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Unformatted text preview: PROBLEM4£2
Eight identical 20 x 30in. 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 nonconcurrent, 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 noncurrent, nonparallel 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 nonconcurrent, nonparallel 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 concurrent 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, nonparallel 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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 Spring '08
 Jenkins
 Statics

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