For the plane trusses shown in Figures P3-29 and P3-30, determine the horizontal and vertical displacements of node 1 and the stresses in each element. All elements have E = 210 GPa and A = 4.0 × 10–4 m². %3D %3D 1) 2 m 3 m 1 60° 5 m 40 kN (3 E 3.
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- A solid aluminum bar (G = 27 GPa ) of diameter d = 40 mm is subjected to torques T = 300 N - m acting in the directions shown in the figure, Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.A hemispherical window (or viewport) in a decompression chamber (see figure) is subjected to an internal air pressure of 85 psi. The window is attached to the wall of the chamber by 14 bolts. (a) Find the tensile force Fin each bolt and the tensile stress (T in the viewport if the radius of the hemisphere is 14 in. and its thickness is 1.25 in. (b) If the yield stress for each of the 14 bolts is 50 ksi and the factor of safety is 3.0, Find the required bolt diameter. (c) If the stress in the viewport is limited to 500 psi, find the required radius of the hemisphere.A capped cast-iron pipe is compressed by a brass rod, as shown. The mil is turned until it is just snug, then add an additional quarter turn to pre-compress the cast-iron pipe. The pitch of the threads of the bolt ap = 52 mils (a mil is one-thousandth of an inch). Use the numerical properties provided. (a) What stresses a and arwill be produced in the cast-iron pipe and brass rod. respectively, by the additional quarter turn of the nut? (b) Find the bearing stress ahbeneath the washer and the shear stress t(in the steel cap.
- Because of foundation settlement, a circular tower is leaning at an angle a to the vertical (see figure). The structural core of the tower is a circular cylinder of height ft, outer diameter d2, and inner diameter d1.For simplicity in the analysis, assume that the weight of the tower is uniformly distributed along the height. Obtain a formula for the maximum permissible angle a if there is to be no tensile stress in the tower.A copper bar with a rectangular cross section is held without stress between rigid supports (see figure). Subsequently, the temperature of the bar is raised 50°C (a) Determine the stresses on all faces of the elements A and B, and show these stresses on sketches of the elements. (Assume = 17.5 × 10-6/? and E = 120 GPa ) (b) If the shear stress at B is known to be 48 MPa at some inclination 8, find angleThe flat bars shown in parts a and b of the figure are subjected to tensile forces P = 2.5 kN. Each bar has thickness t = 5.0 mm. (a) For the bar with a circular hole, determine the maximum stresses for hole diameters d = 12 mm and d = 20 mm il" the width h = 60 mm. (b) For the stepped bar with shoulder fillets, determine the maximum stresses Tor fillet radii R = 6 mm and R = 10 mm if the bar widths are h = 60 mm and c = 40 mm.
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