S p a c e e l e v a t o r. Structure selection and design Prof Schierle 1

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1 S p a c e e l e v a t o r Structure selection and design Prof Schierle 1

2 Selection criteria: 1 Morphology 2 Capacity Limits 3 Code Requirements 4 Cost 5 Load Conditions 6 Resources and Technology 7 Sustainability 8 Synergy Structure selection and design Prof Schierle 2

3 Morphology Vertical / lateral systems: 1 Shear walls are least flexible but good for apartments and hotels with party walls 2 Cantilevers provide the least intrusion at ground floor 3 Moment frames are most flexible, good for office buildings 4 Braced frames are more flexible than walls but less flexible than moment frames bracing is usual around central cores B A B Concrete moment resistant joint: rebars extend through beam and column Steel moment resistant joint: beam flanges welded to column flanges; stiffener plates between column flanges resist bending stress of beam flanges Structure selection and design Prof Schierle 3

4 Morphology Correlation of functional and structural morphologies should be considered in selecting structural systems. Shear walls complement apartments and hotels to serve also as sound barriers between units Moment frames complement office buildings to allow flexible plans for changing needs Long span structures complement exhibit halls, auditoria and arenas for unobstructed view Morphology also applies to elements: Trusses restrict duct passage Vierendeel girders allow duct passage Structure selection and design Prof Schierle 4

5 Horizontal steel systems 1 Flush framing (top of joists flush with beams) Expensive joist/beam connections Ducts below beam increase total depth 2 Layered framing (joists on top of beams) Low-cost joist/beam connections Reduced total depth assuming: Ducts run between beams Feeder ducts between joists Small depth greatly cuts curtain wall and AC costs! 3 S-shape joist and wide flange beams 4 Beam / column moment joint 5 Twin channel beam, allows passage of pipes 6 Tubular beam and column (unusual) 7 Castillated beam cut from T-beams to increase depth and strength without material increase A Concrete slab on metal deck B Joist (S-shape, optimal spacing ~ 10 ) C Beam (wide flange, optimal spacing ~ 30 ) D Spandrel beam E Wide flange column (W14 is most common) Structure selection and design Prof Schierle 5

6 Capacity Limits Beam depth and weight increase with span very long beam fails under its own weight Economic limit is reached before most capacity is required to support self-weight Short spans cost less than long spans Just like beams, other structures have capacity limits Capacity limits include minimum spans; for example: Cost of joints makes short span trusses expensive Cost of fittings makes short span cables expensive Structure selection and design Prof Schierle 6

7 Span / depth ratios Structure elements and systems have optimal L/d (span / depth) ratios that may be defined as rule: L/d = 10 for trusses and suspension cables L/d = 20 for beams L/d = 30 for slabs and decks Chinese carpentry proportions are documented in Building Standards by Li Chieh, construction superintendent of Emperor Hui-tsung ( ); considering beauty and structure as unified theme. Structure selection and design Prof Schierle 7

8 Type of Construction examples: Type I Code Requirements Good design practice starts with code check: UBC (Uniform Bui1ding Code) and other codes define Type of Construction based on fire resistance. Floor area and height limits depend on occupancy and Type of Construction Type I may be steel, concrete, or masonry with no height and floor area limitation Type II may be steel, concrete, or masonry with some height and floor area limitation Type V Type III, IV, and V may be of any material permitted by code but are limited regarding height and floor area Codes define allowable stress and design methods for material: wood, steel, concrete, and masonry Codes define floor live loads based on occupancy and roof live load based on location Codes define design methods and required loads for gravity, wind, and seismic forces Structure selection and design Prof Schierle 8

9 Rupture Length = stress/mass ratio Cost Cost is a major and often deciding factor to select systems and material Costs of alternate systems are usually evaluated General rules: Wood structures cost less than other materials but are limited to low-rise buildings In the US wood platform framing is more common and costs less than heavy timber Short spans cost less than long spans Low-rise structures cost less than high-rise Simple structures cost less than complex ones Wall structures cost less than moment frames and braced frames A comparative cost factor: Rupture length = length at which suspended material breaks under self-weight, defined as: L r = / = stress before breakage = specific gravity Note: Rupture length defines efficiency of long-span structures, such as glass fiber fabric structures Structure selection and design Prof Schierle 9

10 Horizontal elements Span ranges and span/depth ratios of structure elements Structure and Design, page 600 Span L Depth D Span Range: Recommended min. and max. spans Span/Depth ratio: For simple supports, use average ratio Adjust Depth: heavy load and wide spacing cantilevers light load and close spacing elements with overhangs Structure selection and design Prof Schierle 10

11 Horizontal systems Span ranges, span/depth ratios, span/thickness ratios of systems Structure and Design, page 600 Span L Depth D Span Range: Recommended min. and max. spans Span/Thickness ratio: Use average ratio Adjust thickness: light load and close spacing heavy load and wide spacing Span/Depth ratio: For simple supports, use average ratio Adjust Depth: heavy load and wide spacing light load and close spacing Structure selection and design Prof Schierle 11

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14 Snow Load Conditions Location and occupancy define load conditions Roof live load is 20 psf in areas without snow, like Los Angeles, but up to 400 psf in mountains Earthquake Wind Floor load depends on occupancy, for example: Office LL = 50 psf Library stack room LL = 125 psf Light-weight structures are effective in areas of earthquakes, like California, since seismic forces are mass times acceleration (f = m a) Ductile steel and wood structures are effective to absorb dynamic seismic load Stiff concrete shear walls are effective to resist wind load but they increase seismic load Heavy structures are effective in areas of strong wind load, like Florida Thermal loads are critical in areas of great temperature variation, like Chicago Structure selection and design Prof Schierle 14

15 ASCE 7, page 10 ASCE 7 Table 4.1 excerpts of common live loads Residential and schools Office Assembly Manufacturing Library 40 psf 50 psf fixed seating = 60 psf movable seating = 100 psf light = 125 psf heavy = 250 psf reading room = 60 psf stack room = 150 psf Live load reduction Since large members are unlikely fully loaded, ASCE 7 allows live load reductions (except for public spaces and LL 100 psf): For members supporting 600 sq. ft. Reduction shall not exceed 50% for members supporting 1 floor, 60 % for members supporting 2 or more floors Structure selection and design Prof Schierle 15

16 Platform framing Heavy steel Site cast concrete Heavy timber Light gauge steel Precast concrete Resources & Technology Available resources and technology are important factors for structure systems and material. Resources: Wood structures require forests Steel structures require iron ore Concrete and masonry are widely available Technology: Platform framing is very common in the US but unfamiliar in some other countries Steel structures are common in the US Concrete is common in Asia and Europe Precast concrete requires nearby plant to reduce transportation cost Masonry: old technology, labor intensive Membrane structure: new technology Masonry Membrane Structure selection and design Prof Schierle 16

17 Sustainability Sustainability is an important factor to reduce future cost and negative impact on the environment Wood is the only renewable material with the lowest energy consumption for production But wood is combustible and not allowed for type I & II construction) Steel can be recycled but not renewed and requires more energy for production than wood Concrete can be recycled but requires more energy for production than wood Masonry can be recycled but requires more energy for production than wood Structure selection and design Prof Schierle 17

18 Synergy - pragmatic example Synergy is a system, greater than the sum of its parts. NO Synergy Synergy Comparing wood beams of 1 x12 boards. Stiffness is defined by the moment of inertia I: 1 board, I = 12x1 3 /12 I = 1 10 boards, I = 10 (12x1 3 /12) I = boards glued, I = 12x10 3 /12 I = 1000 Strength is defined by Section modulus S = I/c: 1 board, S = 1/o.5 S = 2 10 boards, S = 10/0.5 S = boards, glued, S =1000/5 S = 200 Note: The same amount of material is 100 times stiffer and 10 times stronger when glued to resist shear to engage fibers in tension and compression. Structure selection and design Prof Schierle 18

19 Design Synergy Gothic cathedral example Columns define plan and circulation Vaults define spatial character Buttresses resist vault thrust and define facade Structure selection and design Prof Schierle 19

20 Olympic Dome, Rome Architect: Piacentini Engineer: Nervi Synergy Prefab ribs: Resist buckling Provide lighting Enhance acoustics Define gestalt a stroke of genius Structure selection and design Prof Schierle 20

21 Prestress The effect of prestress on cable structures is shown on a wire with and without prestress, under a load P applied at its center 1. Wire without prestress resists load P in upper link only wire force F = P 2. Wire with prestress PS resists load P in upper and lower link upper link increases F = PS + P/2 lower link decreases F = PS P/2 prestress reduces deflection to half 3. Stress/strain diagram A Stress/strain without prestress B Stress/strain with prestress C Prestress reduced to zero (PS=0) D Prestress wire after PS=0 Note: Prestress should be half the stress under load + a reserve for thermal variation Structure selection and design Prof Schierle 21

22 Schematic design Global moment and shear may be used to analyze Elements like beam, truss, cable or arch. They all resist the global moment by a horizontal couple. The product of couple force F and its lever arm d resist the global moment: M = F d hence F = M / d Designation of force F varies for different structures: T (tension), C (compression), H (horizontal reaction). For simple support and uniform load M and V are: M = w L 2 / 8 V = w L / 2 M = max. global moment V = maximum global shear w = uniform load per unit length L = span For other load or support conditions M and V are computed as for equivalent beams. Structure selection and design Prof Schierle 22

23 Assuming simply supported condition and uniform load, the max. global shear occurs at both supports and max global moment at mid-span Beam Beams resist bending by a couple, with 2/3 beam depth d as lever arm; compression C on top and tension T on bottom. Truss Trusses resist the global moment by a couple, with truss depth d as lever arm; compression C in top and tension T in bottom chord. Max. moment yields max. chord forces. C = T =M / d Web bars resist shear. Max. support shear = max. web force Cable Suspension cables resist the global moment by a couple, with sag f as lever arm. The resisting couple consists of horizontal reaction H and horizontal cable force at mid-pan; with max. cable force at supports, where H, vertical reaction R and cable tension T form an equilibrium vector triangle: T = (H 2 + R 2 ) 1/2 Arch Arches resist global moments by a couple like cables, but in compression instead of tension: C = (H 2 +R 2 ) 1/2 Structure selection and design Prof Schierle 23

24 Radial pressure Referring to A: Radial pressure per unit length acting on a circular ring yields ring tension T = R p T = ring tension R = radius of ring curvature p = uniform radial pressure per unit length Units must be compatible: If p is force per foot, R must be in feet If p is force per meter, R must be in meters. Pressure p acting reversed toward the ring center would reverse tension to compression. Proof Referring to ring segment B: T acts normal to radius R p acts normal to ring segment of length 1 Referring to ring segment B and polygon C: p and T in C represent equilibrium at o in B, thus T / p = R / 1 (similar triangles) hence T = R p Structure selection and design Prof Schierle 24

25 S p a c e e l e v a t o r Structure selection and design Prof Schierle 25