Determine the principle stresses σ1, σ2, σ3 and their orientation φ, if σx, σy and σz are known as shown in Figure Q.4b. sigma x = 80 mpa sigma y = 10 mpa tau z = 40 mpa
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Determine the principle stresses σ1, σ2, σ3 and their orientation φ, if σx, σy and σz are known as shown in Figure Q.4b.
sigma x = 80 mpa
sigma y = 10 mpa
tau z = 40 mpa
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- -18 through 7.4-25 An clement in plane stress is subjected to stresses sx,,sy., andtxy(see figure). Using Mohr’s circle, determine (a) the principal stresses and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.A capped cast-iron pipe is compressed by a brass rod, as shown. The mil is turned until it is just snug, then add an additional quarter turn to pre-compress the cast-iron pipe. The pitch of the threads of the bolt ap = 52 mils (a mil is one-thousandth of an inch). Use the numerical properties provided. (a) What stresses a and arwill be produced in the cast-iron pipe and brass rod. respectively, by the additional quarter turn of the nut? (b) Find the bearing stress ahbeneath the washer and the shear stress t(in the steel cap.Solve the preceding problem if F =90 mm, F = 42 kN, and t = 40°MPa
- Solve the preceding problem for an element in plane stress on the bottom surface of a fuel tanker (figure part a); stresses are sx= 105 MPa, sy. = 75 MPa, and ??xy= 25 MPa. Determine the stresses acting on an element oriented at an angle ?? = 40° from the x axis, where the angle is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle ??.Problem 1: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 25 ksi, oy = 12 ksi, and Txy = 10 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 12 ksi 5 25 ksi 10 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the principal stresses, the maximum in-plane shear stress, and the normal stress that acts on the maximum shear stress plane. Label all of these quantities on the circle. (c) Calculate the orientation of the principal planes and the planes of maximum shear stress. Label all of these quantities on the circle. (d) Show all stresses from part (b) on properly oriented stress element(s). Be sure to include all stress components acting on the elements(s).Problem 2: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 18 ksi, oy = 24 ksi, and Txy = 15 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 24 ksi бу 18 ksi 15 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the stress components Ox, Oy, and Txy on an element rotated 25° counter-clockwise from the original element shown. Label all of these quantities on the circle. (c) Show all stresses from part (b) on a properly oriented stress element. Be sure to include all stress components acting on the element.
- For the flat stress state shown in the figure. Use Mohr's circle to determine (show the procedure only with the use of geometry): a. Draw Mohr's circle indicating coordinates of the points that represent the given stress state, center, radius, coordinates of the points that represent the state the maximum and minimum normal stresses, coordinates of the maximum shear and angle of rotation from the stress given to the plane principal. b. Use the results of literal a to draw the element subjected to main forces and the element subjected to maximum shear. 12 MPa 19 MPа y 19 MPа 46 MPа 46 MPа 19 MPа 19 MPа 12 MPaQuestion 2) arm of Figure B from point x z plane, a horizontal angle of θ = 44 ° angled F = 26 kN size and a force C at the point z in the direction of M = 18 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.6 m and L 2 = 1.3 m . It is desired to determine the stress state of point A on the aa section taken from the arm. The radius r of the section is r=0.029 m and the shear modulus of the sleeve material is also G = 79 Gpa . According to this; Question 2-C) Find the normal stress caused by the normal force at point A ( Write your result in MPa .) Question 2-D) Find the normal stress caused by the bending moment at point A. (Your result MPa in the size of your font.)Question 2) arm of Figure B from point x z plane, a horizontal angle of θ = 44 ° angled F = 26 kN size and a force C at the point z in the direction of M = 18 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.6 m and L 2 = 1.3 m . It is desired to determine the stress state of point A on the aa section taken from the arm. The radius r of the section is r=0.029 m and the shear modulus of the sleeve material is also G = 79 Gpa . According to this; Question 2-A) Find the shear stress at point A due to the shear force . ( Write your result in MPa .) Question 2-B) Find the shear stress due to the torsional moment at point A. ( Write your result in MPa .) Question 2-C) Find the normal stress caused by the normal force at point A ( Write your result in MPa .) Question 2-D) Find the normal stress caused by the bending moment at point A. (Your result MPa in the size of your font.)