(a) the strain in the cable at a depth of 700 ft. (b) the total elongation of the cable.
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- A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).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?An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.
- A steel cable is used to support an elevator cage at the bottom of a 2100-ft-deep mineshaft. A uniform normal strain of 240 μin./in. is produced in the cable by the weight of the cage. At each point, the weight of the cable produces an additional normal strain that is proportional to the length of the cable below the point. Assume D = 2100 ft and d = 500 ft. If the total normal strain in the cable at the cable drum (upper end of the cable) is 790 μin./in., determine (a) the strain in the cable at a depth of 500 ft. (b) the total elongation of the cable. Drum Cable Answers: (a) ε = (b) 8 = i i d D Elevator cage X uin./in. in.A steel cable is used to support an elevator cage at the bottom of a 2400-ft-deep mineshaft. A uniform normal strain of 300 μin./in. is produced in the cable by the weight of the cage. At each point, the weight of the cable produces an additional normal strain that is proportional to the length of the cable below the point. Assume D = 2400 ft and d = 200 ft. If the total normal strain in the cable at the cable drum (upper end of the cable) is 620 uin./in., determine (a) the strain in the cable at a depth of 200 ft. (b) the total elongation of the cable. Drum Answers: (a) Cable + ε = i Elevator cage D X uin./in.A steel cable is used to support an elevator cage at the bottom of a 1900-ft-deep mineshaft. A uniform normal strain of 240 pin./in. is produced in the cable by the weight of the cage. At each point, the weight of the cable produces an additional normal strain that is proportional to the length of the cable below the point. Assume D = 1900 ft and d = 500 ft. If the total normal strain in the cable at the cable drum (upper end of the cable) is 780 μin./in., determine (a) the strain in the cable at a depth of 500 ft. (b) the total elongation of the cable. Drum Cable Answers: (a) ε = (b) 8 = i i d Elevator cage D X pin./in. in.
- For the state of a plane strain with Ex, Ey and yxy components: (a) construct Mohr's circle and (b) determine the equivalent in-plane strains for an element oriented at an angle of 30° clockwise. Ex = 250 x 10-6 Ey = 310 x 10-6 Yxy = -100 × 10-6A steel rod is subjected to a gradually applied load (F) which gave a rise to a maximum stress of 200 MPa. The rod is 250 mm long and one part of it's length is square and the remainder is circular with a diameter of 25 mm. If the total strain energy in the rod and modulus elasticity of the material is 1,3 J and 200 GPa, determine the following : 4.1.The applied load F and the total extension of the bar 4.2.The length of the square portion of the bar and the suddenly applied load that will induce the same amount of energy. 4.3.The load that falls from a height of 8 mm induces 1,3 J in the barA rigid steel bar is supported by three rods, as shown. There is no strain in the rods before the load Pis applied. After load P is applied, the normal strain in rod (2) is 840 pin./in. Assume initial rod lengths of L1 = 120 in. and L2 = 71 in. Determine (a) the normal strain in rods (1). (b) the normal strain in rods (1) if there is a 0.032 in. gap in the connections between the rigid bar and rods (1) at joints A and C before the load is applied. (c) the normal strain in rods (1) if there is a 0.032 in. gap in the connection between the rigid bar and rod (2) at joint B before the load is applied. (1) (2) Rigid bar Answers: (a) E1 = i pin./in. (b) E1 = pin./in. (c) Ɛ1 = i pin./in.
- The state of strain in a plane element is Ex = -300 x 10-6 , Ey= 450 x 10-6, and Yxy = 275 x 10-6. (a) Use the strain transformation equations to determine the equivalent strain components on an element oriented at an angle of 0 = 30° counterclockwise from the original position. (b) Sketch the deformed element due to these strains within the x-y plane.The rigid bar AB is supported by a pin at A and by the wire BD. 2,5 m If the load P causes point C to move 8 mm to the left, determine the normal strain in the wire. 3,5 m D 4.0 mA thin polymer plate PQR is deformed such that corner Q is displaced downward a distance L = 0.10 in. to new position Q' as shown. Determine the magnitude of the shear strain at Q' associated with the two edges (PQ and QR). P 25 in. 6862 μrad 8014 μrad O 7358 μrad O 4241 urad O 8668 μrad 4 in. R 10 in. X