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58_Mechanics Homework Mechanics of Materials Solution

58_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: PROBLEM LC“ 1.C4 A 4-kip force P forming an angle a with the vertical is applied as shown to member ABC, which is supported by a pin and bracket at C and by ' a cable BD forming an angle ,8 with the horizontal. (:1) Knowing that the ulti- mate load of the cable is 25 kips, write a computer program to construct a table of the values of the factor of safety of the cable for values of a and B from 0 to 45°, using increments in a and [3 corresponding to 0.1 increments in tan a and tan [3. (b) Check that for any given value of a the maximum value of the factor of safety is obtained for )3 = 38.66” and explain why. (0) Deter- mine the smallest possible value of the factor of safety for B = 38.66", as well as the corresponding value of a, and explain the result obtained. SOLUTION (6‘) WM F 13. DIAGRAM 0F AB .- M P F +52 MC: 0: (Psian/SV’nfli19503008019 A j 3 “(Fcoefi)(/9'ir).)~(F5in/3)[)an,):0 "n” _ J c). F: p $5ch + 30 coax Late—{Did C If C05/3 ‘f' {2 Sin/5 IZM. F. 5. = film/F Wain? VALUES OF FS BETA - 0 5.71 11.31 16.70 21.80 26.56 30.96 34.99 2-0 £13: 3. 3. 3.555 3.712 3.830 3.913 3. 3.994 2. 3. 3.402 3.552 3.666 .745 3. 3. 2. 3. 3.295 3.441 3.551 628 3. 3. 2. 3. 3.227 3.370 3.477 3. 3. . . . 2. 3. 3.190 3.331 3.438 3. 3. t.592 .586 .570 2- 3. 3. 3. 3. 3. 3. 2. 3. 3. 3. 3. 3. 3. I 590 3 5:4 . .: 2. 3. 3. 3. 3. 3. 3.511 :.619 3.612 3.596 2. 3. 3. 3. 3. 3. 3.653 :.661 3.655 3.638 2. 3. 3. 3. 3. 3. 3.706 l.713 3.707 3.690 2. 3. 3 3.499 3.611 689 3.739 3.765 =.773 3.767 3.750 m» (15) Whenp = 38. 65} fan/3 -_.~ 0.8 and Cable 313 is .Pe'F/Dendfcular I“ "Hie leverarm BC, (C) 1753:3579 for oz:26.6°_; P .r's Perpendicular To. 7Lh'é. lever arm AC NOTE: We Vat/Ur: ES. =3.577 1'5 7‘146 Smél/fjf sf That/4.11263 of F5. corresponding To flr38.56° am/ flae lay—(9953f 0f +h05€ Corresponding to (X: 2.6.5“, The Point (#255; [3:33.5fi is a "Saddle point", 0r Winn-nay" of Me. funcTiOr’I ESOYJU: ...
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