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- -11 A rubber cube R of a side L = 3 in. and cross- sectional area A = 9 in2 is compressed inside a steel cube S by a force F = 5 lb that applies uniformly distributed pressure to the rubber. Assume E 0.3ksi and,, = 0.45. (a) Calculate the lateral pressure between the rubber and steel (disregard friction between the rubber and the steel, and assume that the steel block is rigid when compared to the rubber). (b) Calculate the change in volume of the rubber.Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.A hollow circular shaft of inner radius 10 mm outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is?
- The mechanical assembly shown in the figureconsists of an aluminum tube, a rigid end plate, andtwo steel cables. The slack is removed from the cablesby rotating the turnbuckles until the assembly is snugbut with no initial stresses. Afterward, the turnbucklesare tightened by 1.5 turns. Calculate the forces inthe tube and the cables and determine the shorteningof the tube. As = 0.85in2 for each cable, AA = 4.5 in2,L = 20 in., Es = 29,000 ksi, EA = 10,600 ksi, andp = 1/16 in.As shown in the figure, a homogeneous 100-kgrigid block is suspended by the three springs whoselower ends were originally at the same level. Eachsteel spring has 24 turns of 10-mm-diameter on amean diameter of 100 mm, and G = 83 GPa. Thebronze spring has 48 turns of 20-mm-diameterwire on a mean diameter of 150 mm, and G = 42GPa. Compute the maximum shearing stress ineach spring using A.M. Wahl formula.A hollow circular shaft of inner radius 20 mm, outer radius 40 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, Calculate the torsional stiffness of the shaft (in kN-m/rad) is
- A rubber cylinder R of length L and cross sectionalarea A is compressed inside a steel cylinderS by a force F that applies a uniformly distributedpressure to the rubber (see figure).(a) Derive a formula for the lateral pressure pbetween the rubber and the steel. (Disregardfriction between the rubber and the steel, andassume that the steel cylinder is rigid when comparedto the rubber.)(b) Derive a formula for the shortening δ of therubber cylinder.A steel torsion bar AB with diameter d = 34 mm, and ductile material of tensile yield strength Sy = 276 MPa is attached to a rigid arm at A, supported by a bearing at C, and fixed at B, as the picture shows. At the right end of the arm is mounted the wheel on which the vertical force P acts from the ground and which passes through the center of the wheel. If bearing C acts as a simple support and the effect of transverse shear due to P is negligible, determine the maximum force P (in kN) that can be applied to the wheel. Consider a factor of safety n = 2.5. Use the maximum energy of distortion failure criterion and do the analysis on bar AB (torsion bar) in the section where the bearing is.The composite shaft shown in the figure is manufacturedby shrink-fitting a steel sleeve over a brass coreso that the two parts act as a single solid bar in torsion.The outer diameters of the two parts are d1 = 40 mmfor the brass core and d2 = 50 mm for the steel sleeve.The shear moduli of elasticity are Gb = 36 GPa for thebrass and Gs = 80 GPa for the steel.(a) Assuming that the allowable shear stressesin the brass and steel are τb = 48 MPa andτs = 80 MPa, respectively, determine the maximumpermissible torque Tmax that may beapplied to the shaft.(b) If the applied torque T = 2500 kN . m, findthe required diameter d2 so that allowable shearstress τs is reached in the steel.
- A 2.3 m long stick with a uniform mass distribution extends horizontally from abuilding. There are two wires attached to the stick, wire A is attached to the beam 3/5 of theway from the building to the end of the stick, it pulls up at a 63° angle to the stick; wire B isattached 1/6 of the way from the building to the end of the stick, and pulls it down at a 32° angle to the stick.The tension in cable a is 112 N. What is the tension on wire B?Two gondolas on a ski lift are locked in the postion show in the figure while repairs are being made elsewhere.The distance between support towers is L = LOO ft.The length of each cable segement under gondolas weighing WB= 450 lb and Wc=650 lb are DAB=12 ft, DBC=70 a , and DCB=20 ft . The cable sag at B is AB = 3.9 ft and that C is A = 7.1 ft.THe effective cross-sectional area of the cables is Ae=0.12 in". (a) Find the tension force in each segment; neglect the mass of the cable. (b) Find the average stress(σ) in each cable segment.A beam held by a hinge, take 2. The left end of a beam of mass 17.9 kg and length L is fixed to a wall by a hinge. The beam is inclined at 19.8 degrees from the horizontal; it is supported at its right end by a rope forming an angle of 30.3 kg with the horizontal.create a template for:a) the tension in the rope;b) the orientation of the hinge force, relative to the x+ axis.