Mechanic assignment (2)
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This document contains calculations and analysis for mechanics problems involving frames, trusses, and other structural elements. The problems involve calculating forces, moments, stresses, and displacements. Key values calculated include forces of 45.62kN, 14.38kN, 12.91kN, 17.09kN, and displacements ranging from 1cm to 8cm. A truss problem involves calculating 16 forces labeled N1 through N16. Diagrams illustrate the truss and frame structures analyzed.
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Mechanic assignment (2)
- 1. Theory of Mechanics 2013 Mechanic Assignment Department: Civil Engineering Page 1
- 2. Theory of Mechanics MA 2013 0 10 (10Q) 8 By 0 2 4 P 10 P2 5(10Q) 4m(10kN ) 10m(15kN ) 5m(10m)(3.5 kN) 1 8 8 45.62kN 4 P 10 P2 1 By By Fx 0 Ax Fy 0 0 Ay Ay By By P P2 10Q 1 0 P P2 10Q 1 45.62kN 10kN 15kN 10kN (3.5kN ) Ay 14.38 kN By 45.62kN Ay 14.38 kN Ax 0 Frame Department: Civil Engineering Page 2
- 3. Theory of Mechanics 2013 MA 0 2.5m(5kN ) 3m(6Q) 6 By By By Fx 12.5kNm 3m(6m)(5kN / m) 6m 12.91kN 0 Ax Fy 5kN 0 Ay Ay 0 By By 6Q 0 6Q 12.91kN 6m(5kN/ m) Ay 17.09 kN Frame: Department: Civil Engineering Page 3
- 4. Theory of Mechanics 2013 By 12.91kN Ay 17.09 kN Ax 5kN R 10kg =1cm 30kg=3cm 20kg=2cm 60kg=6cm 80kg=8cm Truss Department: Civil Engineering Page 4
- 5. Theory of Mechanics Department: Civil Engineering 2013 Page 5
- 6. Theory of Mechanics 2013 MA 0 P2 (0 2 4 6 8 10 12 14 16) 16 RBy 72 x1kN 16 RBy Fy 4.5kN 0 9 P2 RBy RAy RAy 9kN 4.5kN RAx Fx 0 0 4.5kN 0 0 1 arctan( ) 26.56 2 3 arctan( ) 56.3 2 Truss Fy 0 P2 N1 Fx Ay N1 sin( ) 0 P2 Ay sin( ) 1kN 4.5kN sin(26.56) 0 ( ) N2 N1 cos( ) 0 N2 N1 cos( ) 7.82kN Department: Civil Engineering ( 7.82kN ) cos(26.56) 7 kN Page 6
- 7. Theory of Mechanics 2013 Fy 0 N3 Fx 0 0 ( ) N2 N6 N6 N2 Department: Civil Engineering 0 7kN Page 7
- 8. Theory of Mechanics Fx 0 2013 ( ) N1 cos( ) N 4 cos( ) N 5 cos( ) 0 N1 N4 N4 P2 Fy N5 N3 0 7.82kN (1) 0 N5 N4 N5 1 N5 N4 N1 sin( ) N 5 sin( ) N 4 sin( ) 0 P2 N 3 N1 sin( ) sin( ) 5.58kN (2) 1kN 0 7.82kN sin(26.56) sin(26.56) 5.58kN 2 N4 N5 N5 N4 7.82kN 5.58kN _____________________ 2N4 13.4 N4 6.7kN N5 N5 7.82kN 6.7kN 1.12kN 1.12kN Department: Civil Engineering Page 8
- 9. Theory of Mechanics Fx 0 2013 ( ) N 4 cos( ) N8 cos( ) 0 N8 Fy N4 6.7kN 0 P2 N7 N8 sin( ) N 4 sin( ) 0 N7 N7 Fy 0 P2 P2 0 N7 N 5 sin( ) N 9 sin( ) 0 N7 N 5 sin( ) sin( ) 1.8kN N9 N9 Fx 1kN 0 ( ) N6 N10 N10 ( 1kN ) ( 1.12kN ) sin(26.56) 1.80kN sin(56.3) N10 N 5 cos( ) N 9 cos( ) 0 N 5 cos( ) N 9 cos( ) N 6 1.12kN cos(26.56) 1.8kN cos(56.3) 7 kN Department: Civil Engineering 5kN Page 9
- 10. Theory of Mechanics 2013 Fx 0 ( ) N10 N14 Fy 0 5kN 0 N11 Fy N10 N14 0 0 P2 N11 N8 sin( ) N12 sin( ) N 9 sin( ) N13 sin( ) 0 1 0 ( 6.7 kN ) sin(26.56) N12 sin(26.56) 1.82kN sin(56.3) N13 sin(56.3) 0 0.44 N12 0.83 N12 Fx 0 0.50 3 ( ) N 6 cos( ) N 9 cos( ) N13 cos( ) N12 cos( ) 0 ( 6.7 kN ) cos(26.56) 1.8kN cos(56.3) N13 cos(56.3) N12 cos(26.56) 0 0.55 N13 0,89 N12 3 5 4 4 Department: Civil Engineering Page 10
- 11. Theory of Mechanics 2013 0.44 N12 0.83 N12 0.50 3 0.55 N13 0,89 N12 0.44 N12 0.83N12 0.50 0.55 N13 0.89 N12 5 5 3 4 N12 4 0.5 0.83 N13 0.44 1 1.67 N13 5 0.55 N13 0.89 0.55 N13 2.22 N13 N13 N12 Fx 0.5 0.83N13 0.44 5 4 4 1.80kN 2.22 0.5 0.83( 1.80kN ) 0.44 0 4.5kN ( ) N12 sin( ) N16 sin( ) 0 N16 Fy N12 4.5kN 0 P2 N15 N15 P2 N15 1 2( 4.5kN ) sin(26.56) 3.02 kN Department: Civil Engineering N12 sin( ) N16 sin( ) 0 N12 sin( ) N16 sin( ) Page 11
- 12. Theory of Mechanics 2013 Truss N1 N 28 7.82kN N2 N 29 7 kN N3 N 27 0 N4 N 24 6.7 kN N5 N 25 1.12kN N6 N 26 N7 N 23 1kN N8 N 20 6.7 kN N9 N 21 1.80kN N10 N 22 5kN N11 N19 0 N12 N16 4.5kN N13 N17 1.80kN N14 N18 N15 3.02kN 7 kN 5kN Truss - Department: Civil Engineering Page 12
- 13. Theory of Mechanics 2013 M (2) 0 2 P2 2 RAy 2 N1 sin( ) RAy P2 N1 Fx 0 4.5 1 sin(26.56) sin( ) 7.82kN ( ) N1 cos( ) N6 Fy 0 N6 0 N1 cos( ) ( 7.82kN ) cos(26.56) 7 kN 0 RAy P2 N3 RAy N3 N3 N1 sin( ) 0kN P2 N1 sin( ) 0 4.5 1 ( 7.82 kN) sin(26.56) - Department: Civil Engineering Page 13
- 14. Theory of Mechanics 2013 M 0 3 1N 2 2 P2 N2 N2 Fx 2 P2 0 2 RAy 2m(1kN ) 2m(4.5kN ) ( ) N 4 cos( ) N4 N 5 cos( ) N2 cos( ) 7 cos(26.56) N5 N4 N5 7.8kN 0 1 0 RAy 2 P2 N4 N5 N4 1 0 7 kN N2 Fy 2 RAy N5 N3 N 4 sin( ) N 5 sin( ) RAy 2 P2 N3 sin( ) 5.6kN 0 4.5 2(1kN ) 0 sin(26.56) 2 2 N4 N5 7.8kN 1 N4 N5 5.6kN 2 ______________________ 13.4 N4 6.7 kN 2 N5 7.8kN N 4 7.8kN ( 6.7 kN ) N5 1.1kN - Department: Civil Engineering Page 14
- 15. Theory of Mechanics 2013 Fx 0 ( ) N6 N8 N8 Fy N 5 cos( ) N8 cos( ) 0 N6 N5 cos( ) cos( ) 6.7kN 7 ( 1.1kN ) cos(26.56) cos(26.56) 0 RAy 3P2 N7 N7 RAy 3P2 N8 sin( ) N 5 sin( ) 0 N8 sin( ) N 5 sin( ) 4.5kN 3(1kN ) ( 6.7 kN) sin(26.56) ( 1.1) sin(26.56) N7 1kN - Fy 0 RAy 2 P2 RAy N9 N 9 sin( ) N 4 sin( ) N 7 2 P N 4 sin( ) N 7 6.7 kN sin(26.56) ( 1) sin(56.3) 1.80kN 0 Fx 4.5kN 2kN sin( ) N9 0 ( ) N10 N10 N 4 cos( ) N 9 cos( ) 0 N 4 cos( ) N 9 cos( ) 6.7 kN cos(26.56) 1.80 kNcos(56.3) N10 5kN - Department: Civil Engineering Page 15
- 16. Theory of Mechanics 2013 M 0 7 P2 2 4 6 12 P2 6 RAy N14 Fy 6 RAy 3 N14 12 1kN 3 3 4 P2 5kN N13 sin( ) N12 sin( ) 0 N13 sin( ) N12 sin( ) 0.83N13 0.44 N12 0 RAy 4 P2 4.5 4 0.5 3 ( ) N14 N13 cos( ) N12 cos( ) 0 N13 cos( ) N12 cos( ) 0.55 N13 0.89 N12 4 6 4.5kN 0 RAy Fx 0 5 N14 5 N12 0.5 0.83 N13 0.44 4 5 0.83 N13 0.44 N12 0.5 3 0.55 N13 0.89 N12 5 4 0.55 N13 0.5 0.83 N13 0.44 0.98 1.65 N13 5 2.2 N13 4.02 4 ; 0.55 N13 0.89 N13 N12 5 1.82kN 0.5 0.83( 1.82kN ) 0.44 Department: Civil Engineering 4.6kN Page 16
- 17. Theory of Mechanics 2013 - M 0 9 2 N11 P2 2 4 6 8 20 P2 8RAy N11 0 4 N10 2 N13 sin( ) 1N13 cos( ) 8m 4.5kN 4(5kN ) ( 1.82)(2sin(56.3) cos(56.3)) 2 0.001kN ( ) N10 N16 N16 Fy 4 N10 2 N13 sin( ) 1N13 cos( ) 0 2 20 1kN Fx 8 RAy N13 cos( ) N16 cos( ) 0 N10 N13 cos( ) cos( ) 4.5kN 5 ( 1.82) cos(56.3) cos(26.56) 0 RAy 5 P2 N11 N15 N13 sin( ) N16 sin( ) 0 N15 RAy 5P2 N11 N13 sin( ) N16 sin( ) N15 4.5kN 5(1kN ) 0 ( 1.82kN ) sin(56.3) ( 4.5 kN) sin(26.56) 3.02kN Department: Civil Engineering Page 17 0kN
- 18. Theory of Mechanics 2013 Truss N1 N 28 7.82kN N2 7 kN N3 N 27 0 N4 N 24 6.7 kN N5 N 25 1.12kN N6 N 26 N7 N 23 1kN N8 N 20 6.7 kN N9 N 21 1.80kN N10 N 22 5kN N11 N19 0 N12 N16 4.5kN N13 N17 1.80kN N14 N18 N15 Department: Civil Engineering N 29 3.02kN 7 kN 5kN Page 18