Frame structure Basic properties of plane frame structure Simple open frame structure Simple closed frame structure

Transcription

1 Statics of Building Structures I., RASUS Frame structure Basic properties of plane frame structure Simple open frame structure Simple closed frame structure Department of Structural echanics Faculty of Civil ngineering, VŠB-Technical University of Ostrava

2 Types of plane frames Frames: a) right-angled b) oblique c) branched d) open a), b), c) xamples of simple open plane frame Basic properties of plane frame structure / 5

3 Types of plane frames Frames: a) right-angled b) oblique c) branched d) closed a), b), c) xamples of simple closed plane frame Basic properties of plane frame structure / 5

4 Types of plane frames Branched frame Basic properties of plane frame structure 4 / 5

5 Types of plane frames, coupled frames Coupled frames originates by combining several simple open frames xamples of right-angled and oblique coupled frames Basic properties of plane frame structure 5 / 5

6 Types of plane frames Vierendeel truss originates by combining several closed frames side by side Storey frame - originates by combining several closed frames above each other Vierendeel truss and Storey frame Basic properties of plane frame structure 6 / 5

7 Force method, simple open frame The first step of the Force method Simple open frame structure 7 / 5

8 Force method, simple open frame Different ways to create a basic statically determinate structure within the second step of the Force method Simple open frame structure 8 / 5

9 Force method, simple open frame Replacement of removed links by reactions or interactions in the third step of the Force method Simple open frame structure 9 / 5

10 Force method, simple open frame Deformatio nal conditions for force and thermal loading : quation in pictures illustrating decomposition into loading states Simple open frame structure 0 / 5

11 Force method, simple open frame Deformatio nal conditions canonical equations) can be written for n s n s i, k k m i,k j 0 times statically indetermin ate structure in form : l j Calculatio n of i k j i,0 for i deformatio nal coefficien ts : m l j k N i N k dx j dx j m is number of bars of I A j 0,...n j s ) the frame i, k k, i Calculatio n of deformatio nal coefficien ts due to force loading : m i,0 j 0 l j i Calculatio n of I j 0 dx j m l j j 0 N i N A j 0 dx deformatio nal coefficien ts due j to thermal loading : i,0 t m l j j 0 N i t 0, j dx j t m l j j 0 i t h, j j dx j / 5

12 Force method, simple open frame, support shifting Deformational conditions for support shifting: d d d n s k i, k k i,0 d i for i,..., n s / 5

13 Force method, simple open frame, support shifting Support shifting and directions of shifts : w a a ), w clockwise ), b b ), u a ), u clockwise ) b ), d b d w b d u b 0 * b a a ) a 0 w * b R a w a a a ) w a a l 0 u * b H a u a a a ) u a a v Calculation of deformational coefficients due to support shifting Simple open frame structure / 5

14 4 / 5 Force method, simple open frame, support shifting d d d v u u l w w v u l w u d w d d a a b a a b a b a a a a a b b b is,,,,,

15 Warning Bar c-d is supported against movement in the direction of the axis of the bar. It is necessary to take into account the influence of normal forces on the deflection of the bar c-d. Otherwise, the system of canonical equations singular. Two constraints in the axis of the same bar Simple open frame structure 5 / 5

16 xample 5. I =0,00m, I =I =0,004m l a, c sin l,,8,5m,8 arctg arctg, ),,8, 0,8, cos,5,5 59,0 0,6 0 Simple open frame structure 6 / 5

17 xample 5., solution Loading states and bending moment diagrams for loading states of xample 5. R a0 0kN ), R b0 0, H a0 0 R a kn 5,7 ), R b kn 5,7 ), H a 0 R a,8 kn 5,7 ), R b,8 kn 5,7 ), H a ) Simple open frame structure 7 / 5

18 xample 5., solution continuation Deformational conditions: ,658,5 0,00.,7684 0,00.,7684 0, ,00.,5,5,7684 0,004. 0, ,6 0,658 ) , ,4 0,00., ,5 0,658 0,684 )),6 76,5 0,658 0,004,5 0,684,7684 0,658 50,4 0,658 ),6 0,004,6 04, Simple open frame structure 8 / 5

19 xample 5., solution of linear equations Deformational conditions: ,, 50,4, 76,5, ,6, ,4 04, 50,4 50,4 76,5 4585, ,4 0 04, 64989,4) 50, , , 76,5 50,4 50,4 4570,5 04, 64989,4) 4585,6) 50, , 76,5 50,4 50,4 4570,5,84 kn 6,906 kn Simple open frame structure 9 / 5

20 xample 5., completion, reactions and internal forces diagrams R H R H a b a a b R a0 H R b0 a0 R R a H,84kNmcounter clockwise) b a R R a H b 6,557 kn a ),8 0,84) 6,557) 5,7 5, ,557) 6,557 kn,8 0,84) 6,557) 5,7 5,7 40,8kN ) 0,8kN ) ) Simple open frame structure 0 / 5

21 Simple closed frame Removal of internal links and its replacement by interactions Simple open frame structure / 5

22 Simple closed frame Degree of statical indetermin acy n s I const. First three steps of the Force method Simple open frame structure / 5

23 xample 5., loading states Nonzero reactions only in the loading state "0" i.e."0. stav" in czech) R R R az bz ax R R R az0 bz0 ax0 9, 666kN ) 0, kn ) 8kN ) Notice to bending moment diagram see pic.): Bottom side of horizontal bars is down. Bottom side of vertical bars is considered at the right side of bar. Loading states and corresponding bending moments diagrams for xample 5. Simple open frame structure / 5

24 4 / 5 xample 5., canonical equations I I I I I I I I 78,7,7)),6,7),7,7),7,7) 0,088,6) 5,4,6,6,6,6,6) 0 0,40,6)) 5,4,6,6 ),6,6 8 ),6 ) ),6 5,4 ) ) 5, Calculation of deformational coefficients:

25 5 / 5 xample 5., canonical equations kn V V kn N N knm, I I I I I I ed ec ed ec ed ec 667,, 8,60,,09 : 09,95 787, ,0 0 0,088,4 8, ,95,7)),6 8,8) 6 54,9,7,7) ) 8,8 54,9 8,8,7,7 798,,6)),6 8,8),6,7 54,9,6,7 54,9 8,8 8,95 ),6 8,8) ),7 54,9 ),7 54,9 8, equations canonical Solution of equations: Substitution in canonical coefficien ts: deformatio nal Calculation of

26 6 / 5 xample 5., completion Internal forces can be determined: a) From the equilibrium conditions with knowledge of reactions and statically indeterminate forces b) By superposition of loading states, taking into account real value of statically indeterminate forces see bellow) Ad b): x x x x x x x x x x x x x x x N N N N V V V V V N Simple open frame structure

27 xample 5., completion =-,09kNm, =-8,60kNm, =-,667kN x ac ac 0 x x 8,8,09) 8,60 7,59kNm column) x ab x,6),667,7) 7,59k Nm bd bd 0,09) ),557k Nm 8,60 ba,6),667,557k Nm,7) ca ca 0,09) 4,99k Nm ) 8,60 0),667 cd 4,99k Nm,7) dc dc 0,09) ) 8,60 9,409k Nm db 0),667 9,409k Nm,7) max m a x 54,9,09) 6,4k Nm ) 8,60,6),667 0) Simple open frame structure 7 / 5

28 xample 5., bending moments calculation =-,09kNm, =-8,60kNm, =-,667kN x ac ac 0 x x 8,8,09) 8,60 7,59kNm column) x ab x,6),667,7) 7,59k Nm bd bd 0,09) ),557k Nm 8,60 ba,6),667,557k Nm,7) ca ca 0,09) 4,99k Nm ) 8,60 0),667 cd 4,99k Nm,7) dc dc 0,09) ) 8,60 9,409k Nm db 0),667 9,409k Nm,7) max m a x 54,9,09) 6,4k Nm ) 8,60,6),667 0) Simple open frame structure 8 / 5

29 xample 5., another way to calculate bending moments =-,09kNm, =-8,60kNm, =-,667kN cd ca ac ac better : ac ac ab ba ba,09 8,6,667,7 8,60,6 7,59 kn 7,59 knm ce cd ce ca ab ac,09,667,7 4,99kNm 8,6 8,6 V ab,559 knm V N ec ec,7 7,59 knm N ec 4,99kNm,6,6 4,99 8,6 8,60,6 5,4 0,7 7,59, 5,4 0,7 It is necessary to know some components of internal forces in this shortened calculation e.g. shear force V ab ) Simple open frame structure 9 / 5

30 xample 5., completion Resulting reactions, interactions and diagrams of internal forces for xample 5.. Simple open frame structure 0 / 5

31 Steel frame structure of industrial hall Span 0,5 m xamples of frame structures / 5

32 Hall for manufacturing components for nuclear power plants, Vitkovice Ground0 x 0 m Cranes with capacity 80 and 00 t Undermined area xamples of frame structures / 5

33 Steel frame structure of coupled hall, Vítkovice Span 0 a 4 m Cranes with capacity 80 a 50 t Undermined area xamples of frame structures / 5

34 Sport hall Slavia, Prague xamples of frame structures 4 / 5

35 Administration Building, Glasgow, UK Space steel frame with bracing xamples of frame structures 5 / 5

36 Administration Building, Glasgow, UK Space steel frame with bracing xamples of frame structures 6 / 5

37 Administration Building, Glasgow, UK Space steel frame with bracing - detail xamples of frame structures 7 / 5

38 San Sebastian, Auditorium, Spain Space frame xamples of frame structures 8 / 5

39 San Sebastian, Auditorium, Spain xamples of frame structures 9 / 5

40 Congress Centre, Brno xhibition Centre Visible space frame supporting structure xamples of frame structures 40 / 5

41 University Children's Hospital, Brno Supporting space frame structure with overhanging ends xamples of frame structures 4 / 5

42 lementary School, Brumov Bylnice Frame structure with bracing xamples of frame structures 4 / 5

43 Aula, VŠB-TU Ostrava Space frame of reinforced concrete xamples of frame structures 4 / 5

44 Aula, VŠB-TU Ostrava Space frame of reinforced concrete - detail xamples of frame structures 44 / 5

45 Radio Free urope, Prague Vierendeel truss of 968: Ground 59x8 m 6 pillars xamples of frame structures 45 / 5

46 Radio Free urope, Prague Vierendeel truss of 968: Ground 59x8 m 6 pillars xamples of frame structures 46 / 5

47 Radio Free urope, Prague Vierendeel truss of 968: Ground 59x8 m 6 pillars xamples of frame structures 47 / 5

48 Road bridge, Karviná Darkov Spa RC arched bridge of 95: Vierendeel truss Unique cross-bracing Height 6,5 m Deck length 55,8 m Width 6,5 m xamples of frame structures Photo: Ing. Renata Zdařilová 48 / 5

49 Road bridge, Karviná Darkov Spa Reinforced Concrete arched bridge of 95: xamples of frame structures Photo: Ing. Renata Zdařilová 49 / 5

50 Road bridge, Karviná Darkov Spa Reinforced Concrete arched bridge of 95: Photo: Ing. Renata Zdařilová xamples of frame structures 50 / 5

51 Road bridge, Karviná Darkov Spa xamples of frame structures 5 / 5

52 Road bridge, Karviná Darkov Spa Photo: Ing. Renata Zdařilová xamples of frame structures 5 / 5