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 (0.40 in., -0.55 in.). Assume a - 10 ft, b-7 ft, and h-8 ft. Determine the normal strain in each bar. Answers: EAB Esc i i B P b με με
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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.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 4.75-in, outside diameter polyethylene pipe designed to carry chemical waste is placed in a trench and bent around a quarter-circular 90° bend (see figure). The bent section of the pipe is 52 ft long. Determine the maximum compressive strain If the normal strain cannot exceed 6.1 × 10-3 , what is the maximum diameter of the pipe? If d = 4.75 in., what is the minimum acceptable length of the bent section of the pipe?
- 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 PA 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 = 0,45.6. 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)
- 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 (0.25 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 h5. 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 P1. Strain Gage Rosettes & Principal Stresses-The Cantilever Beam A strain gage experiment was conducted using the tungsten simple cantilever beam shown in the figure. A load was applied at end of the beam and strains from a rectangular strain gage rosette mounted on the top were recorded as follows: € = 50 με; €g = 300 με; €c = 172 με The strains are also shown in the figure. 14 in. b. Fixed End C₂ EA-50UE - E172UE ER=300μLE 12 in (Thickness = 0.125 in) 1.5 in. Load End P=6 lbs a. Reduce the rosette data and draw Mohr's strain circle. Show all three gages at their proper locations on Mohr's circle: Determine Poisson's Ratio for the beam material: Determine the elastic modulus for the beam material: Continue calculations on back of sheet or other paper if necessary, BOX YOUR ANSWERS, PLEASE!!
- The two bars shown in the figure are used to support a load P. When unloaded, joint B has coordinates (0,0). After load Pis applied, joint B moves to the coordinate position (0.40 in., -0.65 in.). Assume a = 10 ft, b = 5 ft, and h = 7 ft. Determine the normal strain in each bar. a b h B P Answers: EAB= EBCThe 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?A circular aluminum tube of L=600mm is loaded in by compressive forces at its ends. The outside and inside diameters are 75mm and 63mm respectively. A strain gage is placed on the outside of the tube to measure nomal strains in the longitudinal direction. E=73 GPa and Poisson’s is 0.33. If the normal stress in the tube is 57 MPa, what is the load P? if the strain is 781 X 10-6, what is the shortening of the tube? What is the percent change in its cross-sectional If the tube in Problem #1 has a constant outer diameter of 75 mm along its entire length but has increased in inner diameter with a normal stress of 70 MPa over the middle third while the rest of the tube remains at 57 MPa and an additional the load of 15 kN is applied to the left at a point L/3, what is the inner diameter at the middle third if an additional load of 15kN is applied directed to the left at a point L/3 from the left, what is the inner diameter at the middle third.