4)The following strains have been measured at a point on the free surface ofa solid body.DirectionabCAngle 0Strain &0°0.002120° (from a)0.002240° (from a)-0.001Determine the principal strains in the plane of the surface, and theprincipal directions of strain relative to direction a.Based on the results from Problem 4:

Answered: 4) The following strains have been…

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 7.7.3P: An element of material in plain strain is subjected to shear strain xy = 0.0003. (a) Determine the...

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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.
An element of material in plain strain has the following strains: x = 0.001 and y = 0.0015. (a) Determine the strains for an element oriented at an angle = 250. (b) Find the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.
- 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?
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.
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 thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).
Three readings are obtained from an equiangular strain gage rosette mounted on a free and unloaded surface of a part. Determine the magnitude of the principal strains and their orientation with respect to the 0° gage. Check the results with a Mohr circle.Assume The three known strains are all linear strains
Q.3) A structural member in plane strain has the following strains at a point: & 360 μ , E, = 230 µ, Ky = 150 µ (a) Determine the strains for an element oriented at an angle of 60° counter clockwise. (b) Determine the principal strains and the maximum shear strain using strain transformation equations. (c) Show the result of parts (a) and (b) via sketches of properly oriented elements. Ey Yxy 1 Ex
5. Please calculate the strain and stress in the following two prompts a. A 1 cm long section of tendon stretches to 1.011 cm when it is subjected to a tensile force of 40,000 N. What is the strain in this segment of tendon? @? 17 b. The section of the patellar ligament in the previous question is 0.02 m² in the cross section. What is the stress in this section of ligament as a result of 50,000 N tensile force? E = Δι 19 0 = A 1.011 cm 50000 0,02 Scoco 40000 1.25 = T % 2500000 strain N/m² on trito flox your wrist, you may notice that your
Question-1: The strain rosette shown in the figure was used to obtain normal strain data at a point on the free surface of a machine part. (a) Determine the strain components &, S, and %, at the point. (b) Determine the principal strains and the maximum in-plane shear strain at the point. (c) Draw a sketch showing the angle 6, the principal strain deformations, and the maximum in-plane shear strain distortions. (d) Determine the magnitude of the absolute maximum shear strain. 45 45 &- 50 με, 8--730 με , ε375 με, ν-0.30
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)
The state of strain in a plane element is Ex = -300 x 10-6 , Ey= 450 x 10-6, and Yxy = 275 x 10-6. (a) Use the strain transformation equations to determine the equivalent strain components on an element oriented at an angle of 0 = 30° counterclockwise from the original position. (b) Sketch the deformed element due to these strains within the x-y plane.

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