A steel shaft of diameter 50 mm and length 1.2 m (E = 210 GPa and v = 0.3) is loaded with multiple force system. At a point in the shaft, the state of stress relative to the x, y, z coordinate system was found to be: [600 0 T = 0 320 0 MPa -480 (a) Draw a cube element showing the stress components on each coordinate face (Hint: No vector lines for zero stresses; Warning: A stress element without reference axes will receive zero point). (b) From the given stress tensor, determine the values of (i) octahedral normal stress (Goet) and (ii) octahedral shear stress (toct). (c) From your answer in (b), determine (i) dilatational strain energy (Ugna ); and (ii) deviatoric strain energy (Udist ). (d) Find the total strain energy at the point.

A steel shaft of diameter 50 mm and length 1.2 m (E = 210 GPa and v = 0.3) is loaded with multiple force system. At a point in the shaft, the state of stress relative to the x, y, z coordinate system was found to be: [600 0 T = 0 320 0 MPa -480 (a) Draw a cube element showing the stress components on each coordinate face (Hint: No vector lines for zero stresses; Warning: A stress element without reference axes will receive zero point). (b) From the given stress tensor, determine the values of (i) octahedral normal stress (Goet) and (ii) octahedral shear stress (toct). (c) From your answer in (b), determine (i) dilatational strain energy (Ugna ); and (ii) deviatoric strain energy (Udist ). (d) Find the total strain energy at the point.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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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).
Question 2) arm of Figure B from point x z plane, a horizontal angle of θ = 38 ° angled F = 29 kN force sized and C from the point z direction M = 17 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.5 m and L 2 = 1.1 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=0.015 m and the shear modulus of the arm material is also G = 78 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) arm of Figure B from point x z plane, a horizontal angle of θ = 38 ° angled F = 29 kN force sized and C from the point z direction M = 17 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.5 m and L 2 = 1.1 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=0.015 m and the shear modulus of the arm material is also G = 78 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-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.)
1. A loaded bicycle pedal crank is shown below. q 750N (2 direction) 72/ A @ Top 8 yo B@ Top d = 15 mm x₁ = 125 mm x2 = 24 mm y₁ = 60 mm у2=X2 a. Sketch elements A and B and show the stress states. Clearly label the coordinate axes on the elements. Make sure you calculate the normal (o) and shear stresses (T). Do not neglect Tv. Find the principal stresses for each element using Mohr's Circle. b.
3) A 25 mm solid round shaft is supported by self-aligning bearings at A and B (the bearings do not support axial loads). Two chain sprockets are attached to the shaft as shown. a. Find the force, F, on the 125 mm diameter sprockets. b. Construct the V-M-N-T diagrams for the shaft. c. Determine the shaft location with the most severe state of stress. d. Sketch the Mohr's circle and find the principal stresses at that location. A 125 mm dia. 50-mm dia. 75 mm 25mm dia. 5000 N 150 mm 75 mm
Question 2) A force of magnitude F=28 kN, which makes an angle of θ=35 ° with the horizontal in the xz plane from point B, and a moment of magnitude M=18 kN.m from point C in the z direction acts on the arm in the figure. The lengths of the arm are also given as L1=1.5 m and L2=1.2 m. It is desired to determine the stress state of point A on the a-a section taken from the arm. The radius r of the section is r=0.012 m and the shear modulus of the arm material is G=75 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. (Write your result in MPa.)
Question 2) A force of magnitude F=28 kN, which makes an angle of θ=35 ° with the horizontal in the xz plane from point B, and a moment of magnitude M=18 kN.m from point C in the z direction acts on the arm in the figure. The lengths of the arm are also given as L1=1.5 m and L2=1.2 m. It is desired to determine the stress state of point A on the a-a section taken from the arm. The radius r of the section is r=0.012 m and the shear modulus of the arm material is G=75 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. (Write your result in MPa.)
Question 2) A force of magnitude F=28 kN, which makes an angle of θ=35 ° with the horizontal in the xz plane from point B, and a moment of magnitude M=18 kN.m from point C in the z direction acts on the arm in the figure. The lengths of the arm are also given as L1=1.5 m and L2=1.2 m. It is desired to determine the stress state of point A on the a-a section taken from the arm. The radius r of the section is r=0.012 m and the shear modulus of the arm material is G=75 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.)
3. As shown, a vertical 200 lb force is applied to the gear and shaft assembly at point D. Shaft ABC is solid and has a 0.5 in. radius. (you may use a coordinate system of your choice, as long it's correct.) y 2.5 in. 10 in. D H B Z X 200 lb a) Determine the state stress (all stresses with their indices) at point H on top of the shaft. b) Determine the principal stresses and max shear stress at point H.
Determine the state of stress at point A of the rectangular post shown loaded with concentrated forces directed along the y axis equal to 75kN and along the x axis equal to 15kN. 1)Determine the total normal stress along the x and y axes at point A (include if tensile or compressive in your final solutions) 75 kN 50 mm 200 mm- 150 mm OAx= 15 kN OAy= 2) Draw the state of stress of point A 800 mm A 50 mm