A plane strain field at certain point in a body is described by the following strains; E. = +200 μ in/in, Eso +300 μ in/in and E120 -100 μ in/in. Analyse the state of strains to determine, principal stresses, maximum shear stresses and their orientations. Take E = 29 x 106 psi, v=0.3.

A plane strain field at certain point in a body is described by the following strains; E. = +200 μ in/in, Eso +300 μ in/in and E120 -100 μ in/in. Analyse the state of strains to determine, principal stresses, maximum shear stresses and their orientations. Take E = 29 x 106 psi, v=0.3.

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: Same problem is considered here again using three equal length elements. Suppose that the strain…

A: Given Data :- Strain energy of element 1 ( u1) = 0.09 N.m Strain energy of element 2 ( u2) = 0.17…

Q: Can you please show me how to calculate the stress and strain on this figure. use this formula or…

A: For stress, σ=FA F - applied load (known to you) A- effective cross section…

Q: ɛ=-100µ 120° 120° ► x ɛ=200µ ɛ=-200µ 3D

Q: The normal strain in a suspended bar of material of varying cross section due to its own weight is…

Q: A strain gauges system mounted at a point on a structural member that is subjected to multiaxial…

A: correct answer is option 4th). For solution refer below images.

Q: Three strain gauges are attached on the surface of the plane frame which is shown in Figure. The…

A: Given data: - The angle between each strain gauges is θ = 63o. The reading of gauge a is εa = 1100…

Q: A force P is applied to ring A connecting the two wires together. As a result, point A is displaced…

Q: A copper wire of length (400+R) cm , diameter of (4+R) mm and mass of (5000 + R) g, if Young's…

Q: a) What are the principal stresses? Sketch the principal stress element and mark its values. b)…

Q: The state of plane strain on an element has components €z = -340(10 6), Ey = 0, and Yzy = 130(10 ®).…

Q: For the given plane strain state, use Mohr's circle to determine the strain state associated with…

A: Write the given data. εx=-500εy=250γxy=120θ=-15°

Q: Calculate the longitudinal strain, if internal pressure is 1.2 N/mm2 and 1 m in diameter along with…

Q: A steel bar 250 mm long, 40 mm wide and 30 mm thick subjected to a pull of 200 kN in the direction…

A: Given data: The length of the steel bar is l=250 mm The width of the steel bar is w=40 mm The…

Q: rate shown below, determine the principal strains Exy -Exx Eyx Eyy Eyz E Ex Egy EN -1.1 0.5 0.5 2.4…

A: solution of above problem is below:

Q: Same problem is considered here again using three equal length elements. Suppose that the Young's…

A: Given: E = 19 GPa = 19×109 Pa P = 35 kN = 35000 N A1= 30 mm2 = 30×10-6 m2 Total length, L = 15 cm =…

Q: The minimum principal strain is:

Q: E, = 200.00 pE Eb = 400.00 pe E = 150.00 pe 600 The strain rosette shown was used to obtain normal…

Q: The strain components at a point in a body under a state of plane strain are shown in fig. Using…

Q: A rectangular titanium plate has the following dimensions. a = 20 mm, b = 15 mm, and c=5 mm.…

Q: A strain gage is mounted to the outer surface of a thin-walled boiler. The boiler has an inside…

Q: A three strain gages have been attached directly to a piston used to raise a medical chair, the…

Q: Same problem is considered here again using three equal length elements. Suppose that the strain…

A: Given Data Strain energy of element 1 ( U1) = 0.07 N.m Strain energy of element 2 ( U2) = 0.17 N.m…

Q: Same problem is considered here again using three equal length elements. Suppose that the strain…

A: Strain energy of element 1 ( u1) = 0.09 N.m Strain energy of element 2 ( u2) = 0.17 N.m Strain…

Q: ain that has the following components: ex = 150µ, ey = 200µ, yxy = -700µ. using the strain…

Q: Deformed length of the elongated diagonal.

A: Given; A rectangular region in a solid is in a state of plane strain. The rectangle is subjected…

Q: A thin polymer plate PQR is deformed such that corner Q is displaced downward a distance L = 0.10…

Q: If a rubber material is deformed as shown in the following figure, determine the normal strain along…

A: As, ∈x=320=0.15&, ∈y=-220=-0.1

Q: Prove that : 2 strain Energy= %3D 2GJ -x Volume 4G

A: Strain energy due to axial load PU=12P×δLSimilarlyStrain energy due to torsion TU=12×T×θ ......1Now…

Q: If a rubber material is deformed as shown in the following figure, determine the normal strain along…

A: As, ∈x=320=0.15and ∈y=-2/20=-0.1 Initial angle, θ1=tan-12020=tan-11=45°

Q: E120 = +625 Eo = +950 Ez40 = +300

A: For solution refer below images.

Q: the nodal displacements are For the plane strain elements shown in the Figure given as (4, 4) uj =…

A: Solution: Given Data:

Q: Q1: The stresses measured at a point on bone are ox =5 MPa ,0y = -7 MPa and txy-2.4 MPa find: 1. The…

A: Given Data σx=5MPa σy=-7MPa Txy=2.4MPa Poison ratio, v=0.3 Principle stress expression

Q: The state of strain at the point on the pin leaf has components of € = 200(10-6) Ey 180(106), and…

Q: For the state of a plane strain with Ex, Ey and yxy components: (a) construct Mohr's circle and (b)…

A: εx = 250 × 10-6εy =310 x 10-6Yxy = -100 × 10-6

Q: Exercise 2 : For the constant strain triangular shown in figure 2. Determine the strain-displacement…

Q: Same problem is considered here again using three equal length elements. Suppose that the Young's…

A: Given data: Young's Modulus, E = 1 GPa = 1×109 pa applied force, P = 29 kN = 29000 N Area of element…

Q: If a rubber material is deformed as shown in the following figure, determine the normal strain along…

Q: For a conductive wire with length L=1cm,w=1mm, h=1mmunder uniaxial strain, the resistance change is…

A: According to the information we have a Uniaxial strain that is e=1 and the Poisson’s ratio is n= 0.3…

Q: 1.40 Given a major principal strain of 600u and strain invariants /, = 400µ and /, = - 4800µ, find…

A: Solution: Given Data: σ1=600μI1=400μI2=-4800μ

Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

A plane strain field at certain point in a body is described by the following strains; E. = +200 μ in/in,
E60 +300 u in/in and E120 -100 μ in/in. Analyse the state of strains to determine, principal stresses,
maximum shear stresses and their orientations. Take E = 29 x 106 psi, v = 0.3.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: Finding normal strain in Y direction

VIEW

Step 3: Finding shear strain

VIEW

Step 4: Finding Principal strain

VIEW

Step 5: Finding principal stresses & maximu shear stresses

VIEW

Step 6: Finding orientation of principal plane & maximum shear stress plane

VIEW

Solution

VIEW

Step by step

Solved in 7 steps with 7 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

A rigid steel bar is supported by three rods as shown. There is no strain in the rods before the load P is applied. After load P is applied, the normal strain in rods (1) is 2410 µm/m. Assume initial rod lengths of L₁ = 1,250 mm and L₂ = 2,000 mm. Determine the normal strain in rod (2). (1) 4₁ (2) Rigid bar O 975 μm/m O 1072 μm/m O 1757 µm/m O 1656 µm/m O 1506 μm/m B P L₂ (1)
The normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E where y = 2.4 lb/in.³ is the specific weight of the material, y = 1.8 in. is the distance from the free (i.e., bottom) end of the bar, L = 9 in. is the length of the bar, and E= 26000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar. Calculate the change in length of the bar due to its own weight. Answer: x10-6 in.
The strains on the surface of an experimentaldevice made of pure aluminum (E = 70 GPa,n = 0.33) and tested in a space shuttle were measuredby means of strain gages. The gages were orientedas shown in the figure, and the measured strainswere εa = 1100 X 10-6 , εb = 1496 X 10-6 and εc = -39.44 X 10-6What is the stress σx in the x direction?
A differential element on the bracket is subjected to plane strain that has the following components: , Ex = 300 x 10-6, Ey = 200 x 10-6, Exy = -500 x 10-6. Use the strain-transformation equations and determine the normal strain Ex' in the x' direction on an element oriented at an angle of 60°. Note, a positive angle is counter clockwise.
5 decimal places Determine the total strain (mm/mm) of a 2.64-m bar with a diameter of 21 mm subjected to a tensile force of 71 kN at a temperature increase of 49 C°. Consider the α=27.3 µm/mC° and E = 122 GPa.
For some element, the displacement is obtained as u = [1 + 3x +4y +5xy]x10^(-3) mm. The normal strain along x-axis at point (1.2, 0.8) m located inside the element is
The normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E where y = 3.0 lb/in.³ is the specific weight of the material, y = 6.3 in. is the distance from the free (i.e., bottom) end of the bar, L = 21 in. is the length of the bar, and E = 27000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar (c) the maximum normal strain in the bar. Answer: (a) d = i (b) avg (c) Emax i x10-6 in. με με
Your answer is partially correct. The strain components for a point in a body subjected to plane strain are ɛ, = -890 µɛ, ɛ, = -690µɛ and yy = -682 prad. Using Mohr's circle, determine the principal strains (ɛp1 > Ep2), the maximum inplane shear strain yip, and the absolute maximum shear strain ymax at the point. Show the angle 0, (counterclockwise is positive, clockwise is negative), the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Answers: Ep1 = 927.99 με. Ep2 = 1116.0 PE. Vip = 188.01 prad. Ymax = -188.01 prad. Op = 36.82