Baixe Resolução Hibbe...- Statics 12ªed - hibbeler - statics 12?ed - cap.4 (2) e outras Provas em PDF para Engenharia Mecânica, somente na Docsity! 255 4–87. Determine the required magnitude of force F, if the resultant couple moment on the beam is to be zero. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. F F 5 kN 5 kN 0.5 m 0.5 m 30 30 4 4 3 3 5 5 3 m A B 3 m 4 Solutions 44918 1/23/09 12:03 PM Page 255 256 *4–88. Two couples act on the frame. If the resultant couple moment is to be zero, determine the distance d between the 40-lb couple forces. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3 ft 60 lb 40 lb 40 lb 30 d y x A B 1 ft 30 3 4 5 4 ft 2 ft 3 4 5 60 lb •4–89. Two couples act on the frame. If , determine the resultant couple moment. Compute the result by resolving each force into x and y components and (a) finding the moment of each couple (Eq. 4–13) and (b) summing the moments of all the force components about point A. d = 4 ft 3 ft 60 lb 40 lb 40 lb 30 d y x A B 1 ft 30 3 4 5 4 ft 2 ft 3 4 5 60 lb 4–90. Two couples act on the frame. If , determine the resultant couple moment. Compute the result by resolving each force into x and y components and (a) finding the moment of each couple (Eq. 4–13) and (b) summing the moments of all the force components about point B. d = 4 ft 3 ft 60 lb 40 lb 40 lb 30 d y x A B 1 ft 30 3 4 5 4 ft 2 ft 3 4 5 60 lb 4 Solutions 44918 1/23/09 12:03 PM Page 256 259 •4–93. If , determine the magnitude and coordinate direction angles of the couple moment. The pipe assembly lies in the x–y plane. F = 80 N © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. x z y 300 mm 200 mm 200 mm 300 mm 300 mm F F 4 Solutions 44918 1/23/09 12:03 PM Page 259 260 4–94. If the magnitude of the couple moment acting on the pipe assembly is , determine the magnitude of the couple forces applied to each wrench. The pipe assembly lies in the x–y plane. 50 N # m © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. x z y 300 mm 200 mm 200 mm 300 mm 300 mm F F 4 Solutions 44918 1/23/09 12:03 PM Page 260 261 4–95. From load calculations it is determined that the wing is subjected to couple moments and . Determine the resultant couple moments created about the and axes.The axes all lie in the same horizontal plane. y¿x¿ My = 25 kip # ft Mx = 17 kip # ft © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. y y x¿ x ¿ 25 My Mx *4–96. Express the moment of the couple acting on the frame in Cartesian vector form. The forces are applied perpendicular to the frame. What is the magnitude of the couple moment? Take .F = 50 N F x y z O 1.5 m 3 m 30 F 4 Solutions 44918 1/23/09 12:03 PM Page 261 264 *4–100. If , , and , determine the magnitude and coordinate direction angles of the resultant couple moment. M3 = 120 lb #ftM2 = 90 lb #ftM1 = 180 lb #ft © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. x z y 2 ft 2 ft 2 ft 3 ft 150 lbft 1 ft 45 45 M1 M2 M3 4 Solutions 44918 1/23/09 12:03 PM Page 264 265 •4–101. Determine the magnitudes of couple moments so that the resultant couple moment is zero.M1, M2, and M3 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. x z y 2 ft 2 ft 2 ft 3 ft 150 lbft 1 ft 45 45 M1 M2 M3 4 Solutions 44918 1/23/09 12:03 PM Page 265 266 4–102. If , determine the magnitude and coordinate direction angles of the resultant couple moment. F1 = 100 lb and F2 = 200 lb © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 2 ft 3 ft 4 ft z yx F2 F1 F2 250 lb 250 lb F1 4 Solutions 44918 1/23/09 12:03 PM Page 266 269 •4–105. Replace the force system acting on the beam by an equivalent force and couple moment at point A. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 2.5 kN 1.5 kN 3 kN A B 4 m 3 4 5 2 m 2 m 30 4–106. Replace the force system acting on the beam by an equivalent force and couple moment at point B. 2.5 kN 1.5 kN 3 kN A B 4 m 3 4 5 2 m 2 m 30 4 Solutions 44918 1/23/09 12:03 PM Page 269 270 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4 Solutions 44918 1/23/09 12:03 PM Page 270 271 4–107. Replace the two forces by an equivalent resultant force and couple moment at point O. Set .F = 20 lb © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 6 in. 30 4 3 5 1.5 in. F 20 lb 2 in. x y O 40 4 Solutions 44918 1/23/09 12:03 PM Page 271 274 4–110. Replace the force and couple moment system acting on the overhang beam by a resultant force and couple moment at point A. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. B A 5 12 13 30 kN 45 kNm 26 kN 0.3 m 0.3 m 2 m2 m 1 m 1 m 30 4 Solutions 44918 1/23/09 12:04 PM Page 274 275 4–111. Replace the force system by a resultant force and couple moment at point O. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 200 N 200 N 500 N 4 3 5 O 750 N 1.25 m 1.25 m 1 m 4 Solutions 44918 1/23/09 12:04 PM Page 275 276 *4–112. Replace the two forces acting on the grinder by a resultant force and couple moment at point O. Express the results in Cartesian vector form. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 250 mm y x z 25 mm 40 mm 150 mm 100 mm O A B F2 {15i 20j 30k} N F1 {10i 15j 40k} N 4 Solutions 44918 1/23/09 12:04 PM Page 276 279 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *4–116. Replace the force system acting on the pipe assembly by a resultant force and couple moment at point O. Express the results in Cartesian vector form. x z 2 ft 1.5 ft 2 ft 2 ft O x F1 {20i 10j 25k}lb F2 {10i 25j 20k} lb 4 Solutions 44918 1/23/09 12:04 PM Page 279 280 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •4–117. The slab is to be hoisted using the three slings shown. Replace the system of forces acting on slings by an equivalent force and couple moment at point O. The force is vertical.F1 y x z 45 6060 45 30 6 m 2 m 2 m F2 5 kN F3 4 kN O F1 6 kN 4–118. The weights of the various components of the truck are shown. Replace this system of forces by an equivalent resultant force and specify its location measured from B. 14 ft 6 ft 2 ft3 ft AB 3500 lb 5500 lb 1750 lb 4 Solutions 44918 1/23/09 12:04 PM Page 280 281 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–119. The weights of the various components of the truck are shown. Replace this system of forces by an equivalent resultant force and specify its location measured from point A. 14 ft 6 ft 2 ft3 ft AB 3500 lb 5500 lb 1750 lb *4–120. The system of parallel forces acts on the top of the Warren truss. Determine the equivalent resultant force of the system and specify its location measured from point A. A 500 N 500 N 500 N 1 kN 2 kN 1 m 1 m 1 m 1 m 4 Solutions 44918 1/23/09 12:04 PM Page 281 284 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–123. Replace the force and couple system acting on the frame by an equivalent resultant force and specify where the resultant’s line of action intersects member BC, measured from B. 3 ft 30 4 ft 35 4 2 ft 150 lb 50 lb 500 lb ft C B A 4 Solutions 44918 1/23/09 12:04 PM Page 284 285 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *4–124. Replace the force and couple moment system acting on the overhang beam by a resultant force, and specify its location along AB measured from point A. B A 5 12 13 30 kN 45 kNm 26 kN 0.3 m 0.3 m 2 m2 m 1 m 1 m 30 4 Solutions 44918 1/23/09 12:04 PM Page 285 286 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •4–125. Replace the force system acting on the frame by an equivalent resultant force and specify where the resultant’s line of action intersects member AB, measured from point A. 2 ft 4 ft 3 ft 25 lb 2 ft 20 lb A B C 30 35 lb 4 Solutions 44918 1/23/09 12:04 PM Page 286 289 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *4–128. Replace the force system acting on the post by a resultant force, and specify where its line of action intersects the post AB measured from point B. 250 N 500 N 0.2 m 0.5 m 3 4 5 300 N 1 m 30 1 m 1 m A B •4–129. The building slab is subjected to four parallel column loadings. Determine the equivalent resultant force and specify its location (x, y) on the slab. Take F2 = 40 kN. F1 = 30 kN, y x 20 kN 3 m 2 m 8 m 6 m 4 m 50 kN F1 F2 z 4 Solutions 44918 1/23/09 12:04 PM Page 289 290 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–130. The building slab is subjected to four parallel column loadings. Determine the equivalent resultant force and specify its location (x, y) on the slab. Take F2 = 50 kN. F1 = 20 kN, y x 20 kN 3 m 2 m 8 m 6 m 4 m 50 kN F1 F2 z 4–131. The tube supports the four parallel forces. Determine the magnitudes of forces and acting at C and D so that the equivalent resultant force of the force system acts through the midpoint O of the tube. FDFC x z A D C y zB O400 mm 400 mm 500 N 200 mm 200 mm 600 N FC FD 4 Solutions 44918 1/23/09 12:04 PM Page 290 291 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *4–132. Three parallel bolting forces act on the circular plate. Determine the resultant force, and specify its location (x, z) on the plate. , , and .FC = 400 lb FB = 100 lbFA = 200 lb 45 30 1.5 ft z x yAB C FB FA FC 4 Solutions 44918 1/23/09 12:04 PM Page 291 294 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •4–137. If , represent the force system acting on the corbels by a resultant force, and specify its location on the x–y plane. FA = 7 kN and FB = 5 kN 750 mm z x y 650 mm 100 mm 150 mm 600 mm 700 mm 100 mm 150 mm 8kN 6 kN FA FB O 4 Solutions 44918 1/23/09 12:04 PM Page 294 295 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–138. Determine the magnitudes of and so that the resultant force passes through point O of the column. FBFA 750 mm z x y 650 mm 100 mm 150 mm 600 mm 700 mm 100 mm 150 mm 8kN 6 kN FA FB O 4 Solutions 44918 1/23/09 12:04 PM Page 295 296 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–139. Replace the force and couple moment system acting on the rectangular block by a wrench. Specify the magnitude of the force and couple moment of the wrench and where its line of action intersects the x–y plane. y x z 300 lb 450 lb 600 lb 2 ft 4 ft 3 ft 600 lbft 4 Solutions 44918 1/23/09 12:04 PM Page 296 299 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–142. Replace the distributed loading with an equivalent resultant force, and specify its location on the beam measured from point A. A B 3 m 3 m 15 kN/m 10 kN/m 3 m 4 Solutions 44918 1/23/09 12:04 PM Page 299 300 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–143. Replace the distributed loading with an equivalent resultant force, and specify its location on the beam measured from point A. B A 8 kN/m 4 kN/m 3 m 3 m 4 Solutions 44918 1/23/09 12:04 PM Page 300 301 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *4–144. Replace the distributed loading by an equivalent resultant force and specify its location, measured from point A. 3 m2 m A B 800 N/m 200 N/m •4–145. Replace the distributed loading with an equivalent resultant force, and specify its location on the beam measured from point A. A B L–– 2 L–– 2 w0 w0 4 Solutions 44918 1/23/09 12:04 PM Page 301 304 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •4–149. The wind pressure acting on a triangular sign is uniform. Replace this loading by an equivalent resultant force and couple moment at point O. 1.2 m 1 m O 1.2 m 0.1 m 150 Pa y x z 4 Solutions 44918 1/23/09 12:04 PM Page 304 305 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–150. The beam is subjected to the distributed loading. Determine the length b of the uniform load and its position a on the beam such that the resultant force and couple moment acting on the beam are zero. 6 ft10 ft b a 60 lb/ft 40 lb/ft 4–151. Currently eighty-five percent of all neck injuries are caused by rear-end car collisions. To alleviate this problem, an automobile seat restraint has been developed that provides additional pressure contact with the cranium. During dynamic tests the distribution of load on the cranium has been plotted and shown to be parabolic. Determine the equivalent resultant force and its location, measured from point A. A w B x w 12(1 2x2) lb/ft 0.5 ft 12 lb/ft 18 lb/ft 4 Solutions 44918 1/23/09 12:04 PM Page 305 306 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *4–152. Wind has blown sand over a platform such that the intensity of the load can be approximated by the function Simplify this distributed loading to an equivalent resultant force and specify its magnitude and location measured from A. w = 10.5x32 N>m. x w A 10 m 500 N/m w (0.5x3) N/m •4–153. Wet concrete exerts a pressure distribution along the wall of the form. Determine the resultant force of this distribution and specify the height h where the bracing strut should be placed so that it lies through the line of action of the resultant force. The wall has a width of 5 m. 4 m h (4 ) kPap 1/2z 8 kPa z p 4 Solutions 44918 1/23/09 12:04 PM Page 306 309 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *4–156. Replace the loading by an equivalent resultant force and couple moment acting at point B. 60 6 ft 50 lb/ft 50 lb/ft 100 lb/ft 4 ft A B 4 Solutions 44918 1/23/09 12:04 PM Page 309 310 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •4–157. The lifting force along the wing of a jet aircraft consists of a uniform distribution along AB, and a semiparabolic distribution along BC with origin at B. Replace this loading by a single resultant force and specify its location measured from point A. x w 24 ft12 ft w (2880 5x2) lb/ft 2880 lb/ft A B C 4–158. The distributed load acts on the beam as shown. Determine the magnitude of the equivalent resultant force and specify where it acts, measured from point A. w (2x2 4x 16) lb/ft x B A w 4 ft 4 Solutions 44918 1/23/09 12:04 PM Page 310 311 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–159. The distributed load acts on the beam as shown. Determine the maximum intensity . What is the magnitude of the equivalent resultant force? Specify where it acts, measured from point B. wmax w (2x2 4x 16) lb/ft x B A w 4 ft 4 Solutions 44918 1/23/09 12:04 PM Page 311 314 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–162. The beam is subjected to the parabolic loading. Determine an equivalent force and couple system at point A. w (25 x2)lb/ft 4 ft 400 lb/ft x w A O 4–163. Two couples act on the frame. If the resultant couple moment is to be zero, determine the distance d between the 100-lb couple forces. d3 ft 4 ft A B 3 ft 30° 100 lb 150 lb 150 lb 100 lb 3 4 5 3 4 5 30° 4 Solutions 44918 1/23/09 12:04 PM Page 314 315 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *4–164. Determine the coordinate direction angles , , of F, which is applied to the end of the pipe assembly, so that the moment of F about O is zero. gba x 10 in. F 20 lb 6 in. 6 in.8 in. z O y •4–165. Determine the moment of the force F about point O. The force has coordinate direction angles of , , . Express the result as a Cartesian vector.g = 45°b = 120° a = 60° x 10 in. F 20 lb 6 in. 6 in.8 in. z O y 4 Solutions 44918 1/23/09 12:04 PM Page 315 316 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 4–166. The snorkel boom lift is extended into the position shown. If the worker weighs 160 lb, determine the moment of this force about the connection at A. 25 ft 50 A 2 ft 4–167. Determine the moment of the force about the door hinge at A. Express the result as a Cartesian vector. FC 0.5 m1 m 30 2.5 m 1.5 m z C A B a a x y FC 250 N *4–168. Determine the magnitude of the moment of the force about the hinged axis aa of the door.FC 0.5 m1 m 30 2.5 m 1.5 m z C A B a a x y FC 250 N 4 Solutions 44918 1/23/09 12:04 PM Page 316