The cross-sectional area of the prismatic bar is 0.02 m². If the normal and shear stresses on the plane P are 0 = 1.25 MPa and Te = -1.5 MPa, what are the angle and the axial force P. Figure 1
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- 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.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.Solve the preceding problem if the norm al and shear stresses acting on the element are sx = 2100 kPa, sy= 300 kPa, and txy= -560 kPa, and the seam is oriented at an angle of 22.5° to the clement.
- The state of stress on an element of material is shown in the figure. Calculate the unit volume change of the element if the stresses x and y. are -20 ksi and 10 ksi, respectively. Assume E = 10,600 ksi and v = 0.33.An clement in plane stress is subjected to stresses a,. cry, and (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle 0 from the x axis. Show these stresses on a sketch of an clement oriented at the angle ??. Now. The angle 0 is positive when count ere clockwise and negative when clockwise. r-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. a
- 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 if the normal and shear stresses acting on element B are 56 MPa, 17 MPa, and 27 MPa (in the directions shown in the figure) and the angle is 40° (clockwise)..4 The stresses on an clement arc known to be sx= 120 MPa, sy= 100 MPa, and txy= 75 MPa. Find the stresses on an inclined section through the element at an angle ? = 45°.
- 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.An clement in plane stress is subjected to stresses a,. cry, and (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle 0 from the x axis. Show these stresses on a sketch of an clement oriented at the angle 0. Now. The angle 0 is positive when count ere clockwise and negative when clockwise.The stresses acting on element A on the web of a train rail (sec figure part a) a re found to be 6500 psi tension in the horizontal direction and 18,500 psi compression in the vertical direction (see figure part b), Also, shear stresses with a magnitude of 3800 psi act in the directions shown. Determine the stresses acting on an clement oriented at a counterclockwise angle of 30° from the horizontal Show these stresses on a sketch of an element oriented at this angle