Show the derivation of the girth and longitudinal stresses of the thin-walled cylindrical container shown below. Say p is the internal pressure, d is the inside diameter of the container and t is vwall thickness See
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- Calculate the minimum wall thickness for a cylindrical vessel that is to carry a gas at apressure of 5.75 MN/m2 . The diameter of the vessel is 400 mm, and the stress is limited to28.75 MPa.Pressure inside the cylinder is 10 bars Is this a thin walled cylinder when the thickness is 10 mm. Estimate theoretically the hoop andlongitudinal stressesThe cylindrical steel tank shown is 3.5m in diameter 5m high and filled with brine solution. Brine has a density of 1198kg/m3. The thickness of the steel shell is 12.5mm. Calculate the tangential stress and the longitudinal stress in the tank, MPa
- A rubber cylinder R of length L and cross sectionalarea A is compressed inside a steel cylinderS by a force F that applies a uniformly distributedpressure to the rubber (see figure).(a) Derive a formula for the lateral pressure pbetween the rubber and the steel. (Disregardfriction between the rubber and the steel, andassume that the steel cylinder is rigid when comparedto the rubber.)(b) Derive a formula for the shortening δ of therubber cylinder.Consider the steel pressure vessel shown in Figure 1, intended to withstand an internalpressure of 40 MPa. The vessel has an outer diameter of 300 mm, an overall length of 500mm and a wall thickness of 30 mm. There is a 30 mm fillet radius where the interior wallsurface joins the end caps, as shown in the section view in Figure 1. The vessel is made ofASTM A27 steel. Use ANSYS Workbench to simulate this component and comment on itssuitability for production given the loading conditions detailed above.THIN-WALLED VESSELa. What is a thin-walled vesselb. Derivation of stress formula for thin-walled vessel (cylindrical and spherical)c. Step by step solution of 2 sample problems each for cylindrical and spherical vessel
- A block R of rubber is confined betweenplane parallel walls of a steel block S (see figure). Auniformly distributed pressure p0 is applied to thetop of the rubber block by a force F.(a) Derive a formula for the lateral pressure pbetween the rubber and the steel. (Disregardfriction between the rubber and the steel, and assume that the steel block is rigid when comparedto the rubber.)(b) Derive a formula for the dilatation e of the rubber.(c) Derive a formula for the strain-energy density uof the rubber.5. In the CN Railwayproject,steel railroad rails of 9.5meters long are to be installed.If the modulus of elasticity of steel is207GPa, and if the lowest temperature considered is 18°C and a maximum temperature of 36°C is designed for, determine the clearance between the rails such that adjoining will just touch at maximum design temperature. Assume α for steel is 11.6 x 10-6/°CA polyethylene bar having rectangular cross section with a width 7.35 in. and depth 7 in. is placed insidea hollow steel square section with side dimension of8 in. The polyethylene bar is then compressed by an axialforce P. At what value of the force P will the gap betweenthe polyethylene bar and the steel tube be closed for thefirst time on one side? What is the remaining gap betweenthe polyethylene bar and the steel tube on the other side?For polyethylene, assume E 5 200 ksi and n 5 0.4.1
- Seatwork: Show your complete solution. Use 4 decimal places. Thermal Stress: In the LRT II project, steel railroad rails of 20 meters long are to be installed. If lowest temperature considered is 22 ℃ and a maximum temperature of 36 ℃ is designed for, and the modulus of elasticity of steel to be 207000 MPa, determine the clearance between rails such that adjoining rail will just touch at maximum design temperature.A cylindrical steel pressure vessel 60 cm in diameter with a wall thickness of 30 mun, is subjected to an internal pressure of 6 Nmm. (a) Calculate the tangential and longitudinal stresses in the steel. (b) To what value may the internal pressure be increased if the stress in the steel is limited to 200 MN/m?Calculate the diameter of a pressure vessel of thickness 0.04 m and the inside pressure is 20 mpa. Assume the permissible stress of the vessel is 100 mpa.