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PROBLEM 6.77 For the frame and loading shown, determine the force acting on member
ABC ((1) at B, (b) at C. SOLUTION Note that BB is a twoforce member FBD member ABC:
(a) Q ZMC = 0: (16 MGFBDJ w (24 in.)(80 1b) = 0
3315
F3”: 1501b, FED = 150.0113 7 369° 4
(b) 1213 = o: Cy m§(1501b)= 0, CV = 901b x o: Cx—%(1501b)+801b=0, Cx=401b l
E? C = 98.5 lb 466.0" 4 PROBLEM 6.84 Determine the components of the reactions at A and E when a 24lb force
directed vertically downward is applied (a) at B, (b) at D. SOLUTION
(a) FBD AC: Note: CE is a twoforce member
2% Q EMA : 0: (8111.)[5C‘i)+ (2 m.)(§@)_(6 in.)(24 1b) =0
2 5,, J5 J5
A .
‘ x 2“ FCE =14.4J§ 1b, so Ex =14.401b —~ 4
C.
Ev =14.401b I 4
E / '
——»2Fx=0: —Ax+14.41b=0 Ax=14401bw4 12:13,=0: Ay—241b+14.401b=0 Ay = 9.60 1b 1 4
(b) FBD CE: Note AC is a twoforce member
Q 2M5 = 0: (3 m.)[5FAC + LFAC) 4 (1 in.)(24 1b) = 0
. Jﬁ Jﬁ
FAC =1.6ﬂ 1b, Ax = 6.40 lb «m 4
Ay = 1.600 lb 1 4
———~>:P;=0: Ex—7:=7(1.6\/ﬁlb)=0, Ex=6.401b—~4 IZF, = 0: E), + %(1.6\/ﬁ1b) 24 1b = 0 r Ey =22.41b I 4 1,51 1211—» 0 PROBLEM 6.104 «1th
2 ‘ ‘3‘“ g 7 7.211 The axis of the threehinge arch ABC is a parabola with vertex at B. ‘ :: gm Knowing that P = 14 kips and Q = 21 kips, determine (a) the
‘ components of the reaction at A, (b) the components of the force exerted
at B on segment AB. SOLUTION
Members FBDs: E
I:( EMA: 0: (12.8 ft)Bx (32 ft)By (20 ﬁ)(14 kips) = o
11:(' 2114C: 0: (7.2 ﬁ)Bx+ (24 11) By— (12 ft)(21kips)= 0
Solving: Bx = 27.5 kips, By = 2.25 kips,
I: ——~ EEC: O: Ax— 27.5 kips = 0, Ax: 27.5 kips, (a) Ax: 27.5 kips ——> {
’( ZFy= 0: Ay— 14 kips — 2.25 kips = 0, Ay= 16.25 kips, Ay= 16.25 kips I 4
(b) Bx: 27.5 kips «—4 By: 2.25 kips l 4 —~—_—_H—___—_—__w—mw__l mm. —.1 PROBLEM 6.106
P Knowing that P = 411 1b and Q = 0, determine for the frame and loading
shown (a) the reaction at D, (b) the force in member BF. I
SOLUTION _l
FBD Frame: (12 in.) Dx — (28 in.)(4111b)= 0 Dx = 9591b —~ 19.7 H I’ FBD DF: Note that BF and CE are twoforce members. W'EF;=02 Solving: FBF = 357 1b, U ( ME 2 01: (22.5 in.)[~1%(357 113)] — (12 in.) Dy = 0 Dy=3151b(, so (a) D=10091b 418.1804 ...
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 Spring '08
 PETRINA

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