In working this problem, we will assume the thread has a machine finish and will use a stress concentration factor of 3.0 for rolled threads.

Transcription

1 BOLTING - EXAMPLE 1 A section of a tension-oaded connection empoyg a confed gaset is shown by Figure 14-3.a of Norton. This connection has been designed to carry a oad which varies between 0 and 1,000 pounds-per-bot. Determe the factor-of-safety of the connection which has been preoaded to 10,000 pounds. The bot is a 5/8"-11UNC-Grade 4 bot,.5-ches ong with roed threads. In worg this probem, we wi assume the thread has a mache fish and wi use a stress concentration factor of 3.0 for roed threads. surface 0.73 size 0.85 e 1 S ut si 3 S e S. surface. size. ut e S e = si The endurance imit has now been determed usg techniques from the chapter on fatigue and data given the probem statement. The next step is determe the proof strength of the bot, the preoad, bot oad, and camped member oads. Foowg that, the oads wi be checed agast the criteria for tensie (positive) tota bot oad and compressive (negative) camped member oads. Fay, the fatigue ife wi be checed usg the factor of safety equation given your notes. From the Tabe 14-6 (page 914 of Norton) we can fd the properties for a cass 4 bot: 65si = proof strength 100 si = yied strength 115 si = utimate strength 0.60 = stress area

2 As a first chec, verify the preoad stress oad is ess than the proof stress square ches pounds σ i σ i = psi This stress is ess that the proof stress (65-si). We can, therefore, contue with our cacuations. The next step is to evauate the stiffness of the components, the camped members and the bot. For these cacuations, note the materia of the camped members is #5 cast iron. We wi need to fd the stiffness (Young's Moduus) for that materia. The camped ength of the jot is 1.5 ches, and the bot diameter 5/8-ch. Because the moduus of easticity for stee is different than that for cast iron, we can not mae the assumption the member stiffness is eight times that of the bot. #5 CI E = 1,000,000 psi, member Stee E = 30,000,000 psi, bot Length = 1.5 ches Diameter d = 0.65 ch E b psi E m psi d 0.65 ch 1.50 ch b π. d E. b 4. b = m. π. d E. m m =

3 Next, the mimum (preoad), mean, maximum, and aternatg stresses are cacuated. This is done to chec the factor of safety fatigue as we as compare the maximum stress to the proof stress and utimate stress of the bot. As mentioned cass, for now we do not determe and chec the camped member stresses. We need to now more about surface fatigue and compressive stresses fatigue to do this, which is beyond the scope of our current course. P m 0 pounds P max 1000 pounds P mean P m P max P at P max P m σ m σ mean. m b m.. mean b m σ m = psi σ mean = psi σ max. max b m σ max = psi σ at. at σ b m A at = psi t F bmax P. b max F b bmax = pounds m σ bmax F bmax σ bmax = psi

4 At this pot, we see the maximum bot stress is ess than the aowabe proof stress; and, we can contue on with our cacuations. For this case we need to chec the mimum externa oad agast the criteria for fange separation. The maximum bot oad is use for strength cacuations. F b,m > 0 F m,max < 0 C F bm b C = 0.38 b m P. m C F bm = pounds F mmax P. max ( 1 C) F mmax = pounds From these cacuations, the criteria has been satisfied. There is a positive oad the bot and a negative (compressive) oad the camped members. The next step is to evauate the factor of safety fatigue usg equation number on page 94 of Norton. S ut σ N f S. m e N S. e σ mean σ m S. f = 0.87 ut σ at

5 This factor of safety, which dicates negative marg of safety fatigue, is unsatisfactory. We have severa options to improve the design so we have a positive marg of safety. Among these are: (1) Use a stronger bot. () Use a arger bot. (3) Use more bots to decrease the externa oad/bot. (4) Change the camped member materia to a stronger materia such as stee. For this exampe, we wi seect option (4), use stee members with a moduus of 30E+06 moduus. This wi affect the portion of the externa oad carried by the members and bot. We need modify ony the equations vovg the member stiffness determation; a others wi rema the same. E b psi E m psi d 0.65 ch 1.50 ch m. π. d E. m m = b π. d E. b 4. b = P m 0 pounds P max 1000 pounds P m P max P mean σ. m m b m. P max P m P at σ m = psi

6 σ mean. mean b m σ mean = psi σ max. max b m σ max = psi σ at. at σ b m A at = psi t F bmax P. b max b m F bmax = pounds σ bmax F bmax σ bmax = psi C b C = b m F mmax P. max ( 1 C) F mmax = pounds F bm P. m C F pounds bm = This cacuation dicates we have a positive oad for the campg force, meang the jot separates. The factor of safety wi aso be checed, just to determe the effect of the materia change. S ut σ N f S. m e N S. e σ mean σ m S. f = ut σ at

7 This vaue is acceptabe. The design, is, however, unacceptabe because the jot separates. Further further cacuations, such as creasg the size of the bots, or creasg the number of bots are required. The ony remag step is to run a hand cacuation to verify the computer resuts. Remember, computer-aide-anaysis, we need to verify our program to avoid "GIGO". Which can be a very embarrassg event to cur, especiay durg a design review.