A-8.15: A thin walled cylindrical tank, under internal pressure p, is compressed by a force F = 75 kN. Cylinder diameter is d = 90 mm and wall thickness t = 5.5 mm. Allowable normal stress is 110 MPa and allowable shear stress is 60 MPa. The maximum allowable internal pressure Pmax is approximately: (A) 5 MPa (B) 10 MPa. (C) 13 MPa (D) 17 MPa
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- : A hollow, pressurized sphere having a radius r = 4.8 in, and wall thickness t = 0.4 in. is lowered into a lake (see figure). The compressed air in the tank is at a pressure of 24 psi (gage pressure when the tank: is out of the water). At what depth D0will the wall of the tank be subjected to a compressive stress of 90 psi?A roadway sign weighs 5.3 kN and is supported by a structural pipe that has an outside diameter of 220 mm and a wall thickness of 14.5 mm. The resultant force of the wind pressure acting on the sign is 13 kN, as shown. Assume a = 8.1 m, b=4m, P₂ = 13 kN, and Py = 5.3 kN. (a) Determine the normal and shear stresses. Txy at point H. (b) Determine the normal and shear stresses Ok Tysk at point K. Answers: 0|| = Tryll = 0k = Tyck= i i MPa. MPa. MPa. MPa.The thin rectangular plate (Fig. 1, not to scale) with sides 6 m and 4 m of thickness 112 mm is subjected to the stresses ox, Oy and txy. An Airy stress function is proposed to be: $(x, y) = Ax° + Bx'y+Cxy, with A=B=C =1 (a) Determine the values of stresses (ox, Oy and txy) at point (x_y) which satisfy the stress function (b) Draw a stress element showing the stresses on the four faces of the element (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). (c) Neglecting body forces, determine the resultant normal and shearing forces on the right face of the plate that are consistent with o (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). 112 mm 4 m 6 m Fig. 1 Biharmonic Equation ô*o(x, y) ôx o*o(x.y) ô*¢(X.y)=v*o(x,y) =0 +2 where o(x.y) is defined as: ô*o(x,y) o o(x, y) ôxcy
- A roadway sign weighs 5.4 kN and is supported by a structural pipe that has an outside diameter of 205 mm and a wall thickness of 14 mm. The resultant force of the wind pressure acting on the sign is 8 kN, as shown. Assume a = 9.6 m, b = 3.7 m, P₂ = 8 kN, and Py = 5.4 kN. (a) Determine the normal and shear stresses Oy, Tyll at point H. (b) Determine the normal and shear stresses OK, Tyzk at point K. P₂ HK Answers: OH = TxyH ők = Tyzk= = i MPa. MPa. MPa. MPa.A wood stave pipe, 120 cm in inside diameter, is to resist a maximum water pressure of 1,200 kPa. If the staves are bound by steel flatbands (10 cm by 2.50 cm), find the spacing of the bands if its allowable stress is 105 MPaQ3 A closed ended, thick-walled cylinder, manufactured from silicon material is designed to contain instrumentation for underwater research. It has an outer radius r = 0.3m and internal radius of r¡ = 0.1m. (a) The cylinder is subjected to an external pressure Po. Show that the radial and circumferential stresses at the internal and external surface may be expressed by the following equations. at ri: at ro: 0₁ = 0 and 60 Or = -P and o = = -2Pok² k² 1 -2.25P −P(k² + 1) k²-1 = -1.25Po (b) Calculate the radial, circumferential, and axial stresses at r₁, when the cylinder is submerged to a depth of 7000 meters under seawater. Consider the density of seawater as 1025kgm-³ and g 9.81ms-². (c) In an effort to reduce the stresses at the inner surface, the operators decide to increase the internal pressure in the cylinder to 20 MPa. If the cylinder is 1.5m long, calculate its change in length when submerged in the sea to a depth of 7000 metres, with this internal pressure applied. Consider…
- a) A cylinder with a 0.30-m inner diameter and a 0.40-mouter diameter is internally pressurized to 100 MPa. Determinethe maximum shear stress at the outer surfaceof the cylinder. b) A thin-walled cylinder containing pressurized gas isfixed by its two ends between rigid walls. Obtain anexpression for the wall reactions in terms of cylinderlength l, thickness th, radius r, and internal pressure pi.(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.Calculate the combined stress (MPa) on the rod shown below using principle stress method.Here, F1 = 0.35 kN, F2 = 0.12 kN, T = 428000 N-mm. Length and diameter of the rod are 75cm and 75 mm, respectively.
- a cylindrical pressure vesssel( diameter =2.8m and wall thickness of 35mm) is made of steel. the maximum pressure inside the tank is 2.0Mpa. Based on the tresca( maximum shear stress criterion) what is the required yield stress of the steel. Show all work and formulasA triangular dam is shown in the figure, base is 6-m and height is 8-m. Compute for the factor of safety against sliding and overturning. Unit weight of concrete is 23.54 kN/cu.m. Consider 1 meter length strip. Disregard hydrostatic uplift pressure. The coefficient between the dam and the foundation is 0.8. hQuestion 2 A thin walled tube of thickness (t) 5mm and diameter (d) 200mm with closed ends is subjected to an internal pressure (p) 7.0 MN/m², producing an axial and circumferential direct stresses given by pd/4t and pd/2t respectively. A torque T = 15.0 kNm is also applied which sets up a shear stress 7 = T/2nr²t where r is the radius. (a) Determine the magnitude and direction of the principal stresses. (b) Calculate the overall maximum shear stress.