If ß-Sn, a tetragonal crystal (point group 4/mmm, a = 0.583 nm, and c = 0.318 nm) is subject to a tensile stress of 63 MPa along [100] and to a shear stress of 18 MPa on the (100) plane in the [010] direction. Determine: a) the tensile stress normal to (110), and b) the shear stress on the (110) plane in the [1-10] direction.
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- Learning Goal: A material is homogenous and isotropic when it has a modulus of elasticity that does not vary with direction and it has uniform properties throughout. When a point in a material is subjected to only normal stresses in three dimensions, but they are not necessarily equal, the state is called triaxial stress. When the response of the material is linear elastic, the strains along the three axes can be calculated using a generalized form of Hooke's law. Each strain depends on all three stresses because of the Poisson effect. €1 Figure 1 [0₂ - V (O₂ +0₂)] a 1 of 1 A cube is subjected to stresses with magnitudes a = 16 MPa, b = 26 MPa, and c = 5 MPa (Figure 1). What is the strain in the y-direction? Let E = 200 GPa and v= 0.26. Express your answer to three significant figures. ► View Available Hint(s) Submit VE ΑΣΦ Part B - Change in volume f change in volume = vec The cube from Part A originally has side length 3.2 cm . What is the change in volume of the cube under the given…Element 1 Ук ** Answer in MPa. 2 cm Element 2 Assume the reaction forces at the origin were solved to be Rf = [325, 100, 0] N and = Rm [10, -2, 5] Nm. We will consider a hypothetical cut at the connection of the dolly to the axle. Z is positive out of the page. What is the value of normal stress in the x-direction Ox for element 2? Answer options: a) Ox < -300 b) -300 ≤ Ox < -100 c) -100 ≤ Ox < -200 d) 0 ≤ Ox < 100 e) 100 ≤ Ox < 300 f) 300 ≤ OxUse the engineering stress strain diagram provided below to answer parts (A) to (H) below (the stress-strain diagram bas already been drawn for you): stress strain diagram 400 350 0 300 0 250 0 200 0 150.0 100.0 50.0 O 05 0 1 0.15 strain A. Determine the tensile strength of this alloy. B. show the elastic, plastic and total strain on the diagram stress (Mpa)
- 2) Use the engineering stress strain diagram provided below to answer parts (A) to (H) below (the stress-strain diagram has already been drawn for you): stress strain diagram 400 350 0 300 0 250 0 200 0 150.0 100.0 50.0 00 0 05 01 0. 15 strain A. Determine the tensile strength of this alloy. B. show the clastic, plastic and total strain on the diagram stress (Mpa)Assume the following elastic loading exists on ablock of copper:σX = 325 MPa; σY = 80 MPa; and τXY = 40 MPaCalculate eX and eZ for this block, assuminga. that it is a random polycrystalline material.b. that it is a single crystal with the tensile and shearaxes lining up along unit cell axes.c. Explain why the relative strain values you calculated along the X axis make sense for the two cases,based on the elastic anisotropy of copper.Problem 4: The state of stress at a particular point in a structure is given below. 10 20 0 ¹-[20 = 20 -10√2 MPa 0 -10√2 10/27/1 [o] (a) Write the characteristic equation (cubic equation) that would be used to determine the principal stresses. (b) Without solving the characteristic equation, verify that one of the principal stresses is Op = 30 MPa. Find its corresponding principal direction (i.e., find its direction cosines). (c) Determine the other principal stresses and their corresponding principal directions. (d) Determine the maximum shear stress.
- The plastic distorts as shown by the dashed lines. (Figure 1) The dimensions are L = 460 mm, H = 345 mm, d₁ = 3 mm, d₂ = 5 mm, d3 = 13 mm, d4 = 8 mm, d5 = 3 mm, and de = 6 mm. Figure H B A dz dg ds + 1 of 1 Part A Determine the shear strain Yzy at corner A. Express your answer to three significant figures and include appropriate units. ol Di μA ? (YA)zy = Value Units Submit Request Answer Part B Determine the shear strain Yzy at corner B. Express your answer to three significant figures and include appropriate units. Di μA ? (YB)Ty = Value Units Submit Provide Feedback Request AnswerA steel [E = 200 GPa] rod with a circular cross section is 9-m long. Determine the minimum diameter D required if the rod must transmit a tensile force of 21 kN without stretching more than 4 mm.Determine the tensile yield strength (0.2% offset) and the maximum strength of a metal alloy having the following tensile stress-strain diagram. Select one: The tensile yield strength Sy = 100 Mpa and the maximum strength Smax = 250 Mpa. The tensile yield strength Sy = 170 Mpa and the maximum strength Smax = 250 Mpa. The tensile yield strength Sy = 150 Mpa and the maximum strength Smax = 200 Mpa. The tensile yield strength Sy = 240 Mpa and the maximum strength Smax = 250 Mpa. The tensile yield strength Sy = 80 Mpa and the maximum strength Smax = 250 Mpa.
- The aluminum rod BC (G= 26 GPa) is bonded to the brass rod AB (G= 39 GPa). Each rod is solid and has a diameter of 12 mm. Take T= 124 N-m. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 200 mm Brass B Aluminum 300 mm T Determine the angle of twist at B. The angle of twist at B is[How many independent stress components are needed to define the stress state of a point in 3-D?The state of stress at a point in a loaded solid is given as [5 0 2 [0]=|0 0 0 MPa 20 -5 (a) Calculate the principal stresses (b) Plot the Mohr's circles for this point and calculate the maximum shear stress (c) Determine the principal directions only for the largest principal stress.