4 of 4(b) The 45° strain rosette is mounted on a steel shaft. The following readings are obtainedfrom each gauge are shown in Figure Q2(b).i.ii.Ea = 800 x 106, & = 520 x 106 and & = -450 x 10-6,Find the strains values in the x-y directions and draw the strain element diagram ofthat direction.Find the principal strain values and draw the strain element diagram of that direction.iii. Find the maximum shear strain value and draw the strain element diagram of thatdirection.iv.If the properties of the structure have E = 208 GPa and v = 0.28, find the magnitudeof the principal stresses.b45°45°Figure Q2(b)[[8 marks]

Answered: Image /qna-images/answer/09398278-33ac-440c-878a-583ff5dfe07c.jpg

Answered: 4 of 4 (b) The 45° strain rosette is…

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 7.7.20P: A strain rosette (see figure) mounted on the surface of an automobile frame gives the following...

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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.
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 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.
- 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?
Question 2 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: E, = 925 x10“ ; &, = 740 x10“ ; ɛ. = -555 ×106 (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. (d) If the structure is made of steel with elastic modulus and Poisson's ratio of 220 GPa and 0.30, respectively, calculate the principal stresses. Show the principal stress element. (e) Determine the normal strain in the n-direction. & Ea
Figure Q2 (b) 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?
A set of strain rosette with three strain gauges at 120° apart is attached onto a steelstructure surface, point P for strain measurement. The state of stress at point P is thendetermined from the acquired strain measurement. The orientation of strain rosette isshown in Figure Q2. When the structure is being loaded the readings of the gaugesare 200μ, -100μ and -200μ at the directions of a, b and c respectively. a) Find the strains values in the x-y directions and draw the strain elementdiagram of that direction.b) Find the principal strain values and draw the strain element diagram of thatdirection.c) Find the maximum shear strain value and draw the strain element diagram ofthat direction.d) If the properties of the structure has E = 208 GPa and ν = 0.28, find themagnitude of the Principal Stresses and draw its stress element diagram.e) Give your comment without calculation on what happen to maximumprincipal strain of the steel (E = 208 GPa) is changed to titanium (E = 110GPa)?
Solve the following question
Q4 A three strain gages have been attached directly to a piston used to raise a medical chair, the strain gages give strains as Ea = 80 µ , Eb = 60 µ and Ec = 20 u . Determine the principal strains and the principal strain directions for the given set of strains. And Compute the strain in a direction -30° (clockwise) with the x axis. 45 Pump
Q1 The 45° strain rosette is mounted on a steel robotic am as shown in Figure Ql. The robotic arm is made from steel with Esel = 200 GRA and poison ratio, v= 0.3. The following readings are obtained for each gauge: E=[Y+Z](10“) E = -250(10-) E= -200(10) Here the value of Y and Z depends on the 5th digit and 6th digit of your matric number as shown in Table 1. For example, if your matrix number is DD 070112 gives the value of Y=300 and Z-60: Table 1 5 digit of matric 6* digit of matric number number 250 300 350 30 2 60 3 400 3 90 4 450 120 5 500 150 6. 550 180 7 600 7 210 650 700 240 270 (a) Prove that &= E, and E, = E. Determine the shear strain, yand the normal strain, E, and &. (b) Estimate the in-plane principal strains and the angle associated with the principal strains, and (c) Calculate the principal stress associated with the prihcipal strains in (c). (d)
P5
2a. The delta strain gauge rosette shown in Figure 2a is attached to a structural component and measures the following strains: ɛ = 775x10°, ɛz = 415x106, ɛ̟ = -515x10°. Determine the principal strain and principal stress components in both magnitude and direction given that the structure has a Young's Modulus of E = 200×10° N/mm? and Poisson's ratio of v = 0.3. Show the directions of the principal stresses on a properly oriented stress element relative to the x,y coordinate system. 60° 60° 60° Figure 2a

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