HW12 - PROBLEM4£2 Eight identical 20 x 30-in rectangular...

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Unformatted text preview: PROBLEM4£2 Eight identical 20 x 30-in. rectangular plates, each weighing 50 lb, are u '7: ”if. _ held in a vertical plane as shown. All connections consist of frictionless :21" 2 f T J pins, rollers, or short links. For each case, answer the questions listed in Problem 4.61, and, wherever possible, compute the reactions. ... , fi?m § ‘Erfl E1 “(‘1‘ 3B1 ii P6.1 The bracket ABC can be supported in the eight different ways shown. All connections consist of smooth pins, rollers, or short links. In each case, determine whether (a) the plate is completely, partially, or improperly constrained, (b) the reactions are statically determinate or indeterminate, (c) the equilibrium of the plate is maintained in the position shown. Also, wherever possible, compute the reactions assuming that the magnitude ofthe force P is 100 N. SOLUTION 1. Three non-concurrent, non—parallel reactions F3013}. c (a) Completely constrained 4 T— D (b) Determinate 4 20th. . . . (C) Equrlibrium 4 A i . From f.b.d. ofplate Y A 50lb D) 2M4 :0; C(30in.)—501b(15in.):0 5 C 2 25.0113 *4 i- 2F, :0: A, :0 +le,.:0: A1—501b+251b:0 A,:251b A:25.01b‘4 2. Three non-current, non-parallel reactions (a) Completely constrained 4 (/7) Detenninate 4 (c) Equilibrium 4 From fibd. of plate 1.32:0: 8:04 +3 2MB 2 0: (so lb)(15 in.) ‘ 13(30 in.) : 0 D: 25.0 lb :4 A ZF). : o: 25.01b—501b+ C : 0 C:25.01b t4 PROBLEM 4.62 CONTINUED 3‘ Four non-concurrent, non-parallel reactions (a) Completely constrained { (h) Indeterminate 1 (c) Equilibrium 4 From f.b.d. ofplate J) ZMD = 0: Ax(201n.)—(501b)(15in.) A. = 37.5 lb a 4 t 2a. : 0; D_\ + 37.51b = 0 DA : 37.5 lb k 4 4. Three concur-rent reactions (a) Improperly constrained 4 (b) Indeterminate 4 (c) No equilibrium ‘ 5. Two parallel reactions (0) Partial constraint 1 (b) Determinate 4 (C) Equilibrium 4 From f.b.d. ofplate 0 EM“ = o: C(30in.)~(501b)(151n.)= 0 C = 25.0 lb ‘ 4 +‘ 2n. :0; D—501b+25 1b :0 D : 25.01b t4 6, Three non—concurrent, non-parallel reactions (a) Completely constrained { (h) Detenninate ‘ (C) Equilibrium { From fib.d. of plate a) 2M” : 0: 3(20 in.) — (50 lb)(15 in.) : 0 B:37.51b4~{ L 2a :0; Dx+37.51b:0 0‘ :37.51b 7» +‘2F‘:0: 0‘750lb:0 Dr‘.:50,01b‘ or D = 62.5 lb )5 53.1°‘ PROBLEM 4.62 CONTINUED 7. Two parallel reactions (a) Improperly constrained 4 (1;) Reactions determined by dynamics 4 (c) No equilibrium 4 8. Four non—concurrent, non—parallel reactions (a) Completely constrained fl ([7) Indeterminate { (C) Equilibrium 4 From f.b.d. ofplale I) ZMD = o: 3(301n.)—(501b)(15m) : 0 B = 25,011) 14 it 2th : 0: D1—501b+25.01b :0 D}, = 25.0 lb M 32550; D‘+C:0 ...
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