A plate is fastened to a fixed member by four 20-mm-diameter rivets arranged as shown in Fig. P-333. Compute the maximum and minimum shearing stress developed
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- The state of stress in a body is uniform and is given by: 0xx = 3MPa; Txy = 2 MPa; Txz = 4MPa Oyy = 5MPa; Tyz = OMPa; ozz 2MPa = a. Determine the principal stresses and their corresponding eigenvectors (work must be performed by hand) b. Determine the stress vector on a plane oriented at nx=.707, ny=.707, n₂=0 c. Determine the normal stress on the plane given in item (b)The state of stress at a point in a machine component is given by ox = 120 MPa, oy = 55 MPa, Oz = -85 MPa, Oxy = -55 MPa, Oxz = -75 MPa, and oyz = 33 MPa. Construct the Mohr's circles of stress for this stress state and find the maximum shear stress.3. At temperature T₁, the two rigidly connected rods just fit the rigid supports. If both sections are identical except for the diameter, prove that the following equations are true when temperature rises to T₂. a. F= b. OAB C. OBC A x(T₂-T₁)лd²E 20 x(T₂-T₁)E 5 9x(T₂-T₁)E 5 -1/2- d B 1/12- d C
- L,=40mm; L,= 120mm; L=100mm and 0,=65°. Find the possible value of 0, and 0, L,=80mm and 3.A stress element in a rock mass making up a slope experiences a 2D stress as follows: σx = 8 MPa, σy = 4 MPa , tauxy = 3 MPa A. By using the stress transformation equation, draw a curve of the stress variation experienced by the stress element at the axis of rotation angle θ = 0-180°. Use the interval θ = 1°, with the x-axis and stress as the y-axis. Mark on the curve where the principal stress and maximum shear stress occur. Draw the three stress curves completely and neatly B. Draw the stress element along with the magnitude and direction of the stress at the angle where the principal stress occurs and at the angle where the maximum shear stress occurs. C. Write down the direction vectors of the orientation of the principal stress (n1, and n₂) and the maximum shear stress (nmax). Write it in unit vector form i and j. D. Prove that the value of the stress invariant (I1, and I2) using the principal stress is reached and prove that the orthogonality condition of the direction cosine is…The internal loadings at a section of the beam in (Eigure 1) are shown Figure 20 mm 100 mm 200 mm 20 mm 10 kNm 20 mm 10/12 60 kN 80 KN 500 N-m Determine the in-plane principal stresses at point C. Also compute the maximum in-plane shear stress at this point Express your answers, separated by commas, to three significant figures. VAZ Ivec 4 d Submit Provide Feedback T Wha Bequest Answer ? MPA, MPA, MPA
- The following mohr's circle has known values for ox, oy and 0p. [ox= 32 MPa, oy= 12 MPa, and 0₁= 23 degrees] T 00000 (Oy, -Txy) (Ox, Txy) 10.4 MPa 4.7 MPa 11.7 MPa 7.5 MPa 20.4 MPa 20p trx t Determine the shear stress, tau_(xy) O1. A circular shaft with a keyway can be approximated by the section shown in Fig. r=b Ay r r=2acose Figure 1: Circular shaft with a keyway. The keyway is represented by the boundary equation r = b and the shaft is represented by the boundary equation r = 2a cos 0. Show that using a Prandtl stress function of the form ²) (₁ (1-2a cos) X v = K (b² − ²) (1 – : will solve the problem of torsion on this shaft and find the constant K (assume an applied torque T). Compute the shear stress components Txz and Tyz. (Hint: start by converting the stress function to Cartesian coordinates).A steel pipe has an inside diameter of d = 250 mm and an outside diameter of D = 268 mm. The length of the pipe is L = 6.0 m. The changes in dimension caused by an increase in temperature of 80°C for the: Outside diameter - Blank 1 mm Inside diameter - Blank 2 mm Lenght - Blank 3 mm Note: All answer must be round off up to 3 decimal places.
- Determine the state of stress at point q. The pipe has an inner diameter of D₁ = 1.0 in and an outer diameter of = 1.8 in. Use the exact expression for Q, if needed. Label the reultant forces on the cross section below. Report your answer (3x3 matrix) in psi to one decimal place. Do 4 in. Y 4 in. 150 lb 6 in. 50 lb 10 in. 200 lb 150 lb X N YThe state of stress at a point on an element of material is shown. Let sigmaX= 49.0 ksi, sigmaY= 17.0 ksi, and Txy= 11.0 ksi. Use this information to represent the principle state of stress and maximum in plane shear stress. Plot the mohr circle and state sigmaX' and sigmaY' and Tx'y' with unit. Also draw the state of stress on the rotated element.Draw and stress tensonr with the following characteristics The stress cube visualization at point A would depict the normal stress (σ_x) acting on two opposite faces and the shear stress (τ_xy) acting tangentially on the four sides associated with torsion.