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9/14/2018

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Chapter 4 Problems Article 4/3 Problems Introductory Problems 4/1 Determine the force in each member of the loaded truss. Explain why knowledge of the lengths of the members is unnecessary.

PROBLEM 4/1

AB = 2000 lb C, AC = 1732 lb T, BC = 3460 lb C 4/2 Determine the force in each member of the loaded truss.

PROBLEM 4/2

AB = 3400 N T, AC = 981 N T, BC = 1962 N C 4/3 Determine the force in each member of the loaded truss.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs119… 1/63

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PROBLEM 4/3

AB = 3000 N T, AC = 4240 N C, AD = 3000 N C BC = 6000 N T, CD = 4240 N T 4/4 Calculate the forces in members BE and BD of the loaded truss.

PROBLEM 4/4

BE = 0, BD = 5.66 kN C 4/5 Determine the force in each member of the loaded truss.

PROBLEM 4/5

AB = 2950 N C, AD = 4170 N T https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs119… 2/63

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BC = 7070 N C, BD = 3950 N C CD = 5000 N T 4/6 Determine the forces in members BE and CE of the loaded truss.

PROBLEM 4/6

BE = 2.10 kN T, CE = 2.74 kN C 4/7 Determine the force in each member of the loaded truss.

PROBLEM 4/7

AB = 5660 lb T, AE = DE = 4800 lb C BC = 16,510 lb T, BD = 12,440 lb C BE = 4500 lb T, CD = 4790 lb T 4/8 Determine the force in each member of the loaded truss.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs119… 3/63

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PROBLEM 4/8

AB = 14.42 kN T, AC = 2.07 kN C BC = 6.45 kN T, BD = 12.89 kN C 4/9 Determine the force in each member of the loaded truss. Make use of the symmetry of the truss and of the loading.

PROBLEM 4/9

AB = DE = 96.0 kN C, AH = EF = 75 kN T BC = CD = 75 kN C, BH = CG = DF = 60 kN T CF = CH = 48.0 kN C, FG = GH = 112.5 kN T 4/10 If the maximum tensile force in any of the truss members must be limited to 24 kN, and the maximum compressive force must be limited to 35 kN, determine the largest permissible mass m which may be supported by the truss.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs119… 4/63

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PROBLEM 4/10

m = 1030 kg 4/11 Determine the forces in members AB, BC, and BD of the loaded truss.

PROBLEM 4/11

Representative Problems 4/12 A drawbridge is being raised by a cable EI. The four joint loadings shown result from the weight of the roadway. Determine the forces in members EF, DE, DF, CD, and FG.

PROBLEM 4/12

EF = 3.87 kips C, DE = 4.61 kips T DF = 4.37 kips C, CD = 2.73 kips T FG = 7.28 kips C 4/13 Determine the forces in members BJ, BI, CI, CH, DG, DH, and EG of the loaded truss. All triangles are 45°-45°-90°. https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs119… 5/63

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PROBLEM 4/13

BI = CH = 3.96 kips T, BJ = 0 CI = 2.8 kips C, DG = 5.94 kips C DH = EG = 4.2 kips T 4/14 Determine the forces in members BC and BG of the loaded truss.

PROBLEM 4/14

BC = 3.46 kN C, BG = 1.528 kN T 4/15 Each member of the truss is a uniform 20-ft bar weighing 400 lb. Calculate the average tension or compression in each member due to the weights of the members.

PROBLEM 4/15 https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs119… 6/63

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4/16 The rectangular frame is composed of four perimeter two-force members and two cables AC and BD which are incapable of supporting compression. Determine the forces in all members due to the load L in position (a) and then in position (b).

PROBLEM 4/16

(a) AB = 0, BC = LT, AD = 0 (b)

4/17 Determine the forces in members BI, CI, and HI for the loaded truss. All angles are 30°, 60°, or 90°.

PROBLEM 4/17

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BI = 2.50 kN T, CI = 2.12 kN T HI = 2.69 kN T 4/18 The signboard truss is designed to support a horizontal wind load of 800 lb. A separate analysis shows that of this force is transmitted to the center connection at C and the rest is equally divided between D and B. Calculate the forces in members BE and BC.

PROBLEM 4/18

BC = 300 lb T, BE = 559 lb T 4/19 Determine the forces in members AB, CG, and DE of the loaded truss.

PROBLEM 4/19

4/20 A snow load transfers the forces shown to the upper joints of a Pratt roof truss. Neglect any horizontal reactions at the supports and solve for the forces in all members.

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PROBLEM 4/20

AB = BC = CD = DE = 3.35 kN C AH = EF = 3 kN T, BH = DF = 1 kN C CF = CH = 1.414 kN T, CG = 0 FG = GH = 2 kN T 4/21 The loading of Prob. 4/20 is shown applied to a Howe roof truss. Neglect any horizontal reactions at the supports and solve for the forces in all members. Compare with the results of Prob. 4/20.

PROBLEM 4/21

AB = DE = 3.35 kN C AH = EF = FG = GH = 3 kN T BC = CD = 2.24 kN C, BG = DG = 1.118 kN C BH = DF = 0, CG = 1 kN T 4/22 Determine the force in each member of the loaded truss.

PROBLEM 4/22

AB = 1.782L T, AG = FG = 2.33L C BC = CD = 2.29L T, BF = 1.255L C BG = 0.347L C, CF = DE = 0 https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs119… 9/63

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DF = 2.59L T, EF = 4.94L C 4/23 Determine the forces in members EH and EI of the double Fink truss. Neglect any horizontal reactions at the supports and note that joints E and F divide into thirds.

PROBLEM 4/23

EH = 1.238L T, EI = 1.426L C 4/24 The 240-ft structure is used to provide various support services to launch vehicles prior to liftoff. In a test, a 10-ton weight is suspended from joints F and G, with its weight equally divided between the two joints. Determine the forces in members GJ and GI. What would be your path of joint analysis for members in the vertical tower, such as AB or KL?

PROBLEM 4/24

GI = 15.38 tons T, GJ = 4.44 tons C 4/25 The rectangular frame is composed of four perimeter two-force members and two cables AC and BD which are incapable of supporting compression. Determine the forces in all members due to the load L in position (a) and https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 10/63

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then in position (b).

PROBLEM 4/25

(a)

(b)

4/26 Determine the force in member CG of the loaded truss. Assume that the four external reactions at A, B, E, and F are equal in magnitude and are directed perpendicular to the local supporting surface.

PROBLEM 4/26

CG = 0

Article 4/4 Problems Introductory Problems 4/27 https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 11/63

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Determine the force in member CG.

PROBLEM 4/27

CG = 14.14 kips T 4/28 Determine the force in member AE of the loaded truss.

PROBLEM 4/28

AE = 5.67 kN T 4/29 Determine the forces in members BC and CG.

PROBLEM 4/29

BC = 15 kips T, CG = 21.2 kips T https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 12/63

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4/30 Determine the forces in members CG and GH of the symmetrically loaded truss.

PROBLEM 4/30

CG = 0, GH = L T 4/31 Determine the force in member BE of the loaded truss.

PROBLEM 4/31

BE = 5.59 kN T 4/32 Determine the force in member BE of the loaded truss.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 13/63

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PROBLEM 4/32

BE = 0.809L T

Representative Problems 4/33 Determine the forces in members DE and DL.

PROBLEM 4/33

DE = 24 kN T, DL = 33.9 kN C 4/34 Calculate the forces in members BC, BE, and EF. Solve for each force from an equilibrium equation which contains that force as the only unknown.

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PROBLEM 4/34

BC = 21 kN T, BE = 8.41 kN T EF = 29.5 kN C 4/35 The truss is composed of equilateral triangles of side a and is supported and loaded as shown. Determine the forces in members BC and CG.

PROBLEM 4/35

4/36 Determine the forces in members BC and FG of the loaded symmetrical truss. Show that this calculation can be accomplished by using one section and two equations, each of which contains only one of the two unknowns. Are the results affected by the statical indeterminacy of the supports at the base?

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 15/63

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PROBLEM 4/36

BC = 600 N T, FG = 600 N C 4/37 Determine the force in member BF.

PROBLEM 4/37

BF = 2.66 kips C 4/38 The members CJ and CF of the loaded truss cross but are not connected to members BI and DG. Compute the forces in members BC, CJ, CI, and HI.

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PROBLEM 4/38

BC = 3.00 kN C, CI = 5.00 kN T CJ = 16.22 kN C, HI = 10.50 kN T 4/39 Determine the forces in members CD, CJ, and DJ.

PROBLEM 4/39

CD = 0.562L C, CJ = 1.562L T, DJ = 1.250L C 4/40 The hinged frames ACE and DFB are connected by two hinged bars, AB and CD, which cross without being connected. Compute the force in AB.

PROBLEM 4/40

AB = 3.78 kN C https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 17/63

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4/41 The truss shown is composed of 45° right triangles. The crossed members in the center two panels are slender tie rods incapable of supporting compression. Retain the two rods which are under tension and compute the magnitudes of their tensions. Also find the force in member MN.

PROBLEM 4/41

FN = GM = 84.8 kN T, MN = 20 kN T 4/42 Determine the force in member BE of the loaded truss.

PROBLEM 4/42

BE = 0.787L T 4/43 Determine the force in member BF of the loaded truss, repeated here from Prob. 4/22.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 18/63

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PROBLEM 4/43

BF = 1.255L C 4/44 Calculate the forces in members CB, CG, and FG for the loaded truss without first calculating the force in any other member.

PROBLEM 4/44

CB = 56.2 kN C, CG = 13.87 kN T FG = 19.62 kN T 4/45 Determine the force in member GK of the loaded symmetrical truss.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 19/63

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PROBLEM 4/45

GK = 2.13L T 4/46 Determine the forces in members DE, EI, FI, and HI of the arched roof truss.

PROBLEM 4/46

DE = 297 kN C, EI = 26.4 kN T FI = 205 kN T, HI = 75.9 kN T 4/47 Determine the force in member CG of the loaded truss, repeated here from Prob. 4/26. The four external reactions at A, B, E, and F are equal in magnitude and are directed perpendicular to the local supporting surfaces.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 20/63

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PROBLEM 4/47

CG = 0 4/48 Determine the force in member DK of the loaded overhead sign truss.

PROBLEM 4/48

DK = 1 kip T 4/49 A design model for a transmission-line tower is shown in the figure. Members GH, FG, OP, and NO are insulated cables; all other members are steel bars. For the loading shown, compute the forces in members FI, FJ, EJ, EK, and ER. Use a combination of methods if desired.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 21/63

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PROBLEM 4/49

EJ = 3.61 kN C, EK = 22.4 kN C ER = FI = 0, FJ = 7.81 kN T 4/50 Determine the force in member DG of the compound truss. The joints all lie on radial lines subtending angles of 15° as indicated, and the curved members act as two-force members. Distance .

PROBLEM 4/50

DG = 0.569L C

Article 4/5 Problems 4/51 The base of an automobile jackstand forms an equilateral triangle of side length 10 in. and is centered under the collar A. Model the structure as one with a ball and socket at each joint and determine the forces in members BC, BD, and CD. Neglect any horizontal reaction components under the feet B, C, and D. https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 22/63

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PROBLEM 4/51

BC = BD = CD = 55.6 lb T 4/52 Determine the forces in members AB, AC, and AD.

PROBLEM 4/52

AB = 4.46 kN C, AC = 1.521 kN C AD = 1.194 kN T https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 23/63

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4/53 Determine the force in member CF.

PROBLEM 4/53

CF = 1.936L T 4/54 The depicted structure is under consideration as the upper portion of a transmission-line tower and is supported at points F, G, H, and I. Point C is directly above the center of rectangle FGHI. Determine the force in member CD.

PROBLEM 4/54

CD = 2.4L T 4/55 The rectangular space truss 16 m in height is erected on a horizontal square base 12 m on a side. Guy wires are attached to the structure at E and G as shown and are tightened until the tension T in each wire is 9 kN. Calculate the force F in each of the diagonal members. https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 24/63

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PROBLEM 4/55

F = 3.72 kN C 4/56 For the space truss shown, check the sufficiency of the supports and also the number and arrangement of the members to ensure statical determinacy, both external and internal. By inspection determine the forces in members CD, CB, and CF. Calculate the force in member AF and the x-component of the reaction on the truss at D.

PROBLEM 4/56

4/57 For the space truss shown, check the sufficiency of the supports and also the number of and arrangement of the members to ensure statical determinacy, both external and internal. Determine the forces in members AE, BE, BF, and CE.

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PROBLEM 4/57

AE = BF = 0, BE = 1.202L C, CE = 1.244L T 4/58 Determine the force in member BD of the regular pyramid with square base.

PROBLEM 4/58

BD = 2.00L C 4/59 Determine the forces in members AD and DG.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 26/63

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PROBLEM 4/59

AD = 0.625L C, DG = 2.5L C 4/60 The pyramidal truss section BCDEF is symmetric about the vertical x-z plane as shown. Cables AE, AF, and AB support a 5-kN load. Determine the force in member BE.

PROBLEM 4/60

BE = 2.36 kN C 4/61 The space truss shown is secured to the fixed supports at A, B, and E and is loaded by the force L which has equal x- and y-components but no vertical z-component. Show that there is a sufficient number of members to provide internal stability and that their placement is adequate for this purpose. Next determine the forces in members CD, BC, and CE. https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 27/63

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PROBLEM 4/61

4/62 A space truss is constructed in the form of a cube with six diagonal members shown. Verify that the truss is internally stable. If the truss is subjected to the compressive forces P applied at F and D along the diagonal FD, determine the forces in members EF and EG.

PROBLEM 4/62

Article 4/6 Problems (Unless otherwise instructed, neglect the mass of the various members and all friction in the problems which follow.)

Introductory Problems 4/63 https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 28/63

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Determine the magnitudes of all pin reactions for the frame loaded as shown.

PROBLEM 4/63

B = D = 1013 N, A = 512 N 4/64 Determine the force which member CD exerts on the pin at C.

PROBLEM 4/64

CD = 57.7 N at ∡ 60° 4/65 For what value M of the clockwise couple will the horizontal component A x of the pin reaction at A be zero? If a couple of that same magnitude M were applied in a counterclockwise direction, what would be the value of A x?

PROBLEM 4/65 https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV80XzAueGZvcm0.enc?course=crs11… 29/63

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M = 150 lb-ft, A x = 86.6 lb 4/66 Determine the components of all forces acting on each member of the loaded frame.

PROBLEM 4/66

Member AC: C = 0.293P left Ax = 0.293P right, Ay = P up Member BC: Symmetric to AC 4/67 Determine the magnitude of the pin force at A.

PROBLEM 4/67

A = 1555 lb 4/68 Determine the magnitudes of the pin reactions at A, B, and C caused by the weight of the uniform 6000-lb beam.

https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyM...