Q1 The 45° strain rosette is mounted on a surface of the bracket as shown in Figure Q1. The bracket is made from steel with Esteel = 120 GPa and poison ratio, v = 0.28. The following readings are obtained for each gauge under loadings: Ea= [ 100+20 ] (10-6) Es = -200(10-6) E = -180(10-6) (а) Prove that E= Eaand &y= Ec. (b) Determine the shear strain, y and the normal strain, Ez and Ey. (c) Estimate the in-plane principal strains and the angle associated with the principal strains, and

Q1 The 45° strain rosette is mounted on a surface of the bracket as shown in Figure Q1. The bracket is made from steel with Esteel = 120 GPa and poison ratio, v = 0.28. The following readings are obtained for each gauge under loadings: Ea= [ 100+20 ] (10-6) Es = -200(10-6) E = -180(10-6) (а) Prove that E= Eaand &y= Ec. (b) Determine the shear strain, y and the normal strain, Ez and Ey. (c) Estimate the in-plane principal strains and the angle associated with the principal strains, and

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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A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?
- 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?
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 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.
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.
Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the gage angle is ß = 750, the measured strains are = 209 × 10-6 and B = -110 × 10, and the material is a magnesium alloy with modulus E = 6.0 X 106 psi and Poisson’s ratio v = 0.35.
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.
600 strain rosette, or delta rosette, consists of three electrical-resistance strain gagesarranged as shown in the figure. Gage A measures the normal strain e, in the directionof the x axis. Gages Band C measure the strains and e in the inclined directions shown.Obtain the equations for the strains 8. e. and y, associated with the x-v axes.
A set of strain rosette with three strain gauges at 120° apart is attached onto a steel structure surface, point P for strain measurement. The state of stress at point P is then determined from the acquired strain measurement. The orientation of strain rosette is shown in Figure. When the structure is being loaded the readings of the gauges are 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 that direction. c) Find the maximum shear strain value and draw the strain element diagram of that 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 =…
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)?
The state of strain at the point on the bracket has components Px = 350(10-6), Py = -860(10-6),gxy = 250(10-6). Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of u = 45° clockwise from the original position. Sketch the deformed element within the x–y plane due to these strains.
Rigid bar ABCD is supported by two bars as shown. There is no strain in the vertical bars before load P is applied. After load P is applied, the normal strain in bar (2) is measured as −3,300 μm/m. Use the dimensions L1 = 1,600 mm, L2 = 1,200 mm, a = 240 mm, b = 420 mm, and c = 180 mm. Determine (a) the normal strain in bar (1). (b) the normal strain in bar (1) if there is a 1 mm gap in the connection at pin C before the load is applied. (c) the normal strain in bar (1) if there is a 1 mm gap in the connection at pin B before the load is applied.