QUESTION 2 a) An element in plane stress is subjected to compressive stresses o, and tension stresses ay with a magnitude 45 MPa and 75 MPa respectively. Also, shear stresses with a magnitude of 15 MPa act in the direction as shown in Figure 3. By using fomulae method, determine: i) the corresponding average stress (o,) and radius (R / Fea). i) the principal planes (Op and 0s), the principal stress (m. and Gan) and sketch the illustration. iii) the normal and shearing stresses after the element shown has been rotated through 30°C clockwise. iv) the normal and shear ing stresses after the element shown has been rotated through 60°C counter clockwise. v) draw the answer for questions (i to iv) in mohr's circle. Element

QUESTION 2 a) An element in plane stress is subjected to compressive stresses o, and tension stresses ay with a magnitude 45 MPa and 75 MPa respectively. Also, shear stresses with a magnitude of 15 MPa act in the direction as shown in Figure 3. By using fomulae method, determine: i) the corresponding average stress (o,) and radius (R / Fea). i) the principal planes (Op and 0s), the principal stress (m. and Gan) and sketch the illustration. iii) the normal and shearing stresses after the element shown has been rotated through 30°C clockwise. iv) the normal and shear ing stresses after the element shown has been rotated through 60°C counter clockwise. v) draw the answer for questions (i to iv) in mohr's circle. Element

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

See similar textbooks

Similar questions

1) The state of stress on an element is shown in following figure. i) Determine the stresses acting on an element oriented at a counterclockwise angle of 48° from the horizontal. Show these stresses on a properly oriented element. ii) Determine the principal stresses and the principal angle. Show these stresses on a properly oriented element. iii) Determine the maximum shear stress, angle for maximum shear stress and normal stresses when maximum shear stress exists. Show these stresses on a properly oriented element. 140 MPa A 42 MPa 60 MPa
The state of plane stress at a point on the surface of the airplane fuselage is represented by the stress element shown in the figure. Using Mohr's Circle, determine a) the principal stresses and the maximum in-plane shear stress specifying the orientation of the element in each case. b) The equivalent state of stress at the point on the element that is oriented {a} clockwise from this position Draw all the corresponding stress elements. Given x = {x} MPa; y = {y} MPa and xy = {xy} MPa xy MPa y y MPa 10000 x MPa →→→→x Solve in terms of variables
1.6-7 A wire of length L = 2.5 m and diameter d = 1.6 mm is stretched by tensile forces P = 600 N. The wire is made of a copper alloy having a stress- strain relationship that may be described mathemat- ically by 124,020ɛ 0 s8s 0.03 (o = MPa) 1+ 300ɛ in which e is nondimensional and o has units of MPa. (a) Construct a stress-strain diagram for the material. (b) Determine the elongation of the wire due to the forces P. (c) If the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
Q5: At a point in a strained material the stresses acting on planes at right angles to each other are o, 30, MN/m² tensile, together with associated shear stresses which assumed clockwise in effect on oy plane. If the maximum principal stress is limited to 1002 MN/m² tensile, and xy-60 MN/m², calculate: (a) the magnitude of the o, and oy; (b) the values of the maximum and minimum principal stresses; (c) the directions of the principal planes; (d) the maximum shear stress.
Plane stress state in the tension member given in the figure with Mohr's Circle; a)Determine the principal stress directions by calculating the principal stress values. b)Determine their direction by calculating the largest and smallest shear stresses.
ante y se IN.. is). Pressure vessels are very common in many industries. The purpose of this exercise is to examine how stresses evolve within the walls of a pressure vessel as a function of position within the wall and wall thickness. Recall the thick-walled cylinder solution developed in class. Re-write the solution to the case of a thick-walled cylinder with inner radius a, outer radius b, internal pressure p₁, and external pressure, p2. Orr σαθ a²p₁b²p2 (6² - a²) a²p₁-b²p2 (6²-a²) axis + 1 (a) Draw a diagram showing the evolution of orr and σ00 from a to b when a/b=0.5 and P2 = 0. (P2 - P₁)a²6² 1 (6²-a²) 2¹ (P2 - P₁)a²6² 1 (b²-a²) 2 (b) Make the assumption that p2 = 0, a + b 2r, bat, and abr to derive the expression for rr and 000 for a thin-walled pressure vessel. For a sanity check, your solution should be orr = 0 and 000 = pir/t. t (c) Now consider the classical strength of materials approach to pressure vessels. Imagine the pressure vessel shown in Fig. 2 (note, the radius of…
3. Listed below is a combination of stresses acting at a point and referred to axes x and y in an elastic material. Using Mohr’s circle of stress determine the principal stresses at the point and their directions for each combination. 1}sigmax -60 n/mm2 , sigmay -36n/mm2 ,TAUxy=5n/mm2 2}}sigmax 30 n/mm2 , sigmay -50n/mm2, TAUxy= 30n/mm2
State of stress at the wall and the roof of the following circular opening bafore the excavation is (a] = |0 4. Find the induced stress components at point a. R W with respect to the given x-y coordinate systerm, and expresst them in the matrix form. b. Find the total stresses at point W, and give them in matrix form. c. Repeat (a) and (b) for the roof. d. Find the stresses oy, Ciy, and tyy at point A which is located at a radial distance twice the radius of the tunnel.
Q2. What is meant by major stresses and major levels? b An element in a plane affected by the stresses shown in the figure using the arithmetic and semi-graphical method. Calculate 1- The main stresses and their trends or levels on which they are located. - The greatest shear stress, the plane on which it lies and the associated vertical stress. - Vertical stresses if the element rotates at an angle of 20 on the main plane. B 5.000 psl 4.000 psl 15,000 psl veroo
The state of stress shown to the left was produced by a combination of loadings on a body that is not shown. Determine the following via Mohr's circle: A) Draw Mohr's Circle for the x-y plane. B) Determine the principal stresses - All 3. C) Sketch a properly oriented differential element showing the principal stresses in the x-y plane. D) Determine the magnitude of the maximum shear stress in the x-y plane. E) Sketch a properly oriented differential element showing the maximum shear stress state in the x-y plane. F) Determine the magnitude of the absolute maximum shear stress (and include the two out of plane circles on your original figure). Use the following values for the magnitudes of the stresses: x = 0₂ Txy Ox X X 10 ksi, σy = 4 ksi, σ₂ = 3 ksi, Txy = 4 ksi
Part C - Counterclockwise Rotation of a Stress Element The state of stress at a point in a member is shown on the rectangular stress element in (Figure 5) where the magnitudes of the stresses are |o₂| = 16 ksi, |oy| 29 ksi, and Try = 8 ksi Determine the state of stress on an element rotated 50° counterclockwise from the element shown. Express your answers, separated by commas, to three significant figures. ► View Available Hint(s) 02 Oy, Tz'y' Submit - VE ΑΣΦ ↓↑ vec Part D-Clockwise Rotation of a Stress Element with No Shear Stress ? ksi, ksi, ksi The state of stress at a point in a member is shown on the rectangular stress element in (Figure 6) where the magnitudes of the stresses are ₂ = 13 ksi and|oy| = 12 ksi Figure Part A - State of Stress on an Inclined Plane <
The state of stress at a point in a structure is shown in the following figure.(a) find the main stresses (Show the results on a sketch ofcorrectly oriented).(b) Find the maximum shear stress with its average stress (Show theresults in a correctly oriented sketch).