Part BAssuming the plane stress condition (o2 = Tyz = Tyz= 0), what is the normal stress in x-direction (o2) at point A?69.1 MPa93.5 MPa52.9 MPaO 110 MPaО 81.3 МPаSubmitRequest AnswerPart CAssuming the plane stress condition (o2 = Tz = Tyz= 0), what is the change in thickness change of the plate?O -2.91x10-6 mO -5.31×10-6 mO -3.43x10-6 mO -4.63x10-6 mO -3.94x10-6 mSubmitRequest Answer A steel plate is under biaxial stress as seen in the figure. A 60° strain rosette is mounted on the surface (point A) of the plate. The recorded strains are e = 3.00×10-4 and e, = E = 2.50x10-4. The steel plate has a thickness (t) of 15.0 mm and thematerial properties with the Poisson's ratio (n) = 0.300 and Young's modulus (E) = 200 GPa. Click here to see the equations.b120°60°Part AThe strain transformation formula is: Ey = €y cos?0 + €, sin20 + Yysin@cose.What is the normal strain in the y-direction (Ey) at point A?O 2.68x10-4O 2.33×10-4O 1.52x10-4O 1.98×10-4O 8.17x10-5SubmitRequest Answer

To obtain the strain in the y direction at point A in the plate, we have to write the transformation…

Part B Assuming the plane stress condition (o, = Tyz = Tyz= 0), what is the normal stress in x-direction (o,) at point A? O 69.1 MPa O 93.5 MPa O 52.9 MPa O 110 MPa O 81.3 MPa Submit Request Answer • Part C Assuming the plane stress condition (o, = Txz = Tyz= 0), what is the change in thickness change of the plate? O -2.91x10-6 m O -5.31×10-6 m O -3.43x10-6 m O -4.63x10-6 m O -3.94×10-6 m Submit Request Answer

Part B Assuming the plane stress condition (o, = Tyz = Tyz= 0), what is the normal stress in x-direction (o,) at point A? O 69.1 MPa O 93.5 MPa O 52.9 MPa O 110 MPa O 81.3 MPa Submit Request Answer • Part C Assuming the plane stress condition (o, = Txz = Tyz= 0), what is the change in thickness change of the plate? O -2.91x10-6 m O -5.31×10-6 m O -3.43x10-6 m O -4.63x10-6 m O -3.94×10-6 m Submit Request Answer

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 7.6.7P: An element of aluminum is subjected to iriaxial stress (see figure). (a) Find the bulk modulus A^for...

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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.
A circular aluminum tube of length L = 600 mm is loaded in compression by forces P (see figure). The outside and inside diameters are d2= 75 mm and d1= 63 mm, respectively. A strain gage is placed on the outside of the lube to measure normal strains in the longitudinal direction. Assume that E = 73 GPa and Poissons ratio is v = 0.33. (a) IF the compressive stress in the tube is 57 MPa, what is the load P? (b) If the measured strain is e = 78 J X 10-6, what is the shortening
Solve the preceding problem if the cube is granite (E = 80 GPa, v = 0.25) with dimensions E = 89 mm and compressive strains E = 690 X l0-6 and = = 255 X 10-6. For part (c) of Problem 7.6-5. find the maximum value of cr when the change in volume must be limited to 0.11%. For part. find the required value of when the strain energy must be 33 J.
-7 The truss A BC Shawn in the figure supports a horizontal load P1= 300 lb and a vertical load P2= 9001b. Both bars have a cross-sectional area A = 2.4 in2 and are made of steel with E = 30 X 106 psi. (a) Determine the strain energy U1of the truss when the load P1acts alone (P2= 0). (b) Determine the strain energy U2when the load P2acts alone (P1= 0). (c) Determine the strain energy U3when both loads act simultaneously.
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.
-7 A steel tube (G = 11.5 x 106 psi) has an outer diameter d2= 2.0 in. and an inner diameter dt=1,5 in. When twisted by a torque 7", the tube develops a maximum normal strain of 170 x 10-6. What is the magnitude of the applied torque T?
7.5-11 in. cube of concrete (E = 4.5 X 106 psi. v = 0.2) is compressed in biaxial stress by means of a framework that is loaded as shown in the figure. Assuming that each load F equals 25 kips. determine the change iv in the volume of the cube and the strain energy U stored in the cube.
An element in plane stress is subjected to stresses ?? = -8400 psi, ??y = 1100 psi, and (see figure). The material is aluminum with modulus of elasticity E = 10,000 ksi and Poisson’s ratio v = 0.33. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 30°, (b) the principal strains, and (C) the maximum shear strains. Show the results on sketches of properly oriented elements.
An element of aluminum is subjected to iriaxial stress (see figure). (a) Find the bulk modulus A^for the aluminum if the following stress and strain data are known: normal stresses are v = 5200 psi (tension), a = —4750 psi (compression); and (7_ = —3090 psi (compression) and normal strains in the v and v directions areet = 713,8 X 10_ (elongation) and £y=-502.3 x 10~6 (shortening), (b) If the element is replaced by one of magnesium, find the modulus of elasticity E and Poisson's ratio eif the following data is given: bulk modulus A' = 6,8 x 10 psi; normal stresses are trx= 4550 psi (tension), o", = —1700 psi (compression), and ex= 900 X 10"6 (elongation),
• - 3 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses u = 67 MPa (tension) and s = -23 MPa (compression). The plate has dimensions 400 X 550 X 20 mm and is made of steel with E = 200 GPa and v = 0.30. (a) Determine the maximum in-plane shear strain ?max in the plate. (b) Determine the change ?t in the thickness of the plate. (c) Determine the change ?t in the volume of the plate.
-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.
Solve the preceding problem for an aluminum plate with h = 10 in.. i = 0.75 in., E = 10,600 ksi, v = 0.33. P = 96 kips. Pt,. = 24 kips. and V =18 kips. For part (b) of Problem 7.5-12, assume that the required strain energy stored is 640 in.-lb. In part (c). the change in volume cannot exceed 0.05%.