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Samenvatting simulatie van structuurelementen Mario Rinke
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- Universiteit Antwerpen (UA)
Samenvatting van de ppt's, lessen en engelse teksten van deel 2 van simulatie van structuurelementen door Mario Rinke
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Samenvatting simulatie van structuurelementen deel 2 Fien SmessaertContents
H0: English vocabulary ............................................................................................................................ 2
H1: Physical models and design in civil and building engineering by Bill Addis ...................................... 3
H2: Arches ............................................................................................................................................... 6
H3: Cable networks, tents and membranes ............................................................................................ 9
H4: Vaults, Domes and shells ................................................................................................................ 10
4.1 Vaults ........................................................................................................................................... 10
4.2 Domes.......................................................................................................................................... 12
4.3 Shells............................................................................................................................................ 12
H5: Trusses ............................................................................................................................................ 13
H6: Stability of compressed members .................................................................................................. 17
H7: Case study Antoni Gaudi 1852-1926............................................................................................... 18
H8: Case study Heinz Iszler 1926-2009 ................................................................................................. 19
H9: Stability ........................................................................................................................................... 21
H10: Frei Otto 1925-2015...................................................................................................................... 23
56 bladzijden tekst:
Examen: in Engels en nederlands: principe, concept, kennis van structuren en toepassingen kunnen
uitleggen → most important relations between typology types, exam single, multiple choice and
open questions, no details about forces, no calculations
bv. explain the difference between a truss and a solid beam. → key thoughts that we discussed
SYSTEM OF INCREASING COMPLEXITY:
Cable → Arch → Cable-Arch → Truss → Slab wall
When extend structures in the space, 3D structures:
Cable-net → Shell / Vault (gewelven) → Spatial Cable-Arch → Grillage
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,H0: English vocabulary
ENGLISH: DUTCH:
Compression Druk
Rampant arch Steunboog
Vicinity Omgeving
Deflecting Afbuigen
To deduce Afleiden
Slenderness ratio Slankheid verhouding
Parabola Parabool
Catenary Kettinglijn
Slope Helling
Ultimate limit state Uiterste grenstoestand
Additional load Bijkomende belasting
Provisions Voorzieningen
Indispensable Onmisbaar
Inevitable Onvermijdelijk
Load-bearing Dragend
Strut Stut
To constrain Beperken
Hinges Scharnieren
Therefore Daarom
To coincide Samenvallen
Barycentric line Zwaartelijn
Ductility Ductiliteit / vervormbaarheid
Indeterminancy Onbepaaldheid
To establish Bewerkstelligen / realiseren
Statically indeterminate Statisch onbepaald
To distinguish Onderscheiden
Weakening Verzwakking
Reinforced Versterkt
Sturdy Stevig
eccentricity Excentriciteit / afwijking van cirkelbaan
Vault Gewelf
Kink Knik
Barrel vault Tongewelf
Groined vault Gegroefd gewelf
Cloister vault Kloostergewelf
To attach Bevestigen
To compare Vergelijken
Folded slabs Gevouwen platen
Resin model Harsmodel
2
,H1: Physical models and design in civil and building engineering by Bill
Addis
THE SCOPE OF THE CIVIL AND BUILDING ENGINEER:
➢ Bridges – arch, girder (ligger), truss, suspension,
➢ Hydraulic engineering – river channels, dams, harbours, coastal erosion, flood defences
(waterkeringen)
➢ Structural engineering for buildings – arch, vault, dome, roof truss, building facade and envelope,
➢ Earthquake-resistant structures – dams, buildings, bridges
➢ Wind loads on structures and air movement around and within buildings
➢ Acoustic performance of concert halls, theatres, congress halls
THE TASK OF THE ENGINEER:
➢ To propose DESIGNS for structures or other constructions that will meet a certain need or SOLVE A
PROBLEM → designen zaken
➢ To raise to a sufficient level the CONFIDENCE of the engineer and builder, that a proposed
structure can be constructed and, once constructed, will work as intended → genereren
vertrouwen in gebouwen (zodat ze stevig genoeg zijn)
➢ To provide DIMENSIONS of components and their relative disposition, as well as MATERIALS
SPECIFICATIONS, to enable a contractor to begin construction → gedetailleerd niveau →
dimensionering van elementen (door berekeningen) en materiaal specificaties
All thinking about structural behaviour uses models → PHYSICAL of MATHEMATICAL models
OPMERKING: modelijk lijkt stevig > < praktijk 100 x zwaarder terwijl maar 10 x grotere dimensies →
opletten voor STIJFHEID en STABILITEIT
OPMERKING: METHODE VAN INGENIEUR > < METHODE VAN MODELLEN (ARCHITECTEN) VOORSPELLING zie schema
WHY DO ENGINEERS USE PHYSICAL MODELS? When no other means are available to achieve the necessary
level of confidence that a design will be satisfactory
(safe):
➢ Engineering theory is inadequate
➢ Calculations are too complex or would take too long
➢ The structure is highly redundant → structuur is te
moeilijk om te ontrafelen, reduntant
➢ The structure is without precedent
HOOKE’S LAW OF THE CATENARY:
➢ In 1585 Simon Stevin defined the equilibrium shape of
a chain loaded with various weights as a CATENARY
➢ In around 1665, Robert Hooke showed that THE FORM OF A STABLE ARCH (in which only
compression forces are acting, no bending or tension) IS THE SAME AS THAT OF A HANGING
CHAIN (in which only tension forces are acting, no bending or compression), BUT INVERTED.
MODELS AND PRINCIPLE OF SCALE:
MODELS AND THE QUESTION OF SCALE: Some structural phenomena vary LINEARLY WITH SCALE:
➢ Linear dimensions
3
,➢ Shape of a hanging chain
➢ Stability of masonry (metselwerk) structures against overturning
➢ Stability of masonry compression structures (arch, vault, dome – following Hooke’s catenary
law)
Other structural phenomena DO NOT VARY LINEARLY WITH SCALE:
➢ Mass of a structure → varies as the cube of the linear scale (GALILEO recognized the “square :
cube law” in 1638) → MASSA variëert met 2e macht
➢ Strength and stiffness of a beam → vary as the square of the linear scale → STERKTE en STIJFHEID
variëert met vierkantswortel
➢ Buckling resistance of a strut or a concrete shell
Hence, scale models work in an intuitive (linear) way for masonry structures, but not for structures
that rely on BENDING or BUCKLING. The Roman engineer VITRUVIUS reports that military engineers knew
they could safely scale up the behaviour of some types of SMALL-SCALE MODELS BY LINEAR PROPORTION,
but not others.
SCALING FACTORS WHEN YOU KNOW THE ENGINEERING SCIENCE: You can calculate the relation between model
behaviour and full size behaviour. For example, for the BENDING OF A STEEL FRAME:
𝑊𝐿3
DEFLECTION (AFBUIGING), y, is proportional to 𝐸𝐼
If scale factors are chosen as follows:
➢ Scale factor, λ, length, L → 1 : 40
➢ Scale factor, λ, I → 1 : 150,000
➢ Scale factor, λ, loads, W → 1 : 200
➢ Scale factor, λ, E → 1 : 5
➢ Then the Scale Factor for deflections → 1 : 17.1
SCALING FACTORS WHEN YOU DO NOT KNOW THE ENGINEERING SCIENCE: If a ratio of certain physical variables
can be found which has no dimensions, then this ratio will be independent of LINEAR SCALE. This
method was first used in HYDRAULIC ENGINEERING by William Froude in the 1870s → he used the
𝑉²
dimensionless ratio (𝐿𝑔 ) to scale up results of tests on 1:20 scale models (2 m long) to determine the
RESISTANCE to motion of full-size ship hulls.
MECHANICAL AND CONSTRUCTION MODELS:
o bv. moving the Vatican Obelisk 150 m. Domenico Fontana 1586
o bv. Machines – e.g. pile drivers, cranes, pumps (this one at Augsburg Museum)
o bv. Roof trusses – since ancient times
o bv. Grubenmann bridges 1750s-80s
o bv. Construction mechanisms. e.g. Mamoru Kawaguchi, Japanese architect
THE USE OF MEASUREMENT MODELS FOR BRIDGE DESIGN 1750S TO TODAY:
o bv. Caspar Walter 1766 – in Brückenbau → 1:20 scale models loaded with 1.25t (corresponding to
25t full-size capacity). Euler (1776) argued that such linear scaling for timber bridges is invalid
o bv. Hanging chain to measure precise geometry, Thomas Telford, 1814
o bv. Fairbairn and Hodgkinson, Britannia Bridge (180m main span) 1846-47 → 𝑜ver 40 model tests
from about 1:20 to 1:6 scale (c.25m long), special form
4
,o bv. Fritz Leonhardt, 1961 → Model studies for a cable-stayed bridge.
THE USE OF MEASUREMENT MODELS FOR DAM DESIGN 1890S-1930S:
o bv. Assuan dam, Benjamin Baker 1895-1905 → models made model of “ordinary jelly” “in an
hour” → to check stress distribution on the base – uniform or parabolic? Tension on water side?
Deformation of rock beneath? Jelly method
Later, in Assuan, he did tests on “a dozen stiff jelly models” “in 3 or 4 hours” to determine the
feasibility of raising the dam. He persuaded people that “it was not such a simple problem as it
seemed at first”
o bv. Aitcheson & Pearson, 1904 → model made of pieces of wood to create internal friction to
determine collapse mechanism (vertical shear) and if the line of thrust was inside the middle
third? (No)
o bv. Wilson & Gore, 1908 → Made model of India rubber 150mm high, measurements to 0.025mm
o bv. Stevenson Creek Test Dam, 1925-30 → A full size experimental structure by the (US) Bureau of
Reclamation → A thin shell (arch) dam, 100’ radius (30m), 60 feet high (19m), top half 2 feet
thick (60cm), bottom half thickens to 7’6” → Beggs’ used Celluloid for 1:40 scale models of
vertical and horizontal cross-sections → measuring to “one-millionth of an inch”
THE USE OF MEASUREMENT MODELS FOR CONCRETE SHELL DESIGN 1920S TO 1970S:
o bv. Sydney Opera House, 1962-63 → model in micro-concrete
o bv. Library roof, Basel, 1962-64, Heinz Hossdorf → model in acrylic
MEASUREMENT OF DEFORMATIONS AND STRESSES IN STRUCTURAL MODELS:
o bv. Pier Luigi Nervi and Guido Oberti, 1935. Hangar in Orvieto → 1/37 scale Celluloid model,
tested in the elastic range
o bv. German Pavilion, Expo’67, Montreal, Frei Otto → Double exposure photograph to measure
deflections of the cable net and device for measuring tension in cables
THE USE OF MEASUREMENT MODELS FOR SHELL STRUCTURES A CASE STUDY:
o bv. Garden festival building, Mannheim, 1973, Frei Otto and Arup → a lot of hangmodels
GARDEN FESTIVAL BUILDING, MANNHEIM, 1973, FREI OTTO AND ARUP:
➢ A wire-mesh model about 1:300 scale To establish the basic form
➢ More accurate, hanging-chain model 1:98.9 to determine the geometry of the boundary
scale supports
➢ Perspex model 1:200 scale wind-tunnel model, loads due to wind
➢ Perspex model of Essen gridshell 1:16 scale To test the modelling technique
➢ Perspex model of main shell at Mannheim 1:60 Structural behaviour under model loads
scale
➢ Woven wire mesh model 1:60 scale determine the number and positions of
cranes
o bv. Bundesgartenschau Multihalle, Mannheim 1973-74, 1:300 scale wire mesh to establish basic
form → 1:200 scale wind tunnel model Pressure measurement & Flow visualization, 1:60 wire-
mesh model to study deformations during erection
THE USE OF MEASUREMENT MODELS FOR WIND LOADS ON STRUCTURES 1890S TO TODAY:
➢ Wind tunnel models to determine wind loads and areas of turbulence
5
, o Empire State Building, 1930
o A recent high-rise building, with pressure taps (drukkranen)
➢ Flow visualisation to identify turbulence and formation of eddies (vorming van wervelingen)
THE USE OF MEASUREMENT MODELS FOR ACOUSTIC DESIGN OF THEATRES, OPERA HOUSES, … 1920S TO TODAY:
➢ Acoustic models 1920s to 1930s
➢ Acoustic models 1950 to today
THE USE OF PHYSICAL MODELS FOR FORM-FINDING OF SHELL AND MEMBRANE STRUCTURES:
➢ HOOKE AND WREN, St Pauls. 1670s → The hanging chain – funicular shapes
➢ HEINRICH HÜBSCH, 1830s
➢ FRIEDRICH GÖSLING, 1890s
➢ ANTONI GAUDÍ, Colónia Güell, Barcelona, 1890s
➢ HEINZ ISLER, 1960s-1990s
➢ FREI OTTO 1960-90 → soap film and fabric models and Montreal Expo 1967 → cable net structures
and Frei Otto + Buro Happold → Jeddah Sports Hall, 1982 → soap film, chain and net models
H2: Arches
ARCHES AND VAULTS:
Dual structures: arches are inverted cables
ROBERT HOOKE, HANGING CHAIN: “As hangs a flexible cable so, inverted, stand the touching pieces of an
arch"
Par example: arches in the Gallerie Vittorio Emanuele by Giuseppe Mengoni
The study of structures subjected to COMPRESSION:
bv. man leaning against wall, rampant arch gothic cathedral
Comparison with structures in tension → similarities, independent of type of load
IDEAL FORM OF AN ARCH → identical to a CABLE subjected to the same load but UPSIDE-DOWN
STRUCTURES UNDER TENSION: STRUCTURES UNDER COMPRESSION:
The structure carries the load by deflecting The load is still in equilibrium with the two
(afbuigen) until the point in which the force of stresses that are deviated → concave shape
deviation (afgeleide kracht) of the stresses → similar configuration to that of CABLES
corresponds to the load itself.
Analysis with free bodies and Cremona diagram
→ similar to cables
𝑙
If slenderness ratio 𝑓 is the same as cable (→
poles are identical) then the vectors in diagram
are also identical
➢ VERTICAL FORCES ON THE SUPPORTS: identical to those of the cable
➢ HORIZONTAL FORCES ON THE SUPPORTS: same intensity but OPPOSITE DIRECTION of cable
➢ INTERNAL FORCES: same intensity, but in COMPRESSION rather than in tension
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