1. The lid on a pressure vessel is held down with 10 bolts that pass through the lid and a flange on the pressure vessel (similar to example 8-4, in the text). The bolts are secured with nuts under the flange. There are no washers. The thickness of the lid is 28 mm and the thickness of the flange is 28 mm. The vessel and lid are both made of steel. The vessel is pressurized to 8 MPa, and the area of the lid exposed to the pressure is 31.4e3 mm². The modulus of elasticity is 207 GPa. The chosen bolts are ISO property class 9.8 (see table 8-11) and are coarse-pitch series, M12. (e) Now find the stiffness coefficient of the joint, c. (f) Calculate the recommended preload, Fi, assuming that the lid will be re- moved and reinstalled repeatedly (See equation 8-31). Also, determine the required tightening torque (See equation 8-27). (g) Draw and annotate a deflection-load diagram similar to what we constructed in class for this problem. (h) Calculate the factors of safety against overproofing (ny) and joint separation (no). Which threat is greater? Table 8-11 Metric Mechanical-Property Classes for Steel Bolts, Screws, and Studs Size Property Range, Class Inclusive Minimum Proof Strength, MPa Minimum Minimum Tensile Strength, MPa Yield Strength,* MPa Material Head Marking 4.6 M5-M36 225 400 240 Low or medium carbon 4.6 4.8 M16 M16 310 420 340 Low or medium carbon 4.8 5.8 M5-M24 380 520 420 Low or medium carbon 5.8 8.8 M16-M36 600 830 660 Medium carbon, Q&T 8.8 9.8 M16 M16 650 900 720 Medium carbon, Q&T 9.8 10.9 M5-M36 830 1040 940 Low-carbon martensite, Q&T 10.9 12.9 M1.6-M36 970 1220 1100 Alloy. Q&T *Minimum strengths are strengths exceeded by 99 percent of fasteners. 12.9 Table A-17 Preferred Sizes and Renard (R-Series) Numbers (When a choice can be made, use one of these sizes; however, not all parts or items are available in all the sizes shown in the table.) Fraction of Inches 11, 1, 1, 14, 1, 2, 2, 24, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20 Decimal Inches 0.010, 0.012, 0.016, 0.020, 0.025, 0.032, 0.040, 0.05, 0.06, 0.08, 0.10, 0.12, 0.16, 0.20, 0.24, 0.30, 0.40, 0.50, 0.60, 0.80, 1.00, 1.20, 1.40, 1.60, 1.80, 2.0, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.6, 5.8, 6.0, 7.0, 7.5, 8.5, 9.0, 9.5, 10.0, 10.5, 11.0, 11.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, 15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, 19.0, 19.5, 20 Millimeters 0.05, 0.06, 0.08, 0.10, 0.12, 0.16, 0.20, 0.25, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.0, 1.1, 1.2, 1.4, 1.5, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0, 9.0, 10, 11, 12, 14, 16, 18, 20, 22, 25, 28, 30, 32, 35, 40, 45, 50, 60, 80, 100, 120, 140, 160, 180, 200, 250, 300 1st choice, R5: 1, 1.6, 2.5, 4, 6.3, 10 2d choice, R10: 1.25, 2, 3.15, 5, 8 Renard Numbers 3d choice, R20: 1.12, 1.4, 1.8, 2.24, 2.8, 3.55, 4.5, 5.6, 7.1, 9 4th choice, R40: 1.06, 1.18, 1.32, 1.5, 1.7, 1.9, 2.12, 2.36, 2.65, 3, 3.35, 3.75, 4.25, 4.75, 5.3, 6, 6.7, 7.5, 8.5, 9.5 *May be multiplied or divided by powers of 10. Table A-31 Dimensions of Nominal Width Hexagonal Nuts Size, in 7 L M Regular Hexagonal Height H Thick or Slotted JAM Nominal Size, mm M5 = 00 8 4.7 5.1 2.7 M6 10 5.2 5.7 3.2 M8 13 6.8 75 4.0 M10 16 8.4 9.3 5.0 M12 18 10.8 12.0 6.0 M14 21 12.8 14.1 7.0 M16 24 14.8 16.4 8.0 M20 30 18.0 20.3 10.0 M24 36 21.5 23.9 12.0 M30 M36 45 46 25.6 28.6 15.0 55 31.0 34.7 18.0 Table 8-7 Suggested Procedure for Finding Fastener Stiffness Given fastener diameter d and pitch p in mm or number of threads per inch Washer thickness: from Table A-32 or A-33 Nut thickness [Fig. (a) only]: H from Table A-31 Grip length: For Fig. (a): I-thickness of all material squeezed between face of bolt and face of nut Sh + 12/2 For Fig. (b): 1- h+d/2. <d h≥d Fastener length (round up using Table A-17*): For Fig. (a): For Fig. (b): L>I+H Lah+15d Threaded length L: Inch series: L- 2d + tin, 2d + tin, L≤ 6 in L> 6 in Metric series: 2d + 6 mm, L-2d+12 mm, L>200 mm Ls 125 mm, d≤ 48 mm 125 L200 mm 2d+25 mm, 4-L-L 4-1-4 Length of unthreaded portion in grip: Length of threaded portion in grip: Area of unthreaded portion: Area of threaded portion: Fastener stiffness: A-md²/4 A, from Table 8-1 or 8-2 AA,E ks- A+ Al (D) Table 8-8 Stiffness Parameters of Various Member Materials Source: J. Wileman, M. Choudury, and I. Green, "Computation of Member Stiffness in Bolted Connections," Trans. ASME J. Mech. Design, vol. 113, December 1991, pp. 432-437. km Ed = A exp (Bd/l) T = KFd Material Poisson Elastic Modulus Used Ratio GPa Mpsi Steel 0.291 207 30.0 0.787 15 0.628 73 Aluminum 0.334 71 10.3 0.796 70 0.638 16 Copper 0.326 119 17.3 0.795 68 0.635 53 Gray cast iron 0.211 100 14.5 0.778 71 0.616 16 General expression 0.789 52 0.629 14 (8-23) (8-27) F₁ = (0.75Fp (0.90Fp for nonpermanent connections, reused fasteners for permanent connections (8-31) Show transcribed image text