A 60° strain rosette is installed on the traction-free surface of a component with one of the strain gages aligned along the y-axis, as illustrated in Figure Q2. The gages show the following strain readings upon loading the structure: 6, = 925 x10* ; &, = 740 ×10“ ; &, = -555 x10“ (a) Determine the strains in the x-y directions and show the corresponding strain element. (b) Calculate the principal in-plane strains and the corresponding principal directions. Show the principal strain element. (c) Calculate the in-plane maximum shear strain and show the corresponding strain element.

A 60° strain rosette is installed on the traction-free surface of a component with one of the strain gages aligned along the y-axis, as illustrated in Figure Q2. The gages show the following strain readings upon loading the structure: 6, = 925 x10* ; &, = 740 ×10“ ; &, = -555 x10“ (a) Determine the strains in the x-y directions and show the corresponding strain element. (b) Calculate the principal in-plane strains and the corresponding principal directions. Show the principal strain element. (c) Calculate the in-plane maximum shear strain and show the corresponding strain element.

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 7.7.7P: A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the...

See similar textbooks

Similar questions

An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.
The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains 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 strain rosette (see figure) mounted on the surface of an automobile frame gives the following readings: gage A,310 × 10-6:gage B,180 × l0-6; and gage C. -160 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
An element of material in plain strain is subjected to shear strain xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 30°. (b) Determine the principal strains of the clement. Confirm the solution using Mohr’s circle for plane strain.
An clement of material subjected to plane strain (see figure) has strains of x=280106 , y=420106 , and xy=150106 . Calculate the strains for an element oriented at an angle = 35°. Show these strains on a sketch of a properly oriented element.
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).
Figure shows a strain rosette that is attached on the surface of a production equipment. The strain readings are εa = -200(10^-6), εb = -65(10^-6) and εc = 130(10^-6).i) Determine the in-plane principal strains and sketch the strain element.ii) Determine the maximum in-plane shear strain and sketch the strain element.iii) What is the angle of orientation (with respect to x-axis) that leads to εx’ = 0?
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?
Consider the given loading on a pipe. A rectangular rosette (45 degree apart) is placed on a point (K) which is located on the half length of the pipe as shown below. Note that the second gage (b) is parallel to the z-axis . When the load is applied, the strain gages read εa=80 µS, εb=60 µS, εc=20 µS. The pipe have an elastic modulus of Est=201 GPa. a. Determine the in-plane principal strains and the principal strain directions for the given set of strains (Use Mohr circle)
A 45° strain rosette (see figure) mounted onthe surface of an automobile frame gives the followingreadings: gage A, 310 X10-6 ; gage B, 180 X10-6 ;and gage C, -160X10 -6 .Determine the principal strains and maximumshear strains, and show them on sketches of properlyoriented elements.
The strains for an element of material in planestrain (see figure) are as follows: εx = 480 X 10-6 ,εy = 140 x10-6 , and yxy = -350 X10-6.Determine the principal strains and maximumshear strains, and show these strains on sketches ofproperly oriented elements.