A steel plate in a state of plane stress has e, =240 µ, e, = 200 u and 7a = 100u Poisson'sratio v = 0.3 and the modulus of elasticityE=210GPA. Use this information to answerquestions281 to 30.28. The maximum principal strain in the planeis most nearly:(a) 215µ(c) 107µ(b) 220и(d) 328µ29. The maximum principal stress in the planeis most nearly:(а) 69MPа(c) 57MPA(b) 75MPA(d) 77 MPa30. The state of plane stress is made of a steelwith oy = 90 MPa. If yield does not occurwhen using the maximum-distortionenergy criterion the factor of safety ismost nearly:(a) 0.53(c) Yield occurs(b) 1.06(d) 1.88

Answered: Image /qna-images/answer/e57fcf34-5a22-4a4a-9614-118a41b204ae.jpg

A steel plate in a state of plane stress has e, = 240 µ, e, = 200 u and 7g = 100u Poisson's ratio v = 0.3 and the modulus of elasticity E=210GPA. Use this information to answer questions281 to 30. 28. The maximum principal strain in the plane is most nearly: (a) 215u (c) 107µ (b) 220р (d) 328µ 29. The maximum principal stress in the plane is most nearly: (а) 69MPа (c) 57MPA (b) 75MPA (d) 77 MPa 30. The state of plane stress is made of a steel with oy = 90 MPa. If yield does not occur when using the maximum-distortion energy criterion the factor of safety is most nearly: (a) 0.53 (c) Yield occurs (b) 1.06 (d) 1.88

A steel plate in a state of plane stress has e, = 240 µ, e, = 200 u and 7g = 100u Poisson's ratio v = 0.3 and the modulus of elasticity E=210GPA. Use this information to answer questions281 to 30. 28. The maximum principal strain in the plane is most nearly: (a) 215u (c) 107µ (b) 220р (d) 328µ 29. The maximum principal stress in the plane is most nearly: (а) 69MPа (c) 57MPA (b) 75MPA (d) 77 MPa 30. The state of plane stress is made of a steel with oy = 90 MPa. If yield does not occur when using the maximum-distortion energy criterion the factor of safety is most nearly: (a) 0.53 (c) Yield occurs (b) 1.06 (d) 1.88

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.4P: An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy =...

See similar textbooks

Related questions

Q: 2. A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are 0.40 x…

Q: In uniaxial loading the poisson's ratio is 0.30 and the strain in the x- direction is 250 x 10^-6 .…

A: Poisson's ratio = - Lateral Strain / Longitudinal Strain Longitudinal strain is strain occur in…

Q: A 5 mm diameter aluminium alloy test bar is subjected to a load of 500 N. If the diameter of the bar…

A: Given, Initial diameter = D0 = 5 mm Final diameter = D = 4 mm Load = P = 500 N True strain is…

Q: A steel bar of 3 m long and 2500 mm2 in area hangs vertically, which is securely fixed on a collar…

A: Given Area, A = 2500 mm2 Load, P = 25 kN Length, L = 3 m E = 200 GPa Find…

Q: 982. The strain components at a given point are x = -533 x 10, 6, = 67 x 10-6, and Y = -626 X 106.…

A: To find The stress components on the face whose normal is 45° from the X axis. Given The strain…

Q: Calculate the moment and axial load capacity of the circular column corresponding to the given…

Q: Rigid bar ABCD is supported by two bars. There is no strain in the vertical bars before load P is…

A: (a) To find: The normal strain in bar 1. Given: The dimensions are L1=1900 mm, L2=1425 mm, a=190 mm,…

Q: Shown in the figures (1) and (2) are trusses containing members that are made of same materials…

A: To choose: The correct option. Given: The modulus of elasticity of material of the members are same…

Q: Rigid bar ABCD is loaded and supported as shown. Steel [E = 31300 ksi] bars (1) and (2) are…

Q: c) A solid homogeneous truss tie-rod has a diameter of 9.52 mm and an original length of 1.75 m…

A: Given Data The daimeter of truss tie rod is:d=9.52 mm The length is:l=1.75 m The stress experienced…

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

Q: Please include a free body diagram Solve for: a) Normal strain in the x- direction −4.0 ×…

Q: The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is made from a…

Q: The internal pressure p of the cylindrical pressure tube seen in Figure 4, whose radius to wall…

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

Q: Strain-gages are attached to the element subject to plane deformation, as shown in the figure, and…

Q: F. b h F What is the change in length (L) of the titanium bar (E = 16.5E6 psi) given: L = 36 in., b…

Q: The strain in the x-direction at point A (shown in fig.) on the steel beam is measured and found to…

A: Given, εx = 139 x 10-6 E = 204 GPa ν= 0.3

Q: 1. The state of plain strain at a point in a body is given by = 800 x 10-6, y = 200 x 10-6, and yxy…

Q: A short column tube of length L = 400 mm is loaded by a compressive force P. The outside and inside…

Q: Refer to the graph below, a. Which material is ductile? Why? 400 350 300 Steel 250 200 Aluminium 150…

Q: Q1) Bar (1) of length 2.8 m and bar (2) of length 0.73 m are fixed at ends A and C. There is a A =…

Q: Bar (1) has a length of L1 = 2.4 m, and bar (2) has a length of L2 = 0.63 m. Initially, there is a…

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

Q: H.W.7 A rigid steel bar ABC is supported by three rods. There is no strain in the rods before load P…

Q: A solid circular bar of diameter d= 50 mm is twisted in a testing machine until the applied torque…

A: Given data: Value of bar diameter = 50 mm Value of Torque T = 500 Nm…

Q: A rectangular metal slab has dimensions 4m, 2m and 1m in the xy and z directions respectively. The…

Q: Q1: A flat plate 2m long, 1m wide and 10mm thick. If a uniform tension is applied in the…

Q: H=8 cm L = 4 cm a = 50° t = 5 mm Sin?a Vz Cos a (H/ - Cos a) The strain value of the structure in…

Q: A force P of 70N is applied by a rider to the front hand brake of a bicycle (P is the resultant of…

Q: Compound axial member ABC has a uniform diameter of d=1.45 in. Segment (1) is an aluminum…

A: Given, A compound axial member made of Aluminum and copper Diameter of the axial member, d=1.45 in.…

Q: Figure 1: P = 400 kN 30° 1000 mm Area 30 mm 20 mm In Figure 1, if the Young modulus is 200 Gpa, the…

Q: find the stress tensor that cause the following strain state

Q: A solid homogeneous truss tie-rod has a diameter of 9.52 mm and an original length of 1.75 m…

Q: Pin-connected rigid bars AB, BC, and CD are initially held in the positions shown by taut wires (1)…

Q: Bars (1) are made of steel [E = 30,000 ksi], and bar (2) is made of an aluminum alloy [E = 10,000…

Q: The strains on the surface of an experimentaldevice made of pure aluminum (E = 70 GPa,n = 0.33) and…

A: Given Pure aluminum: E = 70 GPa Poisson ratio = 0.33 Find Stress in the x direction

Q: The 60° strain rosette shown below, is mounted on the surface of a thin shell. The following…

A: GivenEa=-780×10-6 Eb=400×10-6 &Ec=500×10-6∴ It in a delta connection∵(En)θ…

Q: Find the value of strain stress=30 MPa Modulus of elasticity=65 MPa

A: The value of Strain is ε = 0.4615.

Q: 5. What is most nearly the lateral strain, en of the steel specimen shown if F,= 3000 kN, E=193 GPa,…

A: Given data : Load in X direction (FX)=3000 KNModulus of elasticity (E)=193 GPaPoissons ratio…

Q: h.w: A compressive force was applied in the longitudinal direction of a cross-sectional bar ( A= 10…

Q: 2- When an axial load is applied to the ends of the bar shown in the Figure 2, the total elongation…

Q: some element, the displacement is obtained as u = [1 + 3x +4y +5xy]x10^(-3) mm. The normal strain…

A: A fluid element in the flowing fluid may have the translation, rate of deformation, and rotation. It…

Q: What strain will be produced by a stress of 80 x 106 N/m2, for a given modulus of elasticity 200GPa.…

A: Given, stress = 80 x 106 N/m2 modulus of elasticity (E) = 200GPa= 200x 109 N/m2

Q: A rigid steel bar is supported by three rods as shown. There is no strain in the rods before the…

Q: 3. An aluminum alloy plate (E = 70 GPa and v = 0.3), of thickness t= 8 mm, width b= 150 mm, and…

A: Given Data: The value of E=70 GPa and v=0.3. The value of t=8 mm, b=150 mm, and a=300 mm. The value…

Q: The strains measured with a 60⁰ strain rosette are ϵa = R/3 x 10^-6 , ϵb= - R/2 x 10^-6 , and ϵc =…

A: Given data for 60o strain rosette, εa=R3×10-6εb=-R2×10-6εc=R8×10-6 The 60-degree strain rosette is…

Q: A high-density polyethylene [E = 128 ksi; α= 88 x 10-6/°F; υ = 0.4] bar is positioned between two…

A: Given: E = 128 ksi Coefficient of thermal expansion, α = 88×10-6 /°F Poisson's Ratio, υ = 0.4…

Q: The tensile stress of an object is 250 MPa & the strain is 0.0021 then the value of Youngs's Modulus…

Q: hand written plz Shown in the figures (1) and (2) are trusses containing members that are made of…

A: To choose: The correct option. Given: The modulus of elasticity of material of the members are same…

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

100%

A steel plate in a state of plane stress has e, =
240 µ, e, = 200 u and 7a = 100u Poisson's
ratio v = 0.3 and the modulus of elasticity
E=210GPA. Use this information to answer
questions281 to 30.
28. The maximum principal strain in the plane
is most nearly:
(a) 215µ
(c) 107µ
(b) 220и
(d) 328µ
29. The maximum principal stress in the plane
is most nearly:
(а) 69MPа
(c) 57MPA
(b) 75MPA
(d) 77 MPa
30. The state of plane stress is made of a steel
with oy = 90 MPa. If yield does not occur
when using the maximum-distortion
energy criterion the factor of safety is
most nearly:
(a) 0.53
(c) Yield occurs
(b) 1.06
(d) 1.88

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

A steel plate in a state of plane stress has å_x = 56 ì, å_y = 21 ì and ã_xy = 40ì Poisson's ratio v = 0.3 and the modulus of elasticity E=210GPa.

The state of plane stress is made of a steel with ó_Y = 40 MPa. If yield does not occur when using the maximum-distortion energy criterion the factor of safety is most nearly:

4.2

Yield occurs

0.25

2.1

Solution

by Bartleby Expert

SEE SOLUTION

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

On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses on sketches of properly oriented elements.
- 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?
An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.
During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
A steel plate is subjected to a state of plane stress (E = 200 GPa and v = 0.29) of Oxx = 105 MPa, Oyy = -19 MPa and Oyy = 96 MPa. Calculate the axial strain, ɛ77, at this point in the z direction, normal to the plate's surface. Provide your answer in microstrain, pɛ. You do not need to type the units.
2. The stress-strain behavior of a ductile cast iron of diameter 15.8mm and a gauge length of 60.80mm is shown below, 400 300 200 100 0.00 0.10 Strain Determine the following: (a) the modulus of elasticity (b) yield strength at a strain offset of 0.002. Stress (MPa)
On the free surface of a component, a strain rosette was used to obtain the following normal strain data: €a = 300µɛ, ɛp = 400µs, and Ec = 200µe. Calculate the normal and shear strains in the x-y plane.
The strain rosette shown in figure was used to obtain strain data at a point on the surface of a machine part. If the readings from gages a, b, c were 650, -450, -585 (all in microns) respectively; which of the following is the shear strain on the surface? 45° a Lutfen birini seçin a1370 micron b. 1570 micron c1400 micron d7600 micron
You measure the strains ɛrx = 30E – 6 and ɛyy = 10E – 6 on the surface of a thin part (plane stress). If the part material has a elastic modulus of 100 GPa and a Poisson's ratio of - 0.35. What are the normal stresses in the x and y directions? y-direction normal stress = 2.34 MPа x-direction normal stress = 3.82 MPa O y-direction normal stress = -4.34 MPa x-direction normal stress = -8.27 MPa
Tensile test specimens are extracted from the "X" and "y" directions of a rolled sheet of metal. "x" is the rolling direction, "y" is transverse to the rolling direction, and "z" is in the thickness direction. Both specimens were pulled to a longitudinal strain = 0.15 strain. For the sample in the x-direction, the width strain was measured to be ew= -0.0923 at that instant. For the sample in the y-direction, the width strain was measured to be gw=-0.1000 at that instant. The yield strength of the x-direction specimen was 50 kpsi and the yield strength of the y-direction specimen was 52 kpsi. Determine the strain ratio for the x direction tensile test specimen. Determine the strain ratio for the y-direction tensile test specimen. Determine the expected yield strength in the z-direction. Give your answer in units of kpsi (just the number). If the sheet is plastically deformed in equal biaxial tension (a, = 0, to the point where & = 0.15, calculate the strain, 6, that would be expected.
PROPAGATION OF ERRORS Determine the range of values to which the strain will be calculated.F = 150000 +/- 150 lbfSide length = 1.2 +/- 0.025 inModulus of Elasticity = 25000 +/- 11.5 ksiDetermine the relative error. Is it above or below the accepted 5% relative error?
A body is subjected to uniaxial tensile stress of 20 MPa in the y-direction as well as a temperature decrease of 10 degrees K. The material's elastic modulus is 90 GPa, the Poisson's ratio is 0.20, and the coefficient of thermal expansion is 12E-6 per degree K. What are the normal strains in the x, y, and z directions (microstrain units) ? Exx –102, ɛyy = 51, Ezz 82 -164, ɛ yy -164, Exx %3D Ezz -164 -164, E yy 102, Exx = Ezz = -164 164, E yy - -102, Exx