The state of stress at a point for a given reference xyz is given by the following array of terms : 15 8. -6 8 - 12 5 MPa - 6 5 8 Determine the principal stresses.
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- During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.The state of stress at a point in an engine piston is given in the x-y-z coordinates by: 90 180 [0]=0, MPa = 180 240 yx yy 120 zy Using the matrix transformation law, determine the state of stress at the same point for an element rotated about the x-axis (in the y-z plane) 60° clockwise from its original position. Calculate the stress invariants and write the characteristic equation for the original state of stress, Calculate the deviatoric invariants for the original state of stress, Calculate the principal stresses and the absolute maximum shear stress at the point. What are the stress invariants and the characteristic equation for the transformed state of stress, а. b. С. d. eIn (Figure 1), Tzy = 57.7 MPa. Figure 80 MPa T ▼ Part A Determine the principal stresses. Specify the orientation of the element. Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval (-90°; 90°]. 01, 02, 0p1 = Submit Part B IVE] ΑΣΦ 41 Ivec Request Answer Submit T max =, Javg, ₂ = In-plane Determine the maximum in-plane shear stress and average normal stress. Specify the orientation of the element. Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval (-90°; 90°]. Request Answer < Return to Assignment 15] ΑΣΦ 41 | vec ↑ S ? Provide Feedback D MPa, MPa, º ? MPa, MPa, 0
- 1. Given a combination of stresses on an element shown in the figure, (a) draw a Mohr's circle representing the complete state of stress of the element, i.e. show prinicpal stresses (01,02), maximum shear stresses (Tmax), principal direction (0p), original orientation, and original stresses (Ox, Oy, Txy). (b) draw three-dimensional Mohr's circles showing the three principal stresses and absolute maximum shear stress. Oy = -50 MPa Txy 20 MPa Ox = -150 MPaAt a point in the cross-section of an engineering component an element is subject to the following stresses: σx =100MPa σy =45MPa τxy = -50MPa Construct a Mohr’s Stress Circle and hence determine: (a) The Principal Stresses (σ1 & σ2) and the Directions of the Principal Planes (φ1 & φ2) (b) The Maximum Shear Stress (τmax) (c) Find the Normal Stress (σn) acting on a plane at 40 degs anticlockwise from the y-axisASAP
- The state of stress at a point on a thin plate is as shown in the left side of the Figure below. Determine the state of stress (ox, oy, txy) represented on the element oriented as shown on the right. 120 Sigma_x^prime (MPa) 200 Sigma_y^prime (MPa) 60 Tau_xy^prime (MPa) 30 Alpha (degrees) O x' Oy Txy' Txy Ox▼ Part A - State of Stress on an Inclined Plane The state of stress at a point in a member is shown on the rectangular stress element in (Figure 3), the magnitudes of the stresses are lo 100 MPa, |oy| = 35 MPa, and Try| = 49 MPa. = Using the stress-transformation equations, determine the state of stress on the inclined plane AB. Express your answers, separated by a comma, to three significant figures. ► View Available Hint(s) Or Try Submit VE ΑΣΦ ↓↑ Previous Answers vec X Incorrect; Try Again; 3 attempts remaining ? Part B - Clockwise Rotation of a Stress Element with Only One Normal Stress MPa, MPa Figure ▼ 60° 15⁰ Part A State of Stress on an Inclined Plane B 3 of 6 O 8Consider the following plane stress state: Ox=30 MPa, y= -60 MPa, Txy= 30 MPa cw Calculate the following: 1. The coordinates of the center of the Mohr's circle C The location of the center of the Mohr's circle Cis ( 2. Principal normal stresses (01, 02) The principal normal stresses are σ₁ = 39.08 3. Maximum shear stress (7) The maximum shear stress is 54.08 MPa. 4. The angle from the x axis to 0₁ (p) The angle from the x axis to 0₁ (p) is -16.85 5. The angle from the x axis to 7 (s) The angle from the x axis to T (s) is 28.15 6. The radius of the Mohr's circle The radius of the Mohr's circle is 54.08. ✰ MPa. MPa and 02 = -69.08 MPa. O -15 MPa, CW CCW O MPa).
- A composite shaft consists of 3 cylinders that are made from aluminum, copper and steel. Multiple axial loads are applied. The radii and Elastic Moduli of the cylinders are given. Neglect the size of collars B and C. F₁ Aluminum Eal r1 F₁ F₂ F3 FA d₁ d₂ d3 F₂ H F₂ B d₁ Copper Ecu r2 T1 72 T3 Ealuminum Ecopper Esteel Value C 1.75 KN 5.75 KN 2 KN 5.75 KN 0.5 m 0.2 m 0.3 m 0.16 m 0.28 m 0.12 m 74 GPa 112 GPa 202 GPa Steel Est [3 d3 Values for the figure are given in the following table. Note the figure may not be to scale. Variable F₂ F₂ D F₁ a. Determine the normal stress in section AB, OAB. b. Determine the normal stress in section BC, OBC. c. Determine the normal stress in section CD, gcn.Given is the following stress tensor (values in MPa): 48 -4 Oij 62) Calculate the magnitudes of the principal stresses and the failure angle (0).From the stress states in a Cartesian coordinate system, the following tensors are obtained:σxy = [100-100-100-800)]. Determine and graph the principal stresses and the directions associated with them using the mohr's circle. determine and graph the maximum shear stresses graph the possible failure planes finally, what is the value of the maximum tangential stress and in what orientations does it take place?