UNIVERSITY OF THESSALY MECHANICAL ENGINEERING DEPARTMENT Instructor: Dr. S.D. Chouliara e-mail: schoul@uth.gr MACHINE ELEMENTS Task 2 1. Let the bolt in the following Figure be made from cold-drawn steel. The bolt and the clamped plates are of the same length. Assume that the threads stop immediately above the nut. The clamped steel plates have a stiffness kc six times the bolt stiffness kb. The load fluctuates continuously between 0 and 8000N. (a)find the minimum required value of initial preload to prevent loss of compression of the plates. (b)find the minimum force in the plates for the fluctuating load when the preload is 8500N. 2. The cylinder head of a piston-type air compressor is held in place by ten bolts. The total joint stiffness is four times total bolt stiffness. Each bolt is tightened to an initial tension of 5000 N. The total external force acting to separate the joint fluctuates between 0 and 20.000 N. Assume that the bolt size and material are such that the bolt load remains within the elastic range. Draw a graph (plotting force versus time) showing three or four external load fluctuations, and corresponding curves showing the fluctuations in total bolt load and total joint clamping force.
3. Repeat previous problem 2, except that the external joint separating force varies between 10.000 and 20.000 N. 4. Two parts of a machine are held together by bolts that are initially tightened to provide a total initial clamping force of 10,000 N. The elasticities are such that kc = 2kb. (a) What external separating force would cause the clamping force to be reduced to 1000 N (assume that the bolt remains within its elastic range)?
(b) If this separating force is repeatedly applied and removed, what are the values of the mean and alternating forces acting on the bolts? 5. Two parts of a machine are held together by bolts, each of which carries a static tensile load of 3100N. (a) What size of class 5.8 metric bolt is required using a safety factor of 4 (based on proof strength)? (b) What is the least number of threads that must be engaged for the thread shear strength to be equal to the bolt tensile strength if the nuts are made of steel whose yield and proof strengths are 70 percent those of the bolt steel? 6. The bolts that attach a bracket to an industrial machine must each carry a static tensile load of 4 kn. (a) Using a safety factor of 5 (based on proof strength), what size of class 5.8 metric bolts is required?
(b) If the nuts are made of a steel with two-thirds the yield strength and proof strength of the bolt steel, what is the least number of threads that must be engaged for the thread shear strength to be equal to the bolt tensile strength? 7. The following figure shows a pressure vessel with a gasketed end plate. The internal pressure is sufficiently uniform that the bolt loading can be considered static. The gasket supplier advises a gasket clamping pressure of at least 13 MPa (this includes an appropriate safety factor) to ensure a leak-proof joint. To simplify the problem, you may neglect the bolt holes when calculating gasket area. If 12-mm, 16-mm, and 20-mm bolts that have coarse threads and are made of SAE class 8.8 or 9.8 steel (whichever is appropriate) are to be used, determine the number of bolts needed. If the ratio of bolt spacing to bolt diameter should not exceed 10 in order to maintain adequate flange pressure between bolts, and if this ratio should not be less than 5 in order to provide convenient clearance for standard wrenches, which of the bolt sizes considered gives a satisfactory bolt spacing?
8. An M14 2 hex-head bolt with a nut is used to clamp together two 15-mm steel plates (a) Determine a suitable length for the bolt, rounded up to the nearest 5 mm. (b) Determine the bolt stiffness. (c) Determine the stiffness of the members. 9. Repeat problem 8, with one of the plates having a threaded hole to eliminate the nut. 10. A 30-mm thick AISI 1020 steel plate is sandwiched between two 10-mm thick 2024-T3 aluminum plates and compressed with a bolt and nut with no washers. The bolt is M10 1.5, property class 5.8. (a) Determine a suitable length for the bolt, rounded up to the nearest 5 mm. (b) Determine the bolt stiffness. (c) Determine the stiffness of the members. 11. Repeat problem 10 with the bottom aluminum plate replaced by one that is 20 mm thick. 12. Repeat problem 10 with the bottom aluminum plate having a threaded hole to eliminate the nut.