Under the assumption of plane stress, which one of the following is correct?
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- 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 clementA 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).An element in plane stress on the fuselage of an airplane (figure part a) is subjected to compressive stresses with a magnitude of 42 MPa in the horizontal direction and tensile stresses with a magnitude of 9.5 MPa in the vertical direction (sec figure part b). Also, shear stresses with a magnitude of 15.5 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 40g from the horizontal. Show these stresses on a sketch of an element oriented at this angle.
- -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..4-2 An element in uniaxial stress is subjected to tensile stresses sx= 57 MPa. as shown in the figure. Using Mohr’s circle, determine the following. (a) The stresses acting on an clement oriented at an angle 0 = 33° from the x axis (minus means clockwise). (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.The polyethylene liner of a settling pond is subjected to stresses ax= 350 psi. a = 112 psi. and = -120 psi, as shown by the plalte-stress element in the figure part a. Determine the normal and shear stresses acting on a seam oriented at an angle 01300 to the element, as shown in the figure part b. Show these stresses on a sketch of an element having its sides parallel and perpendicular to the seam.
- -18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element.Plastic bar of diameter d = 32 mm is compressed in a testing device by a Force P = 190 N that is applied as shown in the figure. (a) Determine the normal and shear stresses acting: on all faces of stress elements oriented at (1 ) an angle 8 = 00, (2) an angle ?? = 22.5s, and (3) an angle ?? = 45°. In each case, show the stresses on a sketch of a properly oriented element. What are smaxtmax (b) Find smax and tmax in the plastic bar if a re-cantering spring of stiffness k is inserted into the testing device, as shown in the figure. The spring stillness is 1/6 of the axial stiffness of the plastic bar.-18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. 7.3-18 a=2I50kPa, ay=375kPa.Txy.=-460kPa
- Solve the preceding problem for an element in plane stress on the bottom surface of a fuel tanker (figure part a); stresses are sx= 105 MPa, sy. = 75 MPa, and ??xy= 25 MPa. Determine the stresses acting on an element oriented at an angle ?? = 40° from the x axis, where the angle is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle ??.- 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?• - 7.4-7 An element on the surface of a drive shaft is in pure shear and is subjected to stresses ??xy= 2700 psi, as shown in the figure. Using Mohr’s circle, determine the following. (a) The stresses acting on an element oriented at a counterclockwise angle ?= 52° from the y axis. (b) The principal stresses. Show all results on sketches of properly oriented elements.