The stresses at a point in a bar are o, N/mm2 (tensile) and o2 Nmm2 (compressive) as shown in Figure 2.
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- -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-4. - An element in plane stress is subjected to stresses ??x= 105 MPa, ??y= 75 MPa, and sxy= 25 MPa (see the figure for Problem 7.3-1). Determine the principal stresses and show them on a sketch of a properly oriented element.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 clement
- 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.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 ??.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.
- The stresses acting on an element are x= 750 psi, y= 600 psi, and xy = 400 psi. Determine the principal stresses and show them on a sketch of a properly oriented element.-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.Acting on the sides of a stress element cut from a bar in uniaxial stress are tensile stresses of 10,000 psi and 5000 psi, as shown in the figure. (a) Determine the angle 0 and the shear stress T and show all stresses on a sketch of the element. (b) Determine the maximum normal stress amaxand the maximum shear stress Tmax in the material.
- The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.-26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and compressive stress a. If it is known that the normal stress along the diagonal t—t is ??t= -6.57 kPa, find stress ??y on element A. aAn element on the top surface of the fuel tanker in Problem 7.2-1 is in biaxial stress and is subjected to stresses a = -48 MPa and ay = 19 MPa, as shown in the figure. Using Mohr’s circle, determine the following. (a) The stresses acting on an clement oriented at a counterclockwise angle ?? = 25° from the x axis. (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.