A close ends long thin walled cylindrical shell i subjected to an internal pressure. What is the ratio of the hoop stress to longitudinal stress developed in the shell ?
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- - A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle ? = 20° and show the full stress state on a sketch of a properly oriented element.A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?The hollow drill pipe for an oil well (sec figure) is 6,2 in. in outer diameter and 0.75 in. in thickness. Just above the bit, the compressive force in the pipe (due to the weight of the pipe) is 62 kips and the torque (due to drilling) is 185 kip-in. Determine the maximum tensile, compressive, and shear stresses in the drill pipe.
- I solved the principal stresses but having a hard time on determing the theta-P (orientation of principla plances), could you help me?PLSS ANSWER ASAPPP Which is correct about spherical shell? a It has the same formula as hoop stress b The wall of the pressurized spherical vessel is subjected to uniform comporessive stress in all directions c It has the same formula as the tangential stress d The wall of the pressurized spherical vessel is subjected to uniform tensile stress in all directions(a) Construct Mohr's circle for an element in a uniaxial state of stress (b) Use this Mohr's circle to derive the equation for the normal stress On and shear stress En on the n-face. The equations should depend on Ox and θ (c) Use the Mohr's circle to determine the planes on which the maximum shear stress acts. Sketch a properly oriented maximum-shear-stress element and indicate the normal and shear stresses acting on its faces. Ơn nt o, Note: for (b), the angle θ is between 0 and 90° and is positive
- Find the interal normal stress in all relevant segments of the bar in the picture.A 30 ?? square plate is subjected to uniform pressure as shown in Figure.1. The 2D loading stressesare described. If the modulus of elasticity is 200 ??? and the lateral constant (Poisson's ratio ? = 0.3). Estimatethe change in length in the vertical, horizontal and diagonal sides as well as determine the volumetric strain.Illustrate the effect of two-dimensionalstrain by constructing appropriate sketches (before and after deformation).Repeat the analysis for lower value of pressure and higher value in the range of [20 -100 MPa] and comment onthe overall results.What are the equation used for part a)? for the axial stress, why do we not use Axial Stress = Pr/(2t)? Also, the math for the pricipal stresses is incorrect.
- (b) Determine the thickness of a plain cylinder head for 0.3m cylinder. The maximum gas pressure is approximately 3.2N/mm. Design the studs also for the cylinder cover. Assume the allowable hoop stress =42 N/mm' for cast iron; the allowable tensile stress for material of studs =63 N/mm?The bend steel rod for pipeline system has a diameter (d) and is subjected to the tensileforce (P) as shown in Figure 5. It has been determine that a critical element occurs atpoint A on the surface of rod. The critical element at point A is subjected to plane stressescomponent which are tensile stress of 35 MPa in xz-plane and compressive stress of75 MPa in xy-plane. By using Transformation Equations; iii) Calculate the maximum shear stresses and their location acting at the point A.iv) Calculate the normal and shear stresses on plane if the element rotate through of26° clockwise from the x-axis.A brittle material made of ASTM grade 30 cast iron has ultimate strength in tension of 31 kpsi and ultimate strength in compression of 109 kpsi and undergoes the following plane of stress state: o, = 20 kpsi and Tyy = 10 kpsi (CW). a) using the 3D Mohr's circle, find all three principal normal stresses. b) using the Brittle-Coulomb-Mohr theory and Modified-Mohr theory, find the factors of safety for the given plane of stress state.