3) The rigid horizontal bar AB is supported by three vertical rods as shown in the figure and carries the load of 110 kN. The system is stress free before the load is applied. After the load was applied, the temperature of all wires is raised by 20°C. Use a = 12x10-6/°C for steel, a = 18x10-6/°C for copper and a = 20x10-6/°C for brass. Neglecting the weight of the bar AB, determine the location of the 110 kN force in order that AB remains horizontal. steel bar: A=130mm brass bar: A=325mm? copper bar: A=195mm? A B 110 kN 3.00m 2.00m 1.80m 1.20m 1.50m
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- A steel cable with a nominal diameter of 25 mm (see Table 2-1) is used in a construction yard to lift a bridge section weighing 38 kN. as shown in the figure. The cable has an effective modulus of elasticity E = 140 GPa. (a) If the cable is 14 m long, how much will it stretch when the load is picked up? (b) If the cable is rated for a maximum load of 70 kN, that is the factor of safety with respect to failure of the cable?A pressurized circular cylinder has a sealed cover plate fastened with steel bolts (see figure). The pressure P of the gas in the cylinder is290psi, the inside diameter D of the cylinder is 10.0 in., and the diameter dBof the bolts is 0.50 in. I f the allowable tensile stress in the bolts is 10,000 psi, find the number n of bolts needed to fasten the cover.A hollow circular pipe (see figure} support s a load P that is uniformly distributed around a cap plate at the top of the lower pipe. The inner and outer diameters of the upper and lower parts of the pipe are d1= 50 mm, d2= 60 mm, rf3 = 57 mm, and d1= 64 mm, respectively. Pipe lengths are Lt= 2 m and L, = 3 m. Neglect the self-weight of the pipes. Assume that cap plate thickness is small compared to I, and E,. Let E = 110 MPa. (a) If the tensile stress in the upper part is d = 10.5 MPa. what is load PI Also, what are reactions ft, at the upper support and R-, at the lower support? What is the stress ar(MPa) in the lower part? (b) Find displacement S(mm) at the cap plate. Plot the axial force diagram (AFD) [Ar(.f)] and axial displacement diagram (ADD)[5(.t)]. (c) Add the uniformly distributed load q along the censorial axis of pipe segment 2. Find q (kN/m) so that It, = 0. Assume that load P from part (a) is also applied.
- The assembly shown in the figure consists of a brass core (diameter d:= 0.25 in.) surrounded by a steel shell {inner diameter d2= 0.23 in., outer diameter di= 0.35 in.}. A load .P compresses the core and shell that both have a length L = 4.0 in. The module of elasticity of the brass and steel are Eb=15 X 10fi psi and Es= 30 X 10fi psi, respectively. (a) What load P will compress the assembly by 0.003 in? (b) IF the allowable stress in the steel is 22 ksi and the allowable stress in the brass is 16 ksi. what is the allowable compressive load Pallow? (Suggestion: Use the equations derived in Example 2-8.)A two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load P:equals 400 KN, and the second-floor load P-, equals 720 kN. Each column has a length L = 3.75 m. The cross-sectional areas of the first- and second-floor columns are 11,000 mm" and 3900 mm", respectively. (a) Assuming that E = 206 GPa. determine the total shortenings aof the two columns due to the combined action of the loads Ptand P,. (b) How much additional load P0can be placed at t he top of t he column (point C) if t he total shortening: SACis not to exceed 4.0 mm?A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?
- A hollow circular tube T of a length L = 15 in. is uniformly compressed by a force P acting through a rigid plate (see figure). The outside and inside diameters of the tube are 3.0 and 2.75 in., respectively. A concentric solid circular bar B of 1.5 in. diameter is mounted inside the lube. When no load is present, there is a clearance c = 0.0I0 in. between the bar B and the rigid plate. Both bar and tube are made of steel having an c[autoplastic stress-strain diagram with E = 29 X LO3 ksi and err= 36 ksi. (a) Determine the yield load Pt- and the corresponding shortening 3yof the lube. (b) Determine the plastic load Ppand the corresponding shortening Spof the tube. (c) Construct a load-displacement diagram showing the load Pas ordinate and the shortening 5 of the tube as abscissa. Hint: The load-displacement diagram is not a single straight line in the region 0 ^ P ^ PrA metal bar AB of a weight Ills suspended by a system of steel wires arranged as shown in the figure. The diameter of the wires is 5/64 in., and the yield stress of the steel is 65 ksi. Determine the maximum permissible weight W max for a factor of safety of 1.9 with respect to yielding.Two bars AC and BC of the same material support a vertical load P (see figure). The length L of the horizontal bar is fixed, but the angle fl can be varied by moving support A vertically and changing the length of bar AC to correspond with the new position of support A. The allowable stresses in the bars are the same in tension and compression. When the angle ft is reduced, bar AC becomes shorter, but the cross-sectional areas of both bars increase because the axial forces are larger. The opposite effects occur if the angle 0 is increased. Thus, the weight of the structure (which is proportional to the volume) depends upon the angle ft. Determine the angle ft so that the structure has minimum weight without exceeding the allowable stresses in the bars. Note: The weights of the bars are very small compared to the force P and may be disregarded.
- A rigid bar of weight W = SOO N hangs from three equally spaced vertical wines( length L = 150 mm, spacing a = 50 mm J: two of steel and one of aluminum. The wires also support a load P acting on the bar. The diameter of the steel wires is ds= 2 mm, and the diameter of the aluminum wire is d = A mm. a Assume £,=210 GPa and EB« 70 GPa. What load Pallowcan be supported at the mitl-point of the bar (x = a) if the allowable stress in the steel wires is 220 MPa and in the aluminum wire is 80 MPa? (See figure part (b) What is /*,Ikw» if the load is positioned at .v = all1? (See figure part a.) (c) Repeat part (b) if the second and third wires are switched as shown in the figure part b.A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If? (c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"? (d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?A plane frame with a pin support at A and roller supports at C and £ has a cable attached at E. which runs over Frictionless pulleys al D and B (see figure). The cable force is known to be 400 N. There is a pin connection just Lo the left of joint C. (a) Find reactions at supports^, C, and E. (b) Find internal stress, resultants N, V, and M just to the right of joint C. (c) Find resultant force in the pin near C.