Transform the set of cartesian strain components, = 400 ue(yy = 250 ue125 ue%3D%3DYay = 275 µe%3DYy: = 175 µeYes = 225 µeinto a new set of cartesian strain components relative to an Ox'y'z' set of coordinates,where the direction angles associated with the Ox'y':' axes aren/3R/31/43n/41/4n/2n/3n/3In/4

Answered: Transform the set of cartesian strain…

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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Consider the following strain state: [0.0016 0.0003 [0] = 0.0003 0.0008 0 0 0 0 0.0004] a. Determine the strain matrix for this strain state if the axes are rotated 30° counterclockwise around z-axis. b. Plot Mohr's circle for this strain state.
Q3 coordinates is given by: The 3-dimensional state of strain at a material point in x, y, z xx [ε] = &₁ Ex Exy Evy zy E XZ E 0 0 0 = 0 -1 -3 *10* 0 -3 5 (a) Calculate the characteristic equation and determine the principal strains for the three-dimensional state of strain (b) Calculate the volumetric strain and the deviatoric strain invariants
Q 5(b) Given the Cauchy strain tensor below where 1 = 1.6, calculate the following: (i) First strain invariant (ii) Second strain invariant (iii) Third strain invariant. C =
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Determine whether the following strain field is compatible: Ex = 3y² + xy, Ey₁ = 2y + 4z + 3, ₂ = 3zx + 2xy, Yxy = 4xy, Yyz = 2xz, and Yxz = 2xyz.
Consider that l'm pulling a material with a 5N force as below: Material Hanging 5N mass And I get the following force vs strain curves below (showing how the material stretches) depending on how long the force is applied. 5N 5 N 10 12 3 4 5 6 7 89 10 to 1 2 3 4 5 6 7 89 10 0.05 0.05 0.02 0 12 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time (s) Time (s) What sort of material is this? What are the viscosity and spring constant of the material? What is the time threshold that determines whether the material acts as a liquid or solid? What is the characteristic frequency of the material? What real world material property does this model describe? Strain Force Strain Force
Imagine a 3D state of strain in a mechanical part, measured perhaps by digital volume correlation or other means, given in Cartesian coordinates by €rx = a(x² + y²), €yy = a(y² +2²), Exy=b(xyz), Exz = €yz = €zz = 0, where a and b are constants and x, y, z are coordinates in space. Determine whether this measured strain field is a possible state of strain for a continuum that remains intact and continuous after deformation.
Imagine a 3D state of strain in a mechanical part, measured perhaps by digital volume correlation or other means, given in Cartesian coordinates by = a(x² + y²), €yy = a(y² + 2²), €xy = b(xyz), €xz = €yz = €zz = 0, where and b are constants and x, y, z are coordinates in space. Determine whether this measured strain field is a possible state of strain for a continuum that remains intact and continuous after deformation. '-xx =
Q4. Two are applied to the pipe AB as shown. Knowing that the pipe has inner and outer diameters equal to 35 and 42 mm, respectively. Determine the normal and shear stresses at (a) point a, (b) point b.
4 A water pipe is to beconstructed with a 207 grade in the novth divection and a 10% grade in the cast divection. Deteomint the angle & reguived in the wafer pipe tor the turn from novth to east. Est 5 Find the length and divection for (uxv) X(vxu) 19 for the tollowtings O u=zi+3j , v= -i+j @ u=2i-2j ++k vーit)-2K ® u= irj-K, v=0 @ u= -gi -2j-4K, v= 2i+2j+k O u= i-tjtk, v= i+j+2k Find @the area of the triange determined by the point P,a & R. Othe unit vector perpendicular toplane PaR. O PU, 1,1), Q(2,1,3), R(3,-1,1) @ P (2,-2, 1) , Q (3,-1,2), R(,-1,1) O P(-2,2,0), Q(0,1,-1) , R (-1,2,-2) A Find the volumo of the parallelopiped Cbon) dek mincl by U,v, ond w. u= 2i , v=2j, w= 2k O uz i-j k, v= 2itj-2K, w= -i+2j-k ® u= 2i+j, v=zi-j+k, w= i+2K i+j-2K , v=-i-k, W= zi+4j -2K 8 Let u= 5i-j+k, v=j-5k, w= -isi+3j-3k. Which verdns. if are @ perpendicular ® paralled. T Find the aveas ☺ All,o), B(0,1),<(-l,0), D(0,-1) A (010) , TS (7.3) , e(9,8), D(2,5) A(-12) , B (2,0) , c(7i1) ,D(4,3) of the…
For the area shown below defined by the two curves, to find Iy by integration you use a dA element parallel to the x axis. The expression in the integral is the following: y = x 100 mm 1 100 - X. 100 mm O ly²(10y1.5 – y)]dy O ^(10y².5 – y0.5)|dy O [x?(10y0.5 – y)]dx O [x°(10y0.5 – x)]dy O ly^(10y0.5 – y)]dy
The state of stress at a point in an engine piston is given in the x-y-z coordinates by: 90 180 xx ху XZ [6]=0, |180 240 0 MPa ух yy yz 120 ZX 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. BRE

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