develop if a body is restrained against dimensional change due to temperature change. O True O False1-A thin aluminum plate profile shown in the accompanying figure is subjected to an axial load. deflection and the average normal stresses along the plate using the model shown in the figure. The plate has a thickness of 0.5 cm and a modulus of Approximate the 2 cm 2 cm elasticity E=70 GPa 2 cm 2 сm 3000 N б ст 6 cm 10 cm 2 cm 2 cm
- The lower ends of the three bars shown in the figure are at the same level before the rigid homogeneous W = 100 kN block is attached. The properties of the bars are shown in the table. Steel Bronze Length, L Area, A Modulus of elasticity, E Coefficient of thermal expansion, a 1.00 m 500 mm? 1.60 m 900 mm 200 GPa 83 GPa 11.7x106 /°C 18x10 /°C Bronze Steel Steel W The temperature of the bars is then increased by 80°C. The block is assumed to remain horizontal after all deformations have occurred. Which of the following most nearly gives the stress developed in the steel bar?The difference pressure AP developed by a centrifugal pump to be installed in a pipe system depends on the impeller diameter D, the speed of rotation n, the discharge Q, and the fluid density p. If you are asked to develop a dimensional analysis to find the relationship between dimensionless groups, what should be your 1st step? Build a model Build a prototype Predict the number of dimensionless groups Find the function between the dimensionless groups Measure the pressure change in an existing pump you have in your laboratory. For the problem described in Question 1 above, how many dimensionless groups do you expect? 1 2 3Many of the necessities of everyday life, from rubber bands to suspension bridges,depending on the elastic properties of materials. The greater the deforming forces, thegreater the resulting deformation. This proportionality is called Hooke’s law, and theratio of stress to strain is called the elastic modulus. The modulus of elasticity iscalculated by measuring the strain produced.In Figure Q4, a beam is hung by 2 wires namely BD and CE. If a load P on the beam causes the end C to be displaced to 10 mm downward,(a) Label the deformations produced by P on a free-body diagram Find normal strain in wires BD and CE.