Q. // (A) - An element of bone in plane strain where the state of strain are(Ex = 8 × 10¬4, €y = 5 × 10¬4, Yxy = 12 × 10-4). Find (a) the stresses atorientation a counterclockwise angle (40 deg.) from the x-axis, b) the strainenergy and (c) the failure stress by Von Misses criteria. KnownModulus of elasticity = 2 × 10° N /m² and Poisson's ratio = 0.3

GivenEx=8×10-4Ey=5×10-4γxy=12×10-4μ=ν=0.3 E=2×109Nm2

Answered: Q. // (A) - An element of bone in plane…

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

Similar questions

M13.6 Principal stresses from rosette data scenes -200 µE 23 Eb = 200 με Ec 500 µE 30° 30° Ex (LE) a Ey (µE) Yxy (Lurad) The strain rosette shown was used to obtain normal strain data at a point on the free surface of a steel (E = 200 GPa; v = 0.32) plate. Op1 (MPa) Determine the normal strains, the shear strain, and the principal stresses in the x-y plane. Op2 (MPa) Try One 1st 2nd 3rd attempt enter
Stress Strain Diagram The Data shown in the table have been obtained from a tensile test conducted on a high-strength steel. The test specimen had a diameter of 0.505 inch and a gage length of 2.00 inch. Using software. plot the Stress-Strain Diagram for this steel and determine its: A= TTdT(050s A %3D 1. Proportional Limit, 2. Modulus of Elasticity, 3. Yield Strength (SY) at 0.2% Offset, 4. Ultimate Strength (Su), 5. Percent Elongation in 2.00 inch, 6. Percent Reduction in Area, 7. Present the results (for Steps 1-6) in a highly organized table. e Altac ie sheet (as problelle 4 A = 0.2.002 BEOINNING of the effort Elongation (in) Elongation (In) Load Load #: #3 (Ib) (Ib) 1 0.0170 15 12,300 0.0004 1,500 16 12,200 0.0200 0.0010 3. 3,100 17 12,000 0.0275 0.0016 4,700 18 13,000 0.0335 5. 6,300 0.0022 19 15,000 0.0400 0.0026 6. 8,000 20 16,200 0.055 0.0032 9,500 21 17,500 0.0680 0.0035 8. 11,000 22 18,800 0.1080 0.0041 11,800 23 19,600 0.1515 0.0051 24 20,100 0.2010 10 12,300 0.0071 25…
For a given homogeneous, isotropic, linearly elastic material, E = 15e6 psi and v = 0.3. Solve for the shear modulus. 2.1.1 Homogeneous, isotropic, linearly elastic materials For specimens undergoing small deformations, the stress-strain diagram often ex- hibits a linear behavior. Although this is a very crude approximation to the behavior of actual materials, it is a convenient assumption that is often used for preliminary evaluation. A linear relationship between stress and strain can be expressed as 01 = E €1, (2.1) where the coefficient of proportionality, E, is called Young's modulus or modulus of elasticity. Since strains are non-dimensional quantities, this coefficient has the same units as stress quantities, i.e., Pa. This linear relationship is known as Hooke's law. The elongation of a bar in the direction of the applied stress is accompanied by a lateral contraction that is also proportional to the applied stress. The resulting defor- mations for this uniaxial state of stress…
Q // The tensile tests were performed on longitudinal specimens of compact bone. The E1= 0.0004 65° strain rosette is mounted on a bone were the readings are obtained for each gauge as shown in figure. Determine (a) the principal strains and (b) the shear strain and average normal strain. 50° E2 = - 0.0005 65° €z = 0.0003
1. A 0.015 meter diameter bar of steel is stress tested and the following stress-strain curve is produced Stress (psix 10 60 50 8 20 10 1 MPa 300 100 psi (x 10%) 50 200-30 OL 40- 20- 10 0.05 0.005 1 L 0.010 0.10 Strain a. What is the ultimate tensile strength (MPa)? d. What is the yield strength(MPa)? 0.15 c. What is the percent plastic elongation at the time of fracture? e. What is the Modulus of Elasticity (GPa)? 400 300 200 Stress (MPa) b. What is the greatest load that can be place on this bar before failure(N)? 100 10 0.20
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.
5. Consider a cylindrical specimen of a steel alloy (Figure 6.22) 10 mm in diameter and 75 mm long that is pulled in tension. Determine its elongation when a load of 20,000 N is applied. Stress (MPa) 600 500 400 300 200 100 0 0.00 0.04 Stress (MPa) 500 400 300 200 100 0.000 0.002 0.004 0.006 0.08 Strain Strain 0.12 0.16 0.20 Figure 6.22 Tensile stress-strain behavior for a steel alloy.
A solid bar of length L = 4 m and diameter 200 mm is heated from 20 to 320 degrees celsius and restrained between two solid immovable walls. Young's modulus of the material is 90 GPa and the coefficient of thermal expansion is 22 x 10-6/°C. →Calculate the thermal strain, e, in micro-strain correct to two decimal places. micro-strain. Calculate the thermal stress, o, in megapascals (MPa) correct to two decimal places. E: σ: MPa. Hence calculate the force exerted by the bar in meganewtons (MN) correct to two decimal places: F MN. L
3.3 m 4,9m Ax = 23.370 mm %3D Interconnected rods up to 23.370 mm from the right end it's pulled and fixed. Length of Bar No. 1 3.3 m, cross-sectional area 2.4 cm2 and yield stress 215 MPa; No. 2 length of Rod 4.9 m, cross-sectional area 2.8 cm2 and yield its stretch is 387 MPA. Elasticity of both materials module 207 MPa and materials elastic / excellent since it's plastic: How much plastic elongation amount of Bar No: 1 meters? How many meters is the lengthening of Rod 2? How many normal stresses in Rod Section 2 Is it an MPA? 3.
Q#7: The strains measured with a 60⁰ strain rosette are ϵa = R/3 x 10^-6 , ϵb= - R/2 x 10^-6 , and ϵc = R/8 x 10^-6 . Using E = 200 GPa and µ = 0.3, find the principal stresses and their directions. Show the results on a sketch of a properly oriented element. Use R=980 Note : For Clearance of Question Please Refer to Attached Picture.
Example: Convert the change in length data in Table 3-2 to engineering stress and strain and plot a stress-strain curve Homework- help Table 3-2 The results of a tensile test of a 0.505 in. diameter aluminum alloy test bar, initial length (1o) = 2 in. Calculated LTO Load (Ib) Change in Length (in.) Stress (psi) Strain (in./in.) 0.000 1000 0.001 0.0005 4,993 14,978 24,963 34,948 37,445 39,442 39,941 39,691 37,944 3000 0.003 0.0015 5000 0.005 0.0025 7000 0.007 0.0035 7500 0.030 0.0150 7900 0.080 0.0400 8000 (maximum load) 0.120 0.0600 7950 0.160 0.0800 7600 (fracture) 0.205 0.1025
The figure below shows the tensile engineering stress-strain behavior for a steel alloy. (a) What is the modulus of elasticity? (b) What is the yield strength at a strain offset of 0.002? (c) What is the tensile strength? Stress (MPa) 600 500 400 300 200 100 T I 0.00 Stress (MPa) 0.04 500 400 300 200 100 0.000 0.08 0.002 Strain 0.004 Strain 0.12 I 0.006 0.16 0.20 In the previous problem, A load of 85,000 N (19,100 lbf) is applied to a cylindrical specimen of the steel alloy that has a cross-sectional diameter of 15 mm (0.59 in.). (a) Will the specimen experience elastic and/or plastic deformation? Why? (b) If the original specimen length is 250 mm (10 in.), how much will it increase in length when this load is applied?

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS