Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9781259639272
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 7.4, Problem 7.121P
To determine

Find the distances dB and dD.

Expert Solution & Answer
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Answer to Problem 7.121P

The value of distance is dB=1.733m_.

The value of distance is dD=4.20m_.

Explanation of Solution

Given information:

The value of distance is dC=3m.

Assumption:

Apply the sign convention for calculating the equations of equilibrium as below.

  • For the horizontal forces equilibrium condition, take the force acting towards right side as positive (+) and the force acting towards left side as negative ().
  • For the vertical forces equilibrium condition, take the upward force as positive (+) and downward force as negative ().
  • For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive.

Apply the following sign convention for calculating the bending moment at any section x-x while approaching from the left hand side.

  • Take clockwise moment as positive and anticlockwise moment as negative

Apply the following sign convention for calculating the shear force at any section x-x while approaching from the left hand side.

Take downward force as negative and upward force as positive.

Calculation:

Show the free-body diagram of the converted beam as in Figure 1.

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics, Chapter 7.4, Problem 7.121P , additional homework tip  1

Find the vertical reaction at point E by taking moment about point A.

MA=0Ey(10)10(7)5(4)5(2)=010Ey702010=0Ey=10kN()

Find the vertical reaction at point A by resolving the vertical component of forces.

Fy=0Ay5510+Ey=0Ay20+10=0Ay=10kN()

Show the calculation of shear force as follows;

Shear force at x=0;

V|x=0(Justleft)=0V|x=0(Justright)=Ay=10kN

Shear force at x=2m;

V|x=2m(Justleft)=10kNV|x=2m(Justright)=105=5kN

Shear force at x=4m;

V|x=4m(Justleft)=5kNV|x=4m(Justright)=55=0

Shear force at x=7m;

V|x=7m(Justleft)=0V|x=7m(Justright)=010=10kN

Shear force at x=10m;

V|x=10m(Justleft)=10kNV|x=10m(Justright)=10+Ey=10+10=0

Tabulate the calculated shear force values as in Table 1.

Distance, x (m)Shear force, V (kN)
0 (Just left)0
0 (Just right)10
2 (Just left)10
2 (Just right)5
4 (Just left)5
4 (Just right)0
7 (Just left)0
7 (Just right)–10
10 (Just left)–10
10 (Just left)0

Plot the shear force diagram as in Figure 2.

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics, Chapter 7.4, Problem 7.121P , additional homework tip  2

Show the calculation of bending moment as follows;

Bending moment at x=0;

M|x=0=0

Bending moment at x=2m;

M|x=2m=10(2)=20kN-m

Bending moment at x=4m;

M|x=4m=10(4)5(2)=30kN-m

Bending moment at x=7m;

M|x=7m=10(7)5(5)5(3)=30kN-m

Bending moment at x=10m;

M|x=10m=10(10)5(8)5(6)10(3)=0

Tabulate the calculated bending moment values as in Table 2.

Distance, x (m)Bending moment, M (kN-m)
00
220
430
730
100

Plot the bending moment diagram as in Figure 3.

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics, Chapter 7.4, Problem 7.121P , additional homework tip  3

Show the geometry of the cable as in Figure 4.

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics, Chapter 7.4, Problem 7.121P , additional homework tip  4

Find the distance hC using the relation.

dC=hC+1.6

Substitute 3 m for dC.

3=hC+1.6hC=1.4m

Use the concept given in Problem (7.119);

Write the relationship between the moment and the height h as;

hBMB=hCMC=hDMD (1)

Refer to the Figure 3;

MB=20kN-mMC=30kN-mMD=30kN-m

Substitute 20kN-m for MB, 1.4 m for hC, 30kN-m for MC, and 30kN-m for MD in Equation (1).

hB20=1.430=hD30hB=0.933mhD=1.4m

Refer to Figure 3;

Find the distance dD using the relation.

dD=2.8+hD

Substitute 1.4 m for hD.

dD=2.8+1.4=4.20m

Find the distance dB using the relation.

dB=0.8+hB

Substitute 0.933 m for hB.

dB=0.8+0.933=1.733m

Therefore, the value of distance dB=1.733m_.

Therefore, the value of distance dD=4.20m_.

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Chapter 7 Solutions

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 7.1 - A semicircular rod is loaded as shown. Determine...Ch. 7.1 - Fig. P7.11 and P7.12 7.12 A semicircular rod is...Ch. 7.1 - The axis of the curved member AB is a parabola...Ch. 7.1 - Knowing that the axis of the curved member AB is a...Ch. 7.1 - Prob. 7.15PCh. 7.1 - 7.16 Knowing that the radius of each pulley is 200...Ch. 7.1 - Prob. 7.17PCh. 7.1 - For the frame of Prob. 7.17, determine the...Ch. 7.1 - Knowing that the radius of each pulley is 200 mm...Ch. 7.1 - Fig. P7.19 and P7.20 7.20 Knowing that the radius...Ch. 7.1 - and 7.22 A force P is applied to a bent rod that...Ch. 7.1 - and 7.22 A force P is applied to a bent rod that...Ch. 7.1 - Prob. 7.23PCh. 7.1 - For the rod of Prob. 7.23, determine the magnitude...Ch. 7.1 - A semicircular rod of weight W and uniform cross...Ch. 7.1 - Prob. 7.26PCh. 7.1 - Prob. 7.27PCh. 7.1 - 7.27 and 7.28 A half section of pipe rests on a...Ch. 7.2 - Prob. 7.29PCh. 7.2 - Prob. 7.30PCh. 7.2 - Prob. 7.31PCh. 7.2 - Prob. 7.32PCh. 7.2 - 7.33 and 7.34 For the beam and loading shown, (a)...Ch. 7.2 - 7.33 and 7.34 For the beam and loading shown, (a)...Ch. 7.2 - 7.35 and 7.36 For the beam and loading shown, (a)...Ch. 7.2 - Prob. 7.36PCh. 7.2 - 7.37 and 7.38 For the beam and loading shown, (a)...Ch. 7.2 - 7.37 and 7.38 For the beam and loading shown, (a)...Ch. 7.2 - For the beam and loading shown, (a) draw the shear...Ch. 7.2 - 7.39 through 7.42 For the beam and loading shown,...Ch. 7.2 - Prob. 7.41PCh. 7.2 - 7.39 through 7.42 For the beam and loading shown,...Ch. 7.2 - Assuming the upward reaction of the ground on beam...Ch. 7.2 - Solve Problem 7.43 knowing that P = 3wa. PROBLEM...Ch. 7.2 - Assuming the upward reaction of the ground on beam...Ch. 7.2 - Prob. 7.46PCh. 7.2 - Prob. 7.47PCh. 7.2 - Prob. 7.48PCh. 7.2 - Prob. 7.49PCh. 7.2 - Prob. 7.50PCh. 7.2 - Prob. 7.51PCh. 7.2 - 7.51 and 7.52 Draw the shear and bending-moment...Ch. 7.2 - Two small channel sections DF and EH have been...Ch. 7.2 - Solve Prob. 7.53 when = 60. PROBLEM 7.53 Two...Ch. 7.2 - For the structural member of Prob. 7.53, determine...Ch. 7.2 - For the beam of Prob. 7.43, determine (a) the...Ch. 7.2 - Determine (a) the distance a for which the maximum...Ch. 7.2 - For the beam and loading shown, determine (a) the...Ch. 7.2 - A uniform beam is to be picked up by crane cables...Ch. 7.2 - Knowing that P = Q = 150 lb, determine (a) the...Ch. 7.2 - Prob. 7.61PCh. 7.2 - Prob. 7.62PCh. 7.3 - 7.63 Using the method of Sec, 73. solve Prob....Ch. 7.3 - Prob. 7.64PCh. 7.3 - Prob. 7.65PCh. 7.3 - Prob. 7.66PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.33....Ch. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.34....Ch. 7.3 - Prob. 7.69PCh. 7.3 - 7.69 and 7.70 For the beam and loading shown, (a)...Ch. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.39....Ch. 7.3 - Prob. 7.72PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.41....Ch. 7.3 - Prob. 7.74PCh. 7.3 - Prob. 7.75PCh. 7.3 - Prob. 7.76PCh. 7.3 - 7.77 and 7.78 For the beam and loading shown. (a)...Ch. 7.3 - 7.77 and 7.78 For the beam and loading shown, (a)...Ch. 7.3 - 7.79 and 7.80 For the beam and loading shown, (a)...Ch. 7.3 - For the beam and loading shown, (a) draw the shear...Ch. 7.3 - 7.81 and 7.82 For the beam and loading shown, (a)...Ch. 7.3 - For the beam and loading shown, (a) draw the shear...Ch. 7.3 - (a) Draw the shear and bending-moment diagrams for...Ch. 7.3 - Solve Prob. 7.83 assuming that the 300-lb force...Ch. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - Prob. 7.86PCh. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - Prob. 7.88PCh. 7.3 - Prob. 7.89PCh. 7.3 - Prob. 7.90PCh. 7.3 - Prob. 7.91PCh. 7.3 - Prob. 7.92PCh. 7.4 - Three loads are suspended as shown from the cable...Ch. 7.4 - Knowing that the maximum tension in cable ABCDE is...Ch. 7.4 - Prob. 7.95PCh. 7.4 - Prob. 7.96PCh. 7.4 - 7.97 Knowing that dC = 3 m, determine (a) the...Ch. 7.4 - Prob. 7.98PCh. 7.4 - Prob. 7.99PCh. 7.4 - Prob. 7.100PCh. 7.4 - Knowing that mB = 70 kg and mC = 25 kg, determine...Ch. 7.4 - Prob. 7.102PCh. 7.4 - Prob. 7.103PCh. 7.4 - Prob. 7.104PCh. 7.4 - Prob. 7.105PCh. 7.4 - If a = 4 m, determine the magnitudes of P and Q...Ch. 7.4 - An electric wire having a mass per unit length of...Ch. 7.4 - Prob. 7.108PCh. 7.4 - Prob. 7.109PCh. 7.4 - Prob. 7.110PCh. 7.4 - Prob. 7.111PCh. 7.4 - Two cables of the same gauge are attached to a...Ch. 7.4 - Prob. 7.113PCh. 7.4 - Prob. 7.114PCh. 7.4 - Prob. 7.115PCh. 7.4 - Prob. 7.116PCh. 7.4 - Prob. 7.117PCh. 7.4 - Prob. 7.118PCh. 7.4 - Prob. 7.119PCh. 7.4 - Prob. 7.120PCh. 7.4 - Prob. 7.121PCh. 7.4 - Prob. 7.122PCh. 7.4 - Prob. 7.123PCh. 7.4 - Prob. 7.124PCh. 7.4 - Prob. 7.125PCh. 7.4 - Prob. 7.126PCh. 7.5 - A 25-ft chain with a weight of 30 lb is suspended...Ch. 7.5 - A 500-ft-long aerial tramway cable having a weight...Ch. 7.5 - Prob. 7.129PCh. 7.5 - Prob. 7.130PCh. 7.5 - Prob. 7.131PCh. 7.5 - Prob. 7.132PCh. 7.5 - Prob. 7.133PCh. 7.5 - Prob. 7.134PCh. 7.5 - Prob. 7.135PCh. 7.5 - Prob. 7.136PCh. 7.5 - Prob. 7.137PCh. 7.5 - Prob. 7.138PCh. 7.5 - Prob. 7.139PCh. 7.5 - Prob. 7.140PCh. 7.5 - Prob. 7.141PCh. 7.5 - Prob. 7.142PCh. 7.5 - Prob. 7.143PCh. 7.5 - Prob. 7.144PCh. 7.5 - Prob. 7.145PCh. 7.5 - Prob. 7.146PCh. 7.5 - Prob. 7.147PCh. 7.5 - Prob. 7.148PCh. 7.5 - Prob. 7.149PCh. 7.5 - Prob. 7.150PCh. 7.5 - A cable has a mass per unit length of 3 kg/m and...Ch. 7.5 - Prob. 7.152PCh. 7.5 - Prob. 7.153PCh. 7 - Knowing that the turnbuckle has been tightened...Ch. 7 - Knowing that the turnbuckle has been tightened...Ch. 7 - Two members, each consisting of a straight and a...Ch. 7 - Knowing that the radius of each pulley is 150 mm,...Ch. 7 - Prob. 7.158RPCh. 7 - For the beam and loading shown, (a) draw the shear...Ch. 7 - For the beam and loading shown, (a) draw the shear...Ch. 7 - Prob. 7.161RPCh. 7 - Prob. 7.162RPCh. 7 - Prob. 7.163RPCh. 7 - Prob. 7.164RPCh. 7 - A 10-ft rope is attached to two supports A and B...
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