(a) Explanation Given information: Consider the diameter of the pipe is d = 3 ft . The radius of the pipe is r = 1.5 ft . The length of the pipe between the supports is l = 16 ft . The weight of the pipe is w = 500 lb/ft . Assume 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: Draw the free body diagram of the pipe as in Figure (1). Refer to Figure (1). Calculate the total weight of the pipe ( W y ) as follows: W y = w × l = 500 lb/ft × 16 ft = 8000 lb × 1 kips 10 3 lb = 8 kips Refer the force triangle. Consider the reaction from the contact surfaces are denoted by B and D . B y 3 = D z 5 = W y 4 B y 3 = D z 5 = 8 kips 4 Calculate the reaction B from the contact surface as follows: B y 3 = 8 kips 4 B y = 8 kips × 3 4 B y = 6 kips Calculate the reaction D from the contact surface as follows: D z 5 = W 4 D z = 8 kips × 5 4 D z = 10 kips Draw the pipe as in Figure (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 + 3 5 r ) = 4 5 ( C D ) 8 5 r = 4 5 ( C D ) C D = 2 r Substitute 1.5 ft for r . C D = 2 × 1.5 ft =3 ft The distance CD and CB are Equal. Then, C D = C B = 3 ft Draw the free body diagram of member ABC as in Figure (3) (b) To determine The force exerted at C on the member CDE .

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 6.3, Problem 6.93P

(a)

To determine

The components of the reaction at E.

(b)

To determine

The force exerted at C on the member CDE.

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Chapter 6.3, Problem 6.92P

Chapter 6.3, Problem 6.94P

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Chapter 6 Solutions

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

Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.3P Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.5P Ch. 6.1 - Using the method of joints, determine the force in...Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.8P Ch. 6.1 - 6.9 and 6.10 Determine the force in each member of...Ch. 6.1 - Prob. 6.10P

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