1. (a) Show that for an isotropic lamina in plane stress, the strain-stress relations are€111S1201S12 S11€62(S11 – S12),where S11 = 1/E and S12 = -v/E.(b) Show thatQ11 Q12€102Q12 Q1106€6whereQ11Q12and Q66 = +v) ·1-v² ,

The generalized Hook's law can be expressed for a three-dimensional elastic anisotropic body as,…

Answered: a) Show that for an isotropic lamina in…

Engineering

Mechanical Engineering

a) Show that for an isotropic lamina in plane stress, the strain-stress relations are

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: The three principal stresses at a given point are o; = 60 MPa, o2 = -100 MPa, o3 = -10MPA. If the…

A: Given that, σ1 = 60 MPaσ2 = -100 MPaσ3=-10 MPa Yield strength of Material Syt = 250 MPa

Q: A thin-walled spherical shell made of a high-strength steel, whose forming-limit diagram is as…

A: Given data:- A thin walled spherical shell made of high strength steel with shell diameter =250 mm…

Q: Define different types of stresses, strains and material constants.

Q: 2.2. The stress at a point is defined by the components Oxy =7 ksi, oyy=10 ksi, Ory =-20 ksi. Sketch…

A: givenσXX=7ksiσyy=10ksiσxy=σyx=-20ksi

Q: A stress-strain diagram for a tension test of an alloy steel sample is shown in the diagram below.…

A: Stress-Strain curve describes the relationship between stress and strain under a certain load in…

Q: Q6) Find by calculation, the principal stresses present in a material subjected to a complex stress…

Q: A small room is made up of rectangular metal bars. One bar has a width of 10 mm and would be able to…

A: Given:w=10 mmσc=20 MPa

Q: (c) Describe what is represented by Poisson's ratio and show what it measures with the aid of a…

A: the significance of poisson's ratio is to be described and a relationship between axial stress and…

Q: Using analytical method of transformation equations; (a) The orientation of principal planes and the…

A: Given Data: The stress acting in the horizontal direction is, σx=2R MPa. The stress acting in the…

Q: A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa.…

A: Given data: Yield strength of the material, σy=350 MPa=50.76 kpsi Principal stresses can be…

Q: The principal stresses at a point are 70, 60 and -18 MPa; say o, is the yield point stress of the…

A: Given data

Q: 4) A metal plate has an area of face is 1m x 1 m and thickness of 1cm.One face of a larger area is…

A: (a) The Shear Stress is 4.2 x 108 N/m2. (b) The Shear Strain is 0.005. (c) The Shearing Force is 4.2…

Q: and shear stresses acting on one plane are 8000 psf compression and 2000 psf, respectively. On a…

Q: magnitude of true strain produced in the deformed bar.

A: Given; A bar is compressed to half of its original length, Let assume ; L0=Initial length…

Q: 3. (a) Using Stress transformation equations, determine the principal planes, the principal…

Q: A test piece is cut from a brass bar and subjected to a tensile test. With a load of 6.4 kN the test…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: IAIH, Fectangular plate shown in Figure (6.25) is subjected to a uniform biaxial state of stress…

Q: 10 MPа 4 ksi 10 MPа 4 ksi 10 MPа 2 ksi

A: Mohr circle is a graphical method to determine principal stresses. It's plotted on a graph between…

Q: A mild steel specimen of circular cross-section of length 36.06 mm is subjected to a maximum tensile…

A: As per policy, we can solve first three subparts only.

Q: s, (c) the orientation of the planes maximur num in-plane shearing stress, (e) the cor

A: Given data sigma x = 18 kpsi sigma y = 12 kpsi shear stress = -8 kpsi required Principal stress…

Q: Problem 2: At a point in an elastic material, there are two mutually perpendicular planes, one of…

A: The principal plane position θp=21.263° The shear plane position…

Q: 1. A 1.5-m long circular cross-sectioned bar with r = 1 cm is under a combination of bending moment…

A: DISCLAIMER FOR MULTIPART FROM BARTLEBYSince you have posted a question with multiple sub-parts, we…

Q: At a point in a material under stress, the intensity of the resultant stress on a certain plane is…

A: Draw the Mohr circle indicating the resultant stress on the plane. Write the expression for the…

Q: For a material under uniaxial tension loading, Find the true strain at which necking instability…

A: n=0.42 K=300 MPa

Q: Why do we define engineering and true stresses for tension/compression loading but not for shear…

A: Engineering stress: It is the stress based on the initial or original cross sectional area (Ao)…

Q: A wire of diameter 0.86 mm and length 1.5 m has a force of 160 N applied, extending it by 5.2 mm.…

Q: (a) Construct Mohr's circle for an element in a uniaxial state of stress (b) Use this Mohr's circle…

A: Procedure for Mohr’s circle:

Q: A 10000N tensile force is used to pull a cylindrical rod with an initial diameter of 2 cm. During…

A: Given data: Tensile Force = 10000 N Initial Diameter of Cylinder = 2 cm Final Diameter of Cylinder =…

Q: 8.4 A material is subjected to two mutually perpendicular stresses, one 60 MN/m compressive and the…

Q: bar is 250 mm long and 10 mm square over part of its length, the remainder being circular with a…

A: as per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: Problem 6. Consider the following stress state: [6 4 01 [a] 4 12 0 ksi Lo 0 6] Determine the…

A: Given: σ=6404120006 ksi Young's Modulus ,E=10000 ksi Poisson Ratio ν=0.25

Q: Can you help me with this problem, please: At a material point in plane stress it is known that…

A: Magnitude of principal stresses:The principal stresses can be determined using the stress…

Q: A part made of Aluminum 6061-T6 has a yield strength = 400 MPa. For each stress state below, draw…

Q: The magnitude of the shear stress to cause yielding in a torsion test and the magnitude of the…

A: It is False

Q: A specimen of titanium alloy is tested in torsion and the shear stress–strain diagram is shown in…

A: By inspection, the graph is linear upto point A. Thus, the proportional limit is The maximum shear…

Q: Derive the expression for the strain transformation.

A: Strain transformation:- Strain-Transformation equations are based on the geometry of the…

Q: If an axial member is allowed to freely elongate or contract, a temperature change will (A) cause an…

Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

Question

1. (a) Show that for an isotropic lamina in plane stress, the strain-stress relations are
€1
11
S12
01
S12 S11
€6
2(S11 – S12),
where S11 = 1/E and S12 = -v/E.
(b) Show that
Q11 Q12
€1
02
Q12 Q11
06
€6
where
Q11
Q12
and Q66 = +v) ·
1-v² ,

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

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

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

For some metal alloy, a true stress 345 MPa (50040 psi) produces a plastic true strain of 0.02. How much will a specimen of this material elongate when a true stress of 418 MPa (60630 psi) is applied if the original length is 500 mm (19.69in) ? Assume a value of 0.22 for the strain- hardening exponent, n
(a) Figure 1.1 shows a thick cylinder with inside radius of r;=94 mm and outside radius ro =136 mm was pressurized internally Pi = 56 MPa and externally Po= 26 MPa. Analyse: i. The hoop stress and radial stress on internal and external surface of the cylinder. ii. The hoop stress and radial stress at r= 115 mm. iii. The maximum and minimum shearing stress. iv. Sketch the distribution of hoop stress and radial stress along the cylinder wall. Po Figure 1.1 The thick cylinder
O 0.6% 19% If an isotropic material has a Young's modulus of 85 Gpa and a Poisson's ratio of 0.25, calculate its shear modulus. Select one: O G = 29 Gpa O G = 34 Gpa G = 25 Gpa O G= 77 Gpa O G= 46 Gpa If a rubber material is deformed as shown in the following figure, determine the normal strain along diagonal BD. C 2 mm 4 mm EN DO O
[4] In thin walled sphere, the wall is subjected to ..... O A. Hoop stress only B. Longitudinal stress only. C. Both A & B O D. Radial stress only
Please help. This problem involves torsional stress and strain. Thank you.
Calculate the principal stresses to the given state. Calculate the angle of rotation in the x-y plane. Calculate the extreme shear stresses. Are the extreme shear stresses the maximum shear stresses? Explain, Why or why not?
1. At a point in a piece of elastic material, direct stresses of 92 MN/m2 tensile and -49 MN/m2 compressive are applied on mutually perpendicular planes. The planes are also subjected to a shear stress. If the greater principal stress is limited to 100 MN/m2 tensile, determine the value of shear stress. Give you answer to 2 significant figures in MN/m2
True stress-strain Engineering stress-strain strain Calculate the engineering ultimate tensile strength of a material whose strength coefficient is 535 MPa and of a tensile-test specimen that necks at a true strain of 0.55. 200 MPa O 267 MPa O 244 MPa O 222 MPa stress
An element of material in plain strain is subjected to strains epsilon_x=0.0015, epsilon_y=-0.0002, and gama_xy=0.0003. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.
How is the general state of strain at a point in a body is represented?
[Problem 4] Show that the following strain components are the solutions of a problem in elasticity. E, = 2.xy', E, = -6.xy', E, = 2.x' +x'y-y Where & is defined as the small strain component. urgent solution.please explain properly. will surely upvote
A thin rectangular plate is uniformly deformed as shown. The distance A = 552mm. Determine the shear strain yy at P. State your answer in urad. Note: Do not include units in your answer. -0.8 mm A 1.7 mm 1,000 mm Answer: