eight plates and grids APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2018 lecture STRUCTURAL ANALYSIS AND SYSTEMS ARCH 631

Transcription

1 APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2018 lecture eight plates and grids Plates & Grids 1

2 Term Project Plates & Grids 2

3 Plates, Slabs & Grids plates horizontal plane, rigid slabs thin, flat, rigid extremely common in concrete grids crossed beams see bending shear Plates & Grids 3

4 Plates, Slabs & Grids types & spanning direction Plates & Grids 4

5 Plates, Slabs & Grids Plates & Grids 5

6 Plates, Slabs & Grids loads & behavior comparison with beams Plates & Grids 6

7 Plate Structures waffles & grids Plates & Grids 7

8 Plates, Slabs & Grids compatibility deflections same, even with stiffer side stiffness to EI L twisting causes torsional stresses supports at points flexible continuous Plates & Grids 8

9 One-Way Plates with uniform loads like wide beams moment / unit width uniform curvature with point loads resisted by stiffness of adjacent strips more curvature in middle Plates & Grids 9

10 Moment Redistribution total moment for ½ plate value from basic equilibrium because of curvature, it isn t uniform at support redistribution bigger with big curvature smaller with small curvature Plates & Grids 10

11 Moment Redistribution continuous slabs & beams with uniform loading joints similar to fixed ends, but can rotate change in moment to center = M max for simply supported beam wl 8 2 Plates & Grids 11

12 Moment Distribution Method (a) no load Plates & Grids 12

13 Moment Distribution Method (b) add load Plates & Grids 13

14 Moment Distribution Method (c) release joint 2 Plates & Grids 14

15 Moment Distribution Method (d) release joint 3 Plates & Grids 15

16 Moment Distribution Method (e) exposure of final shape after cycles over initial shape Plates & Grids 16

17 Ribbed Plates Walter P. Moore & Assoc. Plates & Grids 17

18 Ribbed Plates typical in reinforced concrete pans can be standard or wide Plates & Grids 18

19 Ribbed Plates design them as T-beams flange compression stem compression effective flange width Plates & Grids 19

20 Plate Structures slabs & columns Plates & Grids 20

21 Two-Way Plates support conditions columns flexible (beams) simple continuous Plates & Grids 21

22 Two-Way Plates supported by columns M max at midspan of edges Plates & Grids 22

23 Two-Way Plates simply supported maximum curvature at midpoint of plate Plates & Grids 23

24 Two-Way Plates beam vs. wall supports stiffer supports, thinner slab Plates & Grids 24

25 Two-Way Plates bay proportions shorter side has bigger EI L ratio of longer side to shorter side > 1.5 acts like one-way plate Plates & Grids 25

26 Two-Way Plates moments found from tables or handbook solutions depend on support conditions Plates & Grids 26

27 Two-Way Plates other constraint conditions Plates & Grids 27

28 Design Considerations minimize bending (& depth) support conditions effective continuous edge support preferred fixed more than simple continuous surface Plates & Grids 28

29 Design Considerations (cont d) overhangs reverse curvature bay proportions < 1:1.5 load type surface or point span range rigid plates: Plates & Grids 29

30 Reinforced Concrete Design economical & common resist lateral loads Plates & Grids 30

31 Reinforced Concrete Design flat plate 5-10 thick simple formwork lower story heights flat slab same as plate 2 ¼ 8 drop panels Plates & Grids 31

32 Reinforced Concrete Design two-way joist waffle slab 3-5 slab 8-24 stems 6-8 webs beam supported slab 5-10 slabs taller story heights Plates & Grids 32

33 Reinforced Concrete Design simplified frame analysis strips, like continuous beams moments require flexural reinforcement top & bottom both directions of slab continuous, bent or discontinuous Plates & Grids 33

34 Reinforced Concrete Design one-way slabs (wide beam design) approximate analysis for moment & shear coefficients two or more spans ~ same lengths w u from combos uniform loads with L/D 3 n is clear span (+M) or average of adjacent clear spans (-M) Plates & Grids 34

35 Reinforced Concrete Design Plates & Grids 35

36 Reinforced Concrete Design two-way slabs - Direct Design Method 3 or more spans each way uniform loads with L/D 2 rectangular panels with long/short span 2 successive spans can t differ > longer/3 column offset no more than 10% span Plates & Grids 36

37 Reinforced Concrete Design Plates & Grids 37

38 Shear in Concrete at columns want to avoid stirrups can use shear studs or heads Plates & Grids 38

39 Shear in Concrete critical section at d/2 from column face, column capital or drop panel Plates & Grids 39

40 Shear in Concrete at columns with waffle slabs Plates & Grids 40

41 Openings in Slabs careful placement of holes shear strength reduced bending & deflection can increase Plates & Grids 41

42 Space Frame Behavior handle uniformly distributed loads well bending moment tension & compression couple with depth member sizes can vary, but difficult Plates & Grids 42

43 Space Frame Behavior shear at columns support conditions still important point supports not optimal fabrication/construction can dominate design Plates & Grids 43

44 Folded Plates increased bending stiffness with folding lateral buckling avoided Plates & Grids 44

45 Folded Plates common for roofs edges need stiffening Plates & Grids 45

46 Folded Plates State Farm Center (Assembly Hall), University of Illinois Harrison & Abramovitz 1963 Edge-supported dome spanning 400 feet wound with 614 miles of one-fifth inch steel wire Plates & Grids 46