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Solutions-HW1-and-2

Solutions-HW1-and-2 - budynas_SM_ch03.qxd 17:55 Page 15...

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Chapter 3 15 3-2 (a) R A = 2 sin 60 = 1 . 732 kN Ans. R B = 2 sin 30 = 1 kN Ans. (b) S = 0 . 6 m α = tan 1 0 . 6 0 . 4 + 0 . 6 = 30 . 96 R A sin 135 = 800 sin 30 . 96 R A = 1100 N Ans. R O sin 14 . 04 = 800 sin 30 . 96 R O = 377 N Ans. (c) R O = 1 . 2 tan 30 = 2 . 078 kN Ans. R A = 1 . 2 sin 30 = 2 . 4 kN Ans. (d) Step 1: Find R A and R E h = 4 . 5 tan 30 = 7 . 794 m + M A = 0 9 R E 7 . 794(400 cos 30) 4 . 5(400 sin 30) = 0 R E = 400 N Ans . F x = 0 R Ax + 400 cos 30 = 0 R Ax = − 346 . 4 N F y = 0 R Ay + 400 400 sin 30 = 0 R Ay = − 200 N R A = 346 . 4 2 + 200 2 = 400 N Ans. D C h B y E x A 4.5 m 9 m 400 N 3 4 2 30 ° 60 ° R Ay R A R Ax R E 1.2 kN 60 ° R A R O 60 ° 90 ° 30 ° 1.2 kN R A R O 45 30.96 14.04 135 ° 30.96 ° 30.96 ° 800 N R A R O O 0.4 m 45 ° 800 N 0.6 m A s R A R O B 60 ° 90 ° 30 ° 2 kN R A R B 2 1 2 kN 60 ° 30 ° R A R B budynas_SM_ch03.qxd 01/29/2007 17:55 Page 15
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16 Solutions Manual Instructor’s Solution Manual to Accompany Mechanical Engineering Design Step 2: Find components of R C on link 4 and R D + M C = 0 400(4 . 5) (7 . 794 1 . 9) R D = 0 R D = 305 . 4 N Ans. F x = 0 ( R Cx ) 4 = 305 . 4 N F y = 0 ( R Cy ) 4 = − 400 N Step 3: Find components of R C on link 2 F x = 0 ( R Cx ) 2 + 305 . 4 346 . 4 = 0 ( R Cx ) 2 = 41 N F y = 0 ( R Cy ) 2 = 200 N 3-3 (a) + M 0 = 0 18(60) + 14 R 2 + 8(30) 4(40) = 0 R 2 = 71 . 43 lbf F y = 0: R 1 40 + 30 + 71 . 43 60 = 0 R 1 = − 1 . 43 lbf M 1 = − 1 . 43(4) = − 5 . 72 lbf · in M 2 = − 5 . 72 41 . 43(4) = − 171 . 44 lbf · in M 3 = − 171 . 44 11 . 43(6) = − 240 lbf · in M 4 = − 240 + 60(4) = 0 checks! 4" 4" 6" 4" 1.43 41.43 11.43 60 40 lbf 60 lbf 30 lbf x x x O A B C D y R 1 R 2 M 1 M 2 M 3 M 4 O V (lbf) M (lbf in) O C C D B A B D E 305.4 N 346.4 N 305.4 N 41 N 400 N 200 N 400 N 200 N 400 N Pin C 30 ° 305.4 N 400 N 400 N 200 N 41 N 305.4 N 200 N 346.4 N 305.4 N ( R Cx ) 2 ( R Cy ) 2 C B A 2 400 N 4 R D ( R Cx ) 4 ( R Cy ) 4 D C E Ans. budynas_SM_ch03.qxd 01/29/2007 17:55 Page 16
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Chapter 3 17 (b) F y = 0 R 0 = 2 + 4(0 . 150) = 2 . 6kN M 0 = 0 M 0 = 2000(0 . 2) + 4000(0 . 150)(0 . 425) = 655 N · m M 1 = − 655 + 2600(0 . 2) = − 135 N · m M 2 = − 135 + 600(0 . 150) = − 45 N · m M 3 = − 45 + 1 2 600(0 . 150) = 0 checks! (c) M 0 = 0: 10 R 2 6(1000) = 0 R 2 = 600 lbf F y = 0: R 1 1000 + 600 = 0 R 1 = 400 lbf M 1 = 400(6) = 2400 lbf · ft M 2 = 2400 600(4) = 0 checks! (d) + M C = 0 10 R 1 + 2(2000) + 8(1000) = 0 R 1 = 1200 lbf F y = 0: 1200 1000 2000 + R 2 = 0 R 2 = 1800 lbf M 1 = 1200(2) = 2400 lbf · ft M 2 = 2400 + 200(6) = 3600 lbf · ft M 3 = 3600 1800(2) = 0 checks! 2000 lbf 1000 lbf R 1 O O M 1 M 2 M 3 R 2 6 ft 2 ft 2 ft A B C y M 1200 1800 200 x x x 6 ft 4 ft A O O O B 600 M 1 M 2 V (lbf) 1000 lbf y R 1 R 2 400 M (lbf ft) x x x V (kN) 150 mm 200 mm 150 mm 2.6 655 M (N m) 0.6 M 1 M 2 M 3 2 kN 4 kN/m y A O O O O B C R O M O x x x budynas_SM_ch03.qxd 01/29/2007 17:56 Page 17
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18 Solutions Manual Instructor’s Solution Manual to Accompany Mechanical Engineering Design (e) + M B = 0 7 R 1 + 3(400) 3(800) = 0 R 1 = − 171 . 4 lbf F y = 0: 171 . 4 400 + R 2 800 = 0 R 2 = 1371 . 4 lbf M 1 = − 171 . 4(4) = − 685 . 7 lbf · ft M 2 = − 685 . 7 571 . 4(3) = − 2400 lbf · ft M 3 = − 2400 + 800(3) = 0 checks! (f) Break at A R 1 = V A = 1 2 40(8) = 160 lbf + M D = 0 12(160) 10 R 2 + 320(5) = 0 R 2 = 352 lbf F y = 0 160 + 352 320 + R 3 = 0 R 3 = 128 lbf M 1 = 1 2 160(4) = 320 lbf · in M 2 = 320 1 2 160(4) = 0 checks! (hinge) M 3 = 0 160(2) = − 320 lbf · in M 4 = − 320 + 192(5) = 640 lbf · in M 5 = 640 128(5) = 0 checks! 40 lbf/in V (lbf) O O 160 160 128 192 M 320 lbf 160 lbf 352 lbf 128 lbf M 1 M 2 M 3 M 4 M 5 x x x 8" 5" 2" 5" 40 lbf/in 160 lbf O A y B D C A 320 lbf R 2 R 3 R 1 V A A O O O C M V (lbf) 800 171.4 571.4 3 ft 3 ft 4 ft 800 lbf 400 lbf B y M 1 M 2 M 3 R 1 R 2 x x x budynas_SM_ch03.qxd 01/29/2007 17:56 Page 18
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22 Solutions Manual
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