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Unformatted text preview: Problem 14.1 In Example 71, determine the internal forces and moment at C if the distance from A to C is L/ 2 . Free Body Diagram: Solution: We first determine the reactions at the ends of the beam: M B = 0 = F L 4 A y ( L ) A y = F/ 4 F y = 0 = F + A y + B y = F + F/ 4 + B y B y = 3 F/ 4 F x = 0 = A x A x = 0 Using the FBD of the lefthand portion of the beam: F x = 0 = C x ANS: C x = 0 F y = 0 = A y V C = F/ 4 V C ANS: V C = F/ 4 M A = 0 = F 4 L 2 + M C ANS: M C = F L/ 8 Problem 14.2 Determine the internal forces and mo ment at A , B , and C . STRATEGY In this case you dont need to determine the reactions at the builtin support. Cut the beam at the point where you want to determine the internal forces and moment and draw the freebody diagram of the part of the beam to the left of your cut. Remember that P , V , and M must be in their defined positive directions in your freebody diagrams. Solution: Cut the beam through point A and draw the FBD: F x = 0 = P A ANS: P A = 0 F y = 0 = 2 , 000 N V A ANS: V A = 2 , 000 N M A = 0 = (2 , 000 N)(1 m) + M A ANS: M A = 2 , 000 N m Cut the beam through point B and draw the FBD: F x = 0 = P B ANS: P B = 0 F y = 0 = 2 , 000 N V B ANS: V B = 2 , 000 N M B = 0 = (2 , 000 N)(2 m) + M B ANS: M B = 4 , 000 N m Cut the beam through point C and draw the FBD: F x = 0 = P C ANS: P C = 0 F y = 0 = 2 , 000 N V C ANS: V C = 2 , 000 N M C = 0 = (2 , 000 N)(3 m) + M C ANS: M C = 6 , 000 N m Problem 14.3 Determine the internal forces and the moment at A , B , and C . Solution: The sum of forces exerted by a couple is zero in every direction, so the couple can be omitted from any force equations. Cut through the beam at point A and draw the FBD: F x = 0 = P A ANS: P A = 0 F y = 0 = V A ANS: V A = 0 M A = 0 = 2 , 000 ft lb M A ANS: M A = 2 , 000 ft lb Cut through the beam at point B and draw the FBD: F x = 0 = P B ANS: P B = 0 F y = 0 = V B ANS: V B = 0 M B = 0 = 2 , 000 ft lb M B ANS: M B = 2 , 000 ft lb Cut through the beam at point C and draw the FBD: F x = 0 = P C ANS: P C = 0 F y = 0 = V C ANS: V C = 0 M C 0 = 2 , 000 ft lb M C ANS: M C = 2 , 000 ft lb Problem 14.4 Determine the internal forces and mo ment at A . Solution: Cut the bar through point A and draw the FBD: F x = 0 = (1 , 000 lb)( cos 30 ) P A ANS: P A = 866 lb F y = 0 = (1 , 000 lb)( sin 30 ) V A ANS: V A = 500 lb M A = 0 = (1 , 000 lb)( sin 30 )(6 ft) M A ANS: M A = 3 , 000 ft lb Free Body Diagram: Problem 14.5 Determine the internal forces and moment (a) at B ; (b) at C ....
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This homework help was uploaded on 04/03/2008 for the course MAE 101 taught by Professor Orient during the Winter '08 term at UCLA.
 Winter '08
 ORIENT
 Statics

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