The 3-dimensional state of strain at a material point in x, y, z Q3 coordinates is given by: [8] xx Vt. vy E EV XZ E 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

The 3-dimensional state of strain at a material point in x, y, z Q3 coordinates is given by: [8] xx Vt. vy E EV XZ E 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

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

Related questions

Q: gages to measure a 2D strain field on the surface of a material, which you find to be €xx = 5 + x² +…

Q: Solve the stress tensor at the location of strain gauge (red dot). Find the principle stresses and…

Q: A large thin rectangular plate is subjected to certain traction boundary conditions on its thin…

A: Given : φ(x,y)=Ax4+Bx2y2+Cy2

Q: A cylindrical specimen of aluminum having a cross-sectional area of 3.50 x 105 m? and a gauge length…

A: Given: Stress-strain diagram for a cylindrical specimen of aluminum is given in the first diagram…

Q: Q1 The state of stress at a point of an elastic solid is given in the x-y-z coordinates by: 0 0 XX…

A: The stress along x-direction, σx = 100 MPaThe stress along y-direction, σy = -90 MPaThe stress along…

Q: A very thick structure is subjected to certain traction boundary conditions on its surface. The…

A: “Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: For many materials, the stress-strain curve can be written by the Ramberg-Osgood equation presented…

A: Given; The strain at 140 MPa, ε140 = 0.04 The strain at 280 MPa, ε280 = 0.1 The strain at 420 MPa,…

Q: Stress (MPa) Graph 1 - Stress/Strain plot 400 320 300 200 100 0 (a) 51.472kN (b) 205.89kN (c) 25735N…

Q: A strain gauge has a resistance of 100 Q is connected as a one arm of a whetstone bridge to measure…

Q: 1. Find the relationships between strain components in the polar coordinate and strain components in…

A: To find the relationships between strain components in the polar coordinate and strain components in…

Q: The strain rosette shown has angles 0, = 0° (aligned with the x-axis), 0, = 60°, and 0, = 120°, We…

Q: Four strain gauges are bonded onto a cantilever as shown in Figure 8.20(a). Given that the gauges…

A: A strain gauge is an passive transducer which converts mechanical displacement into charge of…

Q: the stress-strain curve can be written by the Ramberg-Osgood equation presented below, where the…

Q: 3.3 The displacement field at a point in a body is specified as follows: ux = 0.06x + 0.05y - 0.01z…

A: Given:The displacement field at a point in a body is specified as follows;The coordinate of one…

Q: The nodal coordinates and the nodal displacements for some plane stress elastic element is listed in…

Q: 1. (a) If the displacement field is given by u kxy, u, = kxy, u, 2K(x + у)z where k is a constant…

A: u= ux= kxy v= uy= kxy w= uz= 2k(x+y)z Normal stress along X axis and X direction= εxx= du/dx= ky…

Q: 1. A tension test on an aluminum plate resulted in the following engineering stress-engineering…

A: A tension test on a aluminium plate resulted engineering stress, engineering strain data as reported…

Q: sce M13.5 Strain measurement with rosettes Ea 500 µE Eb -200 με %3D Ec 250 με 30° 30° I| ||

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider that l'm pulling a material with a 5N force as below: Material Hanging 5N mass And I get…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Please find the question attached.

A: The 1st compatibility equation is,

Q: A finite element model of a rod (bar), with two quadratic elements as shown below is considered. The…

A: Given the length of the bar. Required: Value of a

Question

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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Volumetric & deviatoric strain calculation

VIEW

Step 3: Finding the characteristic equation

VIEW

Step 4: Principal strain calculation

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

We're measuring axial load in a rectangular bar with two strain gauges: one on the top in the axial direction and the other on the bottom in the transverse direction). An axial load, P, is applied and the ambient temperature is varying with time. P # Strain gages > Р (a) If one strain gauge is connected to leg 1 of the Wheatstone bridge, which leg (2, 3, or 4) would you connect the other strain gauge in order to achieve temperature compensation? Please explain your choice by writing out the equation. (b) Calculate the bridge constant of this arrangement, your (c) If some bending moment were inadvertently applied (in addition to the axial load), would choice in part (a) provide compensation for bending loading? Justify your answer by writing out the equation.
A strain rosette was attached to the outer surface of stainless vessel when the vessel is in a stress-free state. The vessel was then put under a complex loading (pressure, bending and torsion) state. The train readings for the three strain gage elements in the strain rosette were recorded as: Ea=210, Eb=160, Ec-330, all in micro-strains. The mechanical properties of the stainless material are known: E=193 GPa, G=76 GPa, v=0.27, oy=205 MPa. Calculate the following: 1. Principal strains and in-plane maximum shear strain. 2. Principal stresses and absolute maximum shear stress. 3. The factor-of-safety based on the maximum shear stress failure theory. 4. The factor-of-safety based on the maximum distortion energy failure theory. 45° 45° b 45° strain rosette X
2) Which of the following strain fields are possible for a solid structure. Explain. (a) ɛ, = k(x+ y), 8, = k, 8, = kx, Y = ky, 7z = k, Y =0 (b) ɛ, = k(x² + y²), ɛ, = ky, ɛ, = 0, 7y = kxy, Y3z = 0, 7x = 0 (c) ɛ, = kz(x² + y²), 8, = ky²z, 8, = 0, 7 = kxyz, Yyz = 0, 7= = 0
A rectangular plate ABCD with base L = 283 mm and height H = 376 mm experiences the deformation illustrated below, resulting in the deformed plate shown by dotted lines. Determine the average shear strain y at the corner C when a = 3 mm, b = 4 mm, c = 4 mm, d = 4 mm, e = 3 mm and f = 3 mm. Assume small deformations. %Matlab input: L = 283; H = 376; a = 3; b = 4; C = 4; d = 4; e = 3; f = 3: y d B C H b A a L
Can someone please help me to solve the following question using the FACTOR LABEL METHOD OF UNIT CONVERSION. Showing all work and formulas please and thank you!
If a rubber material is deformed as shown in the following figure, determine the normal strain along diagonal AC. D 2 mm 3 mm 20 mm A B 20 mm Select one: 0.0326 0.0607 0.0853 0.1281 0.1402
Question 1 The wedge shaped bar shown in Figure Q1 is to be analysed using a single one dimensional quadratic element as shown. The bar has a rectangular cross section with a constant width and a linearly varying depth. 500 k = 10E 2 100 3 Figure Q1. +1] a) Calculate the strain shape function matrix, [B], for the element. b) Using the strain shape function matrix derived in (a), show that the stiffness matrix for the element is given by the equation: I 255+ ALL DIMENSIONS IN mm (3-5) d h 100- with units of N/mm Where: E = Young's modulus of the material 10 c) Show how the strain shape function matrix may be used to determine the stress from the nodal displacement for this type of element. Do not attempt to calculate the stress. LEGION Question 2 Figure Q2 shows a two-dimensional quadratic element that has been distorted such that one Q Search
A differential element is subjected to plane strain that has the following components; Px = 950(10-6), Py = 420(10-6), gxy = -325(10-6). Use the strain transformation equations and determine (a) the principal strains and (b) the maximum in-plane shear strain and the associated average strain. In each case specify the orientation of the element and show how the strains deform the element.
Q3
The 3-dimensional state of strain at a material point in x, y, z Q4 coordinates is given by: E ya [ε]=Ey Eyy - M E E 20 E יה = -120 0-150 0 0 0 -150 0 240 *10-6 (a) Calculate the volumetric strain and the deviatoric strain invariants (b) Calculate the mean stress and the deviatoric stress tensor (c) Write the characteristic equation of strain (d) Write the characteristic equation of stress The material is linear elastic (E=210GPa, v=0.3).
Given the stress tensor: Find: 3 36 27 0 σ = 27-36 00 0 18 (a) The components of the traction (force per unit area) acting on a plane with unit normal n= 2 21 3 3'3 T (b) The component of the traction in the direction of the normal (c) The angle between the traction and the normal vector (d) The magnitude of the traction vector (e) The net force acting on a cube with corners at (x,y,z)=(±1,±1,±1)
4.7. Show that the direct strain-component in the y-direction is given by (Fig. 4.6). Figure 4.7 (Evv)s an ay Ay A x Ax Ay D' any Ay Figure 4.6 1 Ax