Q7-Q8: A 6-in.-long bronze tube, with closed ends, is 3 in. in diameter with a wall thickness of 0.1O in. With no internal pressure, the tube just fits between two rigid end walls. Calculate the longitudinal and tangential stresses for an internal pressure of 3, 000 psi. Assume Poisson's ratio, v = 1/3 and Modulus of elasticity, E = 12,000 ksi t= 0.10 in Y 3 in Ø L = 6 in
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include also the free body diagram
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- A sign is supported by a pipe (see figure) having an outer diameter 110 mm and inner diameter 90 mm. The dimensions of the sign are 2.0 m X 1.0 m, and its lower edge is 3.0 m above the base. Note that the center of gravity of the sign is 1.05 m from the axis of the pipe. The wind pressure against the sign is 1.5 kPa. Determine the maximum in-plane shear stresses due to the wind pressure on the sign at points /I, B, and C, located on the outer surface at the base of the pipe.A hemispherical window (or viewport) in a decompression chamber (see figure) is subjected to an internal air pressure of 85 psi. The window is attached to the wall of the chamber by 14 bolts. (a) Find the tensile force Fin each bolt and the tensile stress (T in the viewport if the radius of the hemisphere is 14 in. and its thickness is 1.25 in. (b) If the yield stress for each of the 14 bolts is 50 ksi and the factor of safety is 3.0, Find the required bolt diameter. (c) If the stress in the viewport is limited to 500 psi, find the required radius of the hemisphere.A fire extinguisher tank is designed for an internal pressure of 825 psi. The tank has an outer diameter of 4.5 in. and thickness of O.OS in. Calculate the longitudinal stress, the circumferential stress, and the maximum shear stresses (out-of-plane and in-plane) at the outer surface of the tank.
- A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?A cylindrical tank subjected to internal pressure/? is simultaneously compressed by an axial force F = 72 kN (see figure). The cylinder has diameter d = 100 mm and wall thickness t = 4 mm. Calculate the maximum allowable internal pressure /?max based upon an allowable shear stress in the wall of the tank of 60 MPa.A cast aluminum cylinder of a portable hydraulic riveter is d mm in diameter. The pressure of the fluid is p N/mm2 by gauge. Determine suitable thickness of the cylinder wall assuming that the yield point stress is A MPa and factor of safety of B .Calculate the tangential and radial stresses at the inner, middle radius and outer surfaces. Let D = 208 mm P = 15.8 N/mm2 Yield stress = 442 N/mm2 %3D Factor safety = 6.2
- A pipe carrying steam at 3.0 MPa has an outside diameter of 450 mm and a wall thickness of 10 mm. A gasket is inserted between the flange at one end of the pipe and a flat plate used to cap the end. How many 25 mm diameter bolts must be used to hold the cap on if the allowable stress in the bolts is 90 MPa of which 50 MPa is the initial stress? What circumferential stress is developed in the pipe?Define the main difference between thick and thin cylinders and give an example for each type of cylinder Derive the expression of longitudinal stress, o, for a closed thick cylinder which has inner radius, R₁ and outer radius, R₂ and subjected to internal pressure only. Figure Q3 shows a cross section of composite cylinder that is made by shrinking a tube of 330 mm internal diameter and 50 mm thick over another tube of 330 mm external diameter and 50 mm thick. The radial pressure at the common surface, after shrinking is 180 MPa. Suppose the compound cylinder is subjected to an internal fluid pressure of 1200 MPa, determine; i) the hoop stresses at inner radius and outer radius of inner cylinder, ii) the hoop stresses at inner radius and outer radius of outer cylinder. Ro P Figure Q3 R₁Problem 1 of 2: Nodal displacements for the elements 1-3 and 2-3 of a plane truss were determined to be u = 1.5 mm, uz = 0.2 mm, uz = -2.7 mm, v = 3.1 mm, v2 = 3.3 mm, v, =-0.8 mm L. %3D What are their axial stresses, if E = 2.0-101 Pa and L = 2 m for both elements? Solution:
- Problem 7-6 A long hollow cylinder is of 20 cm external diam- eter and is 5 cm thick. It is revolving at a constant speed of 2400 r.p.m. Calculate the maximum radial and hoop stresses induced in the cylin- der. The density of cylinder material is 7600 kg/m³ and Poisson's ratio= 0.30.A spherical pressure vessel is constructed by bolting two hemispheres together along rigid flanges as shown in the sketch. The sphere has an internal diameter of 1.5 m and the plate thickness is 5 mm. Allowable tensile stresses are 45 MPa in the shell and 80 MPa in the bolts. 1. Calculate the allowable gauge pressure 2. Determine the number of bolts required if the bolt diameter is 25 mm (Note: bolt root diameter = 0.84 × nominal bolt diameter) 3. A thin copper tube, 14 mm internal diameter and 0,5 mm wall thickness has closed ends and rotates at 1200 r/min while it is subjected to an internal gauge pressure of 222 Pa. Calculate the total hoop stress in the wall of the tube if the density of copper is 8900 kg/m3.Coefficient of expansion αB= 165.10^-7 1/ 0C , solid copper bar diameter 20 mm , It is placed in a steel pipe with an outer diameter of 30 mm with an inner diameter of 2 mm larger than this bar and an expansion coefficient αÇ = 125.10^-7 1 / 0C, and is joined by a rigid plate from the top so that they move together. Find the stresses that will occur in steel and copper when the system is heated with a temperature difference of Δt = 80 0C. (EÇ = 200 GPa, EB = 100 GPa)