1. The normal strains of a solid under a uniaxial stress of 60MPa are and. When the solid is subject to a hydrostatic stress of 100MPa, determine (a) the bulk modulus (b) the dilatation of the solid.
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- The ring, with dimensions shown, is placed over a flexible membrane which is pumped up with a pressure p. The thickness r,-r; is small compared to r; (a) Determine the axial force F in the ring in terms of p, w and r;. Hint: Consider a FBD by cutting the ring+membrane in two. (b) Determine the hoop stress in the ring. (c) Determine the hoop strain in the ring. The modulus of elasticity for the ring is E. (d) Relate the hoop strain to the change in the inner radius of the ring after this pressure is applied, and use this to get the change in the inner radius in terms of p, E, w, r, and ri- (PLEASE ANSWER ASAP AND CORRECTLY)!The normal strain measured on the outside surface of a spherical pressure vessel is 670 με.The sphere has an outside diameter of 1.20 m and a wall thickness of 10 mm, and it will befabricated from an aluminum alloy [E = 73 GPa;ν = 0.33]. Determine (a) the normal stress inthe vessel wall and (b) the internal pressure in the vesssel4. A 200 x 100 x 50 mm steel block is subjected to a hydrostatic pressure of 15 MPa. The Young's modulus and Poisson's ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of the block in mm is (A) 85 (B) 90 (C) 100 (D) 110
- 2. A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are 0.40 x 10 - in the x direction and 0.30 x 10 in the y direction, determine the stresses in the x and y direction. Also, determine the strain in the z direction. The modulus of elastic and Poisson's ratio of copper is 110 GPa and 0.35 respectively. 3. If the copper in no. 2 is changed into steel with the same dimensions and with a modulus of elasticity of 200 GPa and a Poisson's ratio of 0.30, determine the strains in all direction if the same stresses in no. 2 where to be applied to the steel. €, E,mechanics of deformable bodies The cylindrical tank has an outer radius of 1.5m and a wall thickness of 25 mm. If the tank is pressurized to 1.5 MPa, determine the longitudinal stress.(1) A steel cylinder (Øyp = 260 MPa) of inner radius a and outer radius 3a is subjected to an internal fluid pressure pi (Note: ratio of wall thickness (t) to inner radius indicates that this is a thick-walled cylinder). (a) Determine (i) the maximum radial stress (ơmax); (ii) the maximum tangential stress (o0max). (b) Determine the limiting values of p, using: (i) the maximum distortion energy theory of failure; and (ii) the maximum shear stress theory of failure. (Hint: Maximum radial and tangential stresses occur at the same radial distance, see slide 8 of Lecture 9 notes); use these maximum stresses as your principal stresses). (c) A steel gun barrel of inner radius 0.6 m is subjected to an internal explosive pressure of 80 MPa. The tensile and compressive elastic strengths of the material are 320 MPa. Assuming a factor of safety of 2, design the wall thickness of the gun barrel.
- 1. A solid piece of metal of volume 10,000 mm3 is compressed by a pressure of 70 MPa. Determine the bulk modulus given that the Young’s modulus E is 214 Gpa and the Poisson’s ratio is 0.33. Also determine the change in the volume.2. Starting from the first principles derive the relation between Young’s modulus (E), shear modulus (G) and Poisson’s ratio (υ)A tensile stress is to be applied along the long axis of a cylindrical brass and that has a diameter of 10mm. If the poisons ratio for brass is 0.34 , and a 2.5x10°mm change in diameter. The change in strain in z direction will be: Select one: а. 2.5x103mm b. 2.5x10-4 С. 2.5x10-3 O d. 2.5x10-103. An axial pull of 35000 N is acting on a bar consisting of three lengths as shown below. If the Young's Modulus is 2.1 x 105 N/mm2. Determine (i) Stresses in each section, and; (ii) Total extension of the bar. Section 3 Section 2 Section 1 35000 N 35000 N 2 cm DIA 3 cm DIA 5 cm DIA k-20 cm- 25 cm -22 cm-
- 1. A steel pipe of length 4 ft, outside diameter of 6.0 in., andinside diameter of 4.5 in., is compressed by an axial forceof 140 kips. The material has a modulus of elasticity of30,000 ksi and Poisson’s ratio of 0.30. Determine thefollowing quantities for the pipe:a. The shortening.b. The lateral strain.c. The percentage increase in the outer and theincrease in the inner diameter.d. The percentage increase in the wall thickness.The stress in thin-walled sphere is greater than the thin-walled cylinder. (A) True (B) FalseQuestion 3 - Strain Energy A brass tube with an outside diameter of 20 mm and 4 mm wall thickness is 80 mm long.It is joined to the end of a solid brass rod with a diameter of 20 mm and 120 mm long toform a compound assembly. This assembly is subjected to tension due to a mass of 150kg moving at a speed of 0.4 m/s.3.1. Determine the stresses induced in the rod and the tube respectively.3.2. Determine the change in length of each part, as well as the total change in length ofthe assembly.3.3 Determine the equivalent impact load (in kg) required to have the same effect(produce the same amount of energy) if falls freely from a height of 10 cm onto acollar attached to the bottom of the assembly if the assembly is vertically attachedat its top.3.4 How much strain energy is absorbed by each section of the assembly?(For brass: E = 100 GPa and α = 18×10-6/ 0C)