The two bars shown in the figure are used to support a load P. When unloaded, joint B has coordinates (0, 0). After load P is applied, joint B moves to the coordinate position (0.20 in., -0.55 in.). Assume a = 9 ft, b = 6 ft, and h = 7 ft. Determine the normal strain in each bar. B P b h
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Determine the normal strain AB and BC
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- 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.- 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?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.
- 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 spherical balloon with an outer diameter of 500 mm and thickness 0.3 mm is filled with a gas. Calculate maximum permissible pressure in the balloon if the allowable normal strain at the outer surface of the balloon is O.h Assume E = 4 MPa and v = 0,45.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.
- 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 block B is pushed against three springs by a force P (see figure). The middle spring has a stillness K1and the outer springs each have stiffness k^. Initially, the springs are unstressed, and the middle spring is longer than the outer springs (the difference in length is denoted s). (a) Draw a force-displacement diagram with the force P as ordinate and the displacement x of the block as abscissa. (b) From the diagram, determine the strain energy U1 of the springs when x = 2s. (c) Explain why the strain energy E, is not equal to P6. Two bars are used to support a load P. When unloaded, AB is 5 in. long, AC is 8 in. long, and the ring at A has coordinates (0, 0). If a load is applied to the ring at A, so that it moves it to the coordinate position (0.25 in., -0.73 in.), determine the normal strain in each bar. (Use the figure in Prob.5)
- 5. Two bars are used to support a load. When unloaded, AB is 5 in. long, AC is 8 in. long, and the ring at A has coordinates (0, 0). If a load P acts on the ring at A, the normal strain in AB becomes EAB = 0.02 in/in., and the normal strain in AC becomes EAC = 0.035 in/in. Determine the coordinate position of the ring due to the load. 60 5 in. 8 in. A PThe two bars shown in the figure are used to support a load P. When unloaded, joint B has coordinates (0, 0). After load P is applied, joint B moves to the coordinate position (0.25 in., -0.70 in.). Assume a = 13 ft, b = 7 ft, and h = 10 ft. Determine the normal strain in each bar. Answers: EAB= EBC= i a B b με με X hThe two bars shown in the figure are used to support a load P. When unloaded, joint B has coordinates (0, 0). After load P is applied. joint B moves to the coordinate position (0.40 in., -0.55 in.). Assume a - 10 ft, b-7 ft, and h-8 ft. Determine the normal strain in each bar. Answers: EAB Egc i i B P b με με