Basis of Structural Design Structures
Transcript of Basis of Structural Design Structures
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Basis of Structural Design
Course 1
Introduction to Structures
Structural Materials
Course notes are available for download athttp://www.ct.upt.ro/users/AurelStratan/
Structures
� Man-made structures
– buildings
– bridges
– dams
– masts
– drilling platforms
– ships aircrafts, etc.
� Natural structures
– skeleton of animals
– shell of snails
– spider's web
– tree trunk and branches, etc.
� Structure: something which carries weight or resists loads and forces, and which may form a protective cover or skeleton for an object or living thing.
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Some structures can fail
� 12.02.2009. Mall under construction in Oradea
Some structures can fail
� 12.02.2009. Mall under construction in Oradea
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Some structures can fail
� 12.02.2009. Mall under construction in Oradea
Some structures can fail
� 12.02.2009. Mall under construction in Oradea
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Some structures can fail
� 19.12.2008 – failure of a silo near Vinga
Design criteria
� Suitability for its function: a building should be designed and realised in a manner that will offer to its users a certain function
� Safety and serviceability:
– Structures should resist loads and other external actions without
collapse, protecting its inhabitants
– Structures should not develop excessive deformations and
cracks, nor vibrate alarmingly
� Aesthetics: buildings should be aesthetically pleasant, both individually and as a group
� Economy: generally, the above three criteria need to be fulfilled with a limited budget
– Cost to design and build a structure
– Maintenance cost during the planned life
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Structural materials
� A building consists of the structure and other components used in order to protect and provide for building function and aesthetics (cladding, partitions, floors, etc.)
� Structural material is the one which is used in those parts of the structure which carry loads and give it strength and stiffness
� Properties of structural materials:
– strength
– stiffness
– ductility
.
.
.
deformation
Structural materials: properties
� Strength (ultimate stress): the stress (load per unit area of the cross-section) at which the failure takes place
– tension
– compression
� Stiffness: the resistance of an elastic body to deformation
� Ductility: capacity of the material to deform into the inelastic range without significant loss of its load-bearing capacity
ductility
stiffness
strength
force
deformation
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Structural materials: ductility
ductile
force
deformation
brittle
force
deformation
� Ductile materials: able to deform significantly into the inelastic range
� Brittle materials:
– fail suddenly by cracking or splintering
– much weaker in tension than in compression
Structural materials
� "Traditional" materials: used by builders and engineers since the ancient times
� Stone and timber: occur naturally
� Bricks: man-made
– sun-dried clay/mud bricks - from 4500 B.C.
– fired bricks - from 3000 B.C.
– calcium silicate bricks
� Ancient concrete:
– lime mixed with stone and sand: early civ. of the Middle East
– "hydraulic cement" - lime, stone, sand and silicates: Romans
� Stone, bricks, ancient concrete:
– weak
– weaker in tension than in compression
� Stone and bricks masonry: units interconnected by even weaker mortar
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Structural materials
� Timber:
– substantial tensile strength along the grain
– weak in compression and across the grain (difficult to realise
connections in tension)
� "Modern" materials: Portland cement concrete, steel, aluminium , etc.
� Portland cement concrete:
– mixture of Portland cement, water, aggregates
– weaker in tension
– brittle
� Steel (iron with low carbon content) and Aluminium (duraluminium alloy):
– strong in tension and compression
– ductile
Structural materials: strength
-2000
Very high-strength
prestressingwires
202Normal usePortland cement
concrete
Mo
de
rn
606High strength
355355Mild steel
Iron and steel
700700High strength steel
450450Aluminium alloy (dural)
-3.5Across grain
30120Along grainTimber (spruce)
CompressionTensile
606Brick
405Limestone
20040GraniteStone
Tra
ditio
nal
Ultimate strength σσσσu
(N/mm2)Material
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Specific strength
� All structures have to support their own weight
� Can the size of a structure be increased indefinitely for it to be able to carry its own weight?
� Problem: how long a bar of uniform cross-section can be before it breaks due to its own weight?
� Equate the weight of the bar to its tensile strength:Weight = Tensile resistance
Specific strength
� Weight = Volume ×××× specific weight
W = A ×××× L ×××× ρρρρ ×××× g
� Tensile resistance = Area ×××× ultimate tensile strength
R = A ×××× σσσσu
� Equate weight to resistance:
W = R ⇒⇒⇒⇒ A ×××× L ×××× ρρρρ ×××× g = A ×××× σσσσu ⇒⇒⇒⇒
L = σσσσu / (ρρρρ ×××× g) = S = specific strength
� There is an absolute limit (= S) to the length that the bar can attain without breaking
� Larger a structure is, larger is the proportion of its own weight to the total load that can be carried by itself
� First to realise this: Galileo Galilei
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Specific strength
� For structures subjected to tension/compression, as the size of an object increases, its strength increases with the square of the ruling dimensions, while the weight increases with its cube
� For each type of structure there is a maximum possible size beyond which it cannot carry even its own weight
� Consequences:
– it is impossible to construct structures of enormous size
– there is a limit to natural structures (trees, animals, etc.)
– larger a structure becomes, stockier and more bulky it gets
• large bridges are heavier in proportions than smaller ones
• bones of elephants are stockier and thicker than the ones of mice
– proportions of aquatic animals are almost unaffected by their size
(weight is almost entirely supported by buoyancy)
Specific strength
-26700-2000
Very high-strength
prestressingwires
90090202Normal usePortland cement
concrete
Mo
de
rn
2700270606High strength
45004500355355Mild steel
Iron and steel
80008000600600High strength steel
1700017000450450Aluminium alloy (dural)
-700-3.5Across grain
60002400030120Along grainTimber (spruce)
CompressionTensileCompressionTensile
3200320606Brick
1800225405Limestone
7000140020040GraniteStone
Tra
ditio
nal
Specific strength S (m)Ultimate strength σσσσu
(N/mm2)Material
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Specific strength
� Stone, brick and concrete: used in compression
� Steel: used in tension
� Timber: excellent performance in terms of specific strength, especially in tension
� Aluminium: high specific strength
� Aircrafts must carry loads and must be capable of being
raised into the air under their own power ⇒⇒⇒⇒ materials with high specific strength
– wood was extensively used in early planes
– modern material: aluminium
Structural materials: stress-strain curves
� Stress-strain curves provide "at a glance" information on:
– strength
– stiffness
– ductility
� Elastic region
� Inelastic region
� Steel: elastic region is almost linear
� Stone, brick, concrete, aluminium:elastic region is not linear
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Structural materials: stress-strain curves
� Steel and aluminium: excellent ductility
� Concrete, brick: brittle
� Modulus of elasticity: E = σσσσ / εεεε
� Unloading after loading in the elastic range ⇒⇒⇒⇒ NO permanent deformations
� Unloading after loading in the inelastic range ⇒⇒⇒⇒permanent deformations present
� Permanent deformations need to be avoided in structures
under service loads ⇒⇒⇒⇒ stresses should be kept in the elastic region under service loads
� factor of safety = ultimate strength / design stress
Structural materials: stiffness
� Excessive flexibility is undesirable in structures
– people dislike noticeable vibration and deflections in buildings
and bridges
– large vibrations and deflections can damage (brittle) non-
structural components (partitions, glazing, floors, etc.)
� Materials with large stiffness are generally desirable (steel is more advantageous than aluminium from this point of view)
� Elastic efficiency of materials:
– average stress in the bar:
σσσσ = A××××L××××ρρρρ××××g / (2A) = L××××ρρρρ××××g / 2
– extension of the bar under its own weight
δδδδ = σσσσ ×××× L / E = L2××××ρρρρ××××g / (2××××E) = L2 / (2××××M)
– specific modulus of the material - a measure of material stiffness
M = E / (ρρρρ××××g)the higher the value of M, the less it will extend under its own
weight
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Structural materials: stiffness
� The extension δδδδ of a bar under its own weight is proportional to the square of the scale (a bar which is 10 times longer than a reference one will extend 102 = 100 times more than the reference one)
Structural materials: stiffness and ductility
Low ductility
2.80210 000
Very high-strength prestressingwires
Brittle1.1225 000Normal usePortland
cement concrete
Mo
de
rn
1.8040 000High strength
Large ductility
2.80210 000Mild steel
Iron and
steel
Moderate ductility
2.80210 000High strength steel
Ductile2.8070 000Aluminium alloy (dural)
--Across grainNA
3.0015 000Along grainTimber (spruce)
DuctilitySpecific modulus
M (m × × × ×105)
Modulus of elasticity E (N/mm2)
1.6030 000Brick
1.3530 000Limestone Brittle
1.5745 000GraniteStone
Tra
ditio
nal
Material
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Structural materials: ductility
� Ductility is important for the "ultimate" behaviour of structures
� Most structures are designed to respond in the elastic range under service loads, but, given the uncertainties in real strength of material, behaviour of the structure, magnitude of loading, and accidental actions, a structure can be subjected to inelastic deformations
� A ductile material will sustain large deformations before collapsing, "warning" the people inside
� A ductile material allows for redistribution of stresses in statically indeterminate structures, which are able to support larger loads than in the case of a structure realised of brittle material