Investigate which problem can be solved by the two-dimensional stress distribution 011 = 4x1x2; 012 = B + Cx3;022 = 0, where A, B and C are constants, in the absence of body forces. Assume a rectangular solid defined by 0
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- A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).: 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?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.
- -27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile stress The stresses on element A oriented at angle ?? x1=45° aresy1= 75 psi. tx1y1= 275 psi. . Find the state of stress on the element lilt is rotated clockwise to align the x3 axis with the horizontal x axis.Explain the method of representing the combination of normal and shear stresses acting on any plane through an incremental element on shear stress–normal stress coordinates.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.
- The state of stress at a point can be described by σx = 40 MPa , σy = 64 MPa , and τxy = 18 MPa . A second coordinate system is rotated by θ = 25 ∘ A) What is the normal stress in the direction of the x′-axis? B) What is the shear stress in the y′-direction for the faces with a normal in the x′-direction? C) What is the normal stress in the direction of the y′-axis?1. A thin-walled cylinder with a diameter of 20 cm and a wall thickness of 2 mm is filled with gas at a pressure of 2 MPa. Calculate the longitudinal stress, and circumferential stress in the cylinder wall.A thinwalled, filamentwound pressure vessel is pressurized such that at a point in the wall is in the figure below. ?=[ ????????0 (c)the magnitude of the normal stress acting on the filaments, and (d)the magnitude of the shear stress (b)the magnitude of the traction vector acting alongthe direction of the filament winding. −????????0 Determine: ] suitable stress tensor ?′for a rotated coordinate axis. (You can use Matlab or a calculator to The filament winding angle is ?=53.13°from the longitudinal axis ofthe pressure vesseas shown Noting that the transformation matrix to rotate the x-y coordinate system anticlockwise by ?is: (e)find the magnitude of the normal stress and shear stress acting on the filaments by finding a (a)Write down the stress tensor in the xyzcoordinate system. under a plane-stress state with ???=10.946MPa, ???=21.892MPaand ???=0MPa. 001 perform the tensor multiplications)
- A cylindrical pressure vessel has an inner diameter of 4 ft and a thicknessof 1 2 in. Determine the maximum internal pressure it can sustain so that neither its circumferential nor its longitudinal stress component exceeds 20 ksi. Under the same conditions, what is the maximum internal pressure that a similar-size spherical vessel can sustain?A 1.5-m-diameter cylindrical tank is formed of 6-mm-thick sheet steel (E = 200 Gpa, ν = 0.3). The maximum shear strain occurring in this tank when the contents pressure is 1 MPa, is: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