EBK VECTOR MECHANICS FOR ENGINEERS: STA
EBK VECTOR MECHANICS FOR ENGINEERS: STA
11th Edition
ISBN: 8220102809888
Author: BEER
Publisher: YUZU
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Question
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Chapter 6.3, Problem 6.94P

(a)

To determine

Find the components of the reaction at E.

(a)

Expert Solution
Check Mark

Answer to Problem 6.94P

The reactions at E are Ex=3kips()_ and Ey=1.5kips()_.

Explanation of Solution

Given information:

Consider the diameter of the pipe is d=3ft. Then,

The radius of the pipe is r=1.5ft.

The length of the pipe between the support is l=16ft.

The weight of the pipe is w=500lb/ft.

Consider the surfaces are frictionless.

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.

Calculation:

Show the free body diagram of pipe as shown in Figure 1.

EBK VECTOR MECHANICS FOR ENGINEERS: STA, Chapter 6.3, Problem 6.94P , additional homework tip  1

Refer Figure 1.

Calculate the total weight of the pipe as follows:

Wy=w×l=500lb/ft×16ft=8000lb×1kips103lb=8kips

Refer the force triangle.

Consider the reaction from the contact surfaces are denoted by B and D.

By3=Dy5=Wz4By3=Dy5=8kips4

Calculate the reaction B from the contact surface as follows:

By3=8kips4By=8kips×34By=6kips

Calculate the reaction D from the contact surface as follows:

Dz5=Wy4Dy=8kips×54Dy=10kips

Show the pipe as shown in Figure 2.

EBK VECTOR MECHANICS FOR ENGINEERS: STA, Chapter 6.3, Problem 6.94P , additional homework tip  2

Refer Figure 2.

Show the relation between the OB, OC, and CD as follows:

Horizontal projection of BO+OD=Horizontal projection of CD(r+35r)=45(CD)85r=45(CD)CD=2r

Substitute 1.5ft for r.

CD=2×1.5ft=3ft

The distance CD and CB are Equal. Then,

CD=CB=3ft

Show the free body diagram of member ABC as shown in Figure 3.

EBK VECTOR MECHANICS FOR ENGINEERS: STA, Chapter 6.3, Problem 6.94P , additional homework tip  3

Refer Figure 3.

Consider the horizontal and vertical reaction at A is denoted by Ax and Ay.

Consider the height of the member AC is denoted by h.

Consider the sum of the moment at A is zero. Then,

MA=0Cxh(6kips)(h3)=0Cx=h3h×(6kips) (1)

Substitute 6in. for h in Equation (1).

Cx=636×(6kips)=3kips (2)

Show the free body diagram for the member CDE as shown in Figure 4.

EBK VECTOR MECHANICS FOR ENGINEERS: STA, Chapter 6.3, Problem 6.94P , additional homework tip  4

Refer Figure 4.

Consider the horizontal and vertical reaction at E are denoted by Ex and Ey.

Consider the sum of the moment about the point E is zero. Then,

ME=0(10kips×7ft)(3kips×6ft)(Cy×8ft)=0Cy×8ft=52kipsftCy=52kipsft8ftCy=6.5ft() (3)

The sum of the forces in the horizontal direction is zero. Then,

Fx=03kips+35×10kips+Ex=0Ex=3kips6kipsEx=3kips

Ex=3kips()

The sum of the forces in the vertical direction is zero. Then,

Fy=0Cy45×10kips+Ey=06.5kips8kips+Ey=0Ey=1.5kips()

Thus, the reactions at E are Ex=3kips()_ and Ey=1.5kips()_.

(b)

To determine

Find the force exerted at C on the member CDE.

(b)

Expert Solution
Check Mark

Answer to Problem 6.94P

The force exerted at C on the member CDE are Cx=3kips()_ and Cy=6.5ft()_.

Explanation of Solution

Given information:

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.

Calculation:

Refer Part (a).

Refer Equation (2) and (3).

The force exerted at C on the member CDE are Cx=3kips() and Cy=6.5ft().

Thus, the force exerted at C on the member CDE are Cx=3kips()_ and Cy=6.5ft()_.

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Chapter 6 Solutions

EBK VECTOR MECHANICS FOR ENGINEERS: STA

Ch. 6.1 - Determine the force in each member of the Gambrel...Ch. 6.1 - Determine the force in each member of the Howe...Ch. 6.1 - Using the method of joints, determine the force in...Ch. 6.1 - 6.14 Determine the force in each member of the...Ch. 6.1 - Determine the force in each member of the Warren...Ch. 6.1 - Solve Problem 6.15 assuming that the load applied...Ch. 6.1 - Determine the force in each member of the Pratt...Ch. 6.1 - The truss shown is one of several supporting an...Ch. 6.1 - Determine the force in each member of the Pratt...Ch. 6.1 - Solve Problem 6.19 assuming that the load applied...Ch. 6.1 - Determine the force in each of the members located...Ch. 6.1 - Determine the force in member DE and in each of...Ch. 6.1 - Determine the force in each of the members located...Ch. 6.1 - The portion of truss shown represents the upper...Ch. 6.1 - For the tower and loading of Prob. 6.24 and...Ch. 6.1 - Solve Problem 6.24 assuming that the cables...Ch. 6.1 - Determine the force in each member of the truss...Ch. 6.1 - Determine the force in each member of the truss...Ch. 6.1 - Prob. 6.29PCh. 6.1 - 6.30 Determine whether the trusses of Probs....Ch. 6.1 - 6.31 For the given loading. determine the...Ch. 6.1 - For the given loading, determine the zero-force...Ch. 6.1 - For the given loading, determine the zero-force...Ch. 6.1 - Determine the zero-force members in the truss of...Ch. 6.1 - The truss shown consists of six members and is...Ch. 6.1 - The truss shown consists of six members and is...Ch. 6.1 - The truss shown consists of six members and is...Ch. 6.1 - Prob. 6.38PCh. 6.1 - The truss shown consists of nine members and is...Ch. 6.1 - Solve Prob. 6.39 for P = 0 and Q = (900 N)k. 6.39...Ch. 6.1 - The truss shown consists of 18 members and is...Ch. 6.1 - The truss shown consists of 18 members and is...Ch. 6.2 - 6 .43 A Mansard roof truss is loaded as shown....Ch. 6.2 - Prob. 6.44PCh. 6.2 - Determine the force in members BD and CD of the...Ch. 6.2 - Determine the force in members DF and DG of the...Ch. 6.2 - 6.47 Determine the force in members CD and DF of...Ch. 6.2 - Prob. 6.48PCh. 6.2 - Determine the force in members CD and DF of the...Ch. 6.2 - Determine the force in members CE and EF of the...Ch. 6.2 - Determine the force in members DE and DF of the...Ch. 6.2 - Determine the force in members EG and EF of the...Ch. 6.2 - Determine the force in members DF and DE of the...Ch. 6.2 - Determine the force in members CD and CE of the...Ch. 6.2 - Prob. 6.55PCh. 6.2 - 6.56 A monosloped roof truss is loaded as shown....Ch. 6.2 - A Howe scissors roof truss is loaded as shown....Ch. 6.2 - A Howe scissors roof truss is loaded as shown....Ch. 6.2 - Determine the force in members AD, CD, and CE of...Ch. 6.2 - Determine the force in members DG, FG, and FH of...Ch. 6.2 - 6.61 Determine the force in members DC and FI of...Ch. 6.2 - Prob. 6.62PCh. 6.2 - Prob. 6.63PCh. 6.2 - Prob. 6.64PCh. 6.2 - The diagonal members in the center panels of the...Ch. 6.2 - The diagonal members in the center panels of the...Ch. 6.2 - The diagonal members in the center panels of the...Ch. 6.2 - Solve Prob. 6.67 assuming that the 9-kip load has...Ch. 6.2 - Classify each of the structures shown as...Ch. 6.2 - Classify each of the structures shown as...Ch. 6.2 - 6.70 through 6.74 classify as determinate or...Ch. 6.2 - 6.70 through 6.74 classify as determinate or...Ch. 6.2 - 6.70 through 6.74 classify as determinate or...Ch. 6.2 - 6.70 through 6.74 classify as determinate or...Ch. 6.3 - For the frame and loading shown, draw the...Ch. 6.3 - For the frame and loading shown, draw the...Ch. 6.3 - Draw the free-body diagram(s) needed to determine...Ch. 6.3 - Knowing that the pulley has a radius of 0.5 m,...Ch. 6.3 - 6.75 and 6.76 Determine the force in member BD and...Ch. 6.3 - 6.75 and 6.76 Determine the force in member BD and...Ch. 6.3 - For the frame and loading shown, determine the...Ch. 6.3 - Determine the components of all forces acting on...Ch. 6.3 - Prob. 6.79PCh. 6.3 - Prob. 6.80PCh. 6.3 - Determine the components of all forces acting on...Ch. 6.3 - Determine the components of all forces acting on...Ch. 6.3 - Determine the components of the reactions at A and...Ch. 6.3 - Determine the components of the reactions at D and...Ch. 6.3 - Determine the components of the reactions at A and...Ch. 6.3 - Determine the components of the reactions at A and...Ch. 6.3 - Prob. 6.87PCh. 6.3 - The 48-lb load can be moved along the line of...Ch. 6.3 - The 48-lb load is removed and a 288-lb in....Ch. 6.3 - (a) Show that, when a frame supports a pulley at...Ch. 6.3 - Knowing that each pulley has a radius of 250 mm,...Ch. 6.3 - Knowing that the pulley has a radius of 75 mm,...Ch. 6.3 - 6.93 A 3-ft-diameter pipe is supported every 16 ft...Ch. 6.3 - Prob. 6.94PCh. 6.3 - A trailer weighing 2400 lb is attached to a...Ch. 6.3 - In order to obtain a better weight distribution...Ch. 6.3 - The cab and motor units of the front-end loader...Ch. 6.3 - Solve Problem 6.97 assuming that the 75-kN load...Ch. 6.3 - Knowing that P = 90 lb and Q = 60 lb, determine...Ch. 6.3 - Knowing that P = 90 lb and Q = 60 lb, determine...Ch. 6.3 - For the frame and loading shown, determine the...Ch. 6.3 - For the frame and loading shown, determine the...Ch. 6.3 - 6.103 For the frame and loading shown, determine...Ch. 6.3 - Prob. 6.104PCh. 6.3 - For the frame and loading shown, determine the...Ch. 6.3 - Solve Prob. 6.105 assuming that the 6-kN load has...Ch. 6.3 - The axis of the three-hinge arch ABC is a parabola...Ch. 6.3 - The axis of the three-hinge arch ABC is a parabola...Ch. 6.3 - 6.109 and 6.110 Neglecting the effect of friction...Ch. 6.3 - and 6.110 Neglecting the effect of friction at the...Ch. 6.3 - 6.111, 6.112, and 6.113 Members ABC and CDE are...Ch. 6.3 - 6.111, 6.112, and 6.113 Members ABC and CDE are...Ch. 6.3 - 6.111, 6.112, and 6.113 Members ABC and CDE are...Ch. 6.3 - Prob. 6.114PCh. 6.3 - Solve Prob. 6.112 assuming that the force P is...Ch. 6.3 - Prob. 6.116PCh. 6.3 - Four beams, each with a length of 2a, are nailed...Ch. 6.3 - Four beams, each with a length of 3a, are held...Ch. 6.3 - 6.119 through 6.121 Each of the frames shown...Ch. 6.3 - 6.119 through 6.121 Each of the frames shown...Ch. 6.3 - 6.119 through 6.121 Each of the frames shown...Ch. 6.4 - An 84-lb force is applied to the toggle vise at C....Ch. 6.4 - For the system and loading shown, draw the...Ch. 6.4 - A small barrel weighing 60 lb is lifted by a pair...Ch. 6.4 - The position of member ABC is controlled by the...Ch. 6.4 - The shear shown is used to cut and trim...Ch. 6.4 - A 100-lb force directed vertically downward is...Ch. 6.4 - Prob. 6.124PCh. 6.4 - The control rod CE passes through a horizontal...Ch. 6.4 - Solve Prob. 6.125 when (a) = 0, (b) = 6. Fig....Ch. 6.4 - The press shown is used to emboss a small seal at...Ch. 6.4 - The press shown is used to emboss a small seal at...Ch. 6.4 - The pin at B is attached to member ABC and can...Ch. 6.4 - The pin at B is attached to member ABC and can...Ch. 6.4 - Arm ABC is connected by pins to a collar at B and...Ch. 6.4 - Arm ABC is connected by pins to a collar at B and...Ch. 6.4 - The Whitworth mechanism shown is used to produce a...Ch. 6.4 - Solve Prob. 6.133 when (a) = 60, (b) = 90. Fig....Ch. 6.4 - Prob. 6.135PCh. 6.4 - 6.135 and 6.136 Two rods are connected by a...Ch. 6.4 - 6.137 and 6.138 Rod CD is attached to the collar D...Ch. 6.4 - 6.137 and 6.138 Rod CD is attached to the collar D...Ch. 6.4 - Two hydraulic cylinders control the position of...Ch. 6.4 - Two hydraulic cylinders control the position of...Ch. 6.4 - Prob. 6.141PCh. 6.4 - Prob. 6.142PCh. 6.4 - 6.143 The tongs shown are used to apply a total...Ch. 6.4 - Prob. 6.144PCh. 6.4 - The pliers shown are used to grip a...Ch. 6.4 - Prob. 6.146PCh. 6.4 - In using the bolt cutter shown, a worker applies...Ch. 6.4 - Prob. 6.148PCh. 6.4 - and 6.150 Determine the force P that must be...Ch. 6.4 - and 6.150 Determine the force P that must be...Ch. 6.4 - Because the brace shown must remain in position...Ch. 6.4 - The specialized plumbing wrench shown is used in...Ch. 6.4 - Prob. 6.153PCh. 6.4 - Prob. 6.154PCh. 6.4 - The telescoping arm ABC is used to provide an...Ch. 6.4 - The telescoping arm ABC of Prob. 6.155 can be...Ch. 6.4 - The motion of the backhoe bucket shown is...Ch. 6.4 - Solve Prob. 6.157 assuming that the 2-kip force P...Ch. 6.4 - Prob. 6.159PCh. 6.4 - In the planetary gear system shown, the radius of...Ch. 6.4 - Two shafts AC and CF, which lie in the vertical xy...Ch. 6.4 - Two shafts AC and CF, which lie in the vertical xy...Ch. 6.4 - The large mechanical tongs shown are used to grab...Ch. 6 - Using the method of joints, determine the force in...Ch. 6 - Using the method of joints, determine the force in...Ch. 6 - A stadium roof truss is loaded as shown. Determine...Ch. 6 - A stadium roof truss is loaded as shown. Determine...Ch. 6 - Determine the components of all forces acting on...Ch. 6 - Determine the components of the reactions at A and...Ch. 6 - Knowing that the pulley has a radius of 50 mm,...Ch. 6 - For the frame and loading shown, determine the...Ch. 6 - For the frame and loading shown, determine the...Ch. 6 - Water pressure in the supply system exerts a...Ch. 6 - A couple M with a magnitude of 1.5 kNm is applied...Ch. 6 - The compound-lever pruning shears shown can be...
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