the Mohr's circle
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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).At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with t = 1400 psi and trv = —900 psi, as shown in the figure part a. The figure part b shows an inclined plane aa cut through the same point in the material but oriented at an angle ft Determine the value of the angle 6 between zero and 90° such that no normal stress acts on plane aa. Sketch a stress clement having plane aa as one of its sides and show all stresses acting on the clementRepeat the preceding problem using sx= 5.5 MPa. ??y= 4 MPa. and txy= 3.2 MPa.
- 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?a) Prime planes,b) Prime stresses, c) Maximum shear stress and thisin the plane of the stressdetermine the normal stressA plane stress state is given by the principal stresses σx =25 MPa and σy= -11 MPa. Determine σx' in the case that the system is inclined by 30 degrees (counter-clockwise). Give your answer in MPa to the nearest whole number.
- A stress element in a rock mass making up a slope experiences a 2D stress as follows: σx = 8 MPa, σy = 4 MPa , tauxy = 3 MPa a. Draw the Mohr circle. On Mohr's circle, mark the location of the x and y planes, mark the angle of rotation θ from the x plane to the σ₁,σ3,and taumax plane. Prove that the angle of rotation of the Mohr circle is 2 times the angle of rotation of the element. b. Write down the coordinates of the center of Mohr's circle and calculate its radius.The normal and tangential stresses on a plane inclined at 30° to the axis of the minor principal stress are 75 N/mm2 and 20 N/mm2. The resultant stress on a plane by analytical method isAt a point on the free surface of a machine part (E = 214 GPa, G = 83 GPa), the state of the stress is illustrated in the figure below. For the given plane stress condition determine: -all 3 principle stresses, the max in plane stress, average noemal stress and the absolut max shear stress. - Show the principle stress, the max inplane shear stress and the average normal stress on an appropriate schematic
- At a point in an elastic material under strain, the stresses on the three mutually perpendicular planes are as follows:A normal tensile stress of 60 N/mm^2and shear stress of 40 N/mm2 on one plane and a normal tensile force of 40 N/mm^2and a complimentary shear stress of 40 N/mm^2 on another plane. Find the following using Mohr circle only (take 5 N/mm2 = 1 cm)a. The principal stresses and principal planes.b. The maximum shear stress and its plane.c. The normal and shear stress on a plane inclined at an angle of 30Oto major principal plane.The principal tensile stress at a point across two mutually perpendicular planes are 100 N/mm2 and 40 N/mm2. The normal, tangential and resultant stresses on a plane inclined at 20° to the axis of the minor principal stress by analytical method isA certain streched wire 120 cm long and 2.4 mm indiameter is fastened to a point in the ceiling. An objectweighing 30x10^5 Dynes is hung at the other end of the wire.Compute a) the stress in the wire and b) elongation producedin the wire.