Download Basis of Structural Design Structures

Basis of Structural Design
Course 1
Introduction to Structures
Structural Materials
Course notes are available for download at
http://www.ct.upt.ro/users/AurelStratan/
Structures
Man-made structures
–
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–
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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
force
strength
ductility
stiffness
deformation
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Structural materials: ductility
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
force
force
ductile
brittle
deformation
deformation
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
Material
Traditional
Granite
Limestone
Brick
Along grain
Timber
(spruce) Across grain
Modern
Portland Normal use
cement
High strength
concrete
Mild steel
High strength
steel
Iron and
Very highsteel
strength
prestressing
wires
Aluminium alloy (dural)
Stone
Ultimate strength σu
(N/mm2)
Tensile Compression
40
200
5
40
6
60
120
30
3.5
2
20
6
60
355
355
700
700
2000
-
450
450
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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×ρ×g
Tensile resistance = Area × ultimate tensile strength
R = A × σu
Equate weight to resistance:
W = R ⇒ A × L × ρ × g = A × σu ⇒
L = σu / (ρ × 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
Material
Traditional
Granite
Stone
Limestone
Brick
Along grain
Timber
(spruce) Across grain
Modern
Portland Normal use
cement
High strength
concrete
Mild steel
High strength
steel
Iron and
Very highsteel
strength
prestressing
wires
Aluminium alloy (dural)
Ultimate strength σu
(N/mm2)
Tensile Compression
40
200
5
40
6
60
120
30
3.5
-
Specific strength S (m)
Tensile
1400
225
320
24000
700
Compression
7000
1800
3200
6000
-
2
20
90
900
6
60
270
2700
355
355
4500
4500
600
600
8000
8000
2000
-
26700
-
450
450
17000
17000
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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 = σ / ε
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) nonstructural 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:
σ = A×
×L×
×ρ×g / (2A) = L×
×ρ×g / 2
– extension of the bar under its own weight
δ = σ × L / E = L2×ρ×g / (2×
×E) = L2 / (2×
×M)
– specific modulus of the material - a measure of material stiffness
M = E / (ρ×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 δ 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
Material
Modulus of elasticity
Specific modulus
E (N/mm2)
Ductility
M (m ×10
× 5)
Traditional
Granite
Limestone
Brick
Along grain
Timber
(spruce) Across grain
45 000
30 000
30 000
15 000
-
1.57
1.35
1.60
3.00
-
Portland Normal use
cement
High strength
concrete
25 000
1.12
40 000
1.80
210 000
2.80
210 000
2.80
210 000
2.80
Low
ductility
70 000
2.80
Ductile
Stone
Mild steel
Modern
High strength
Iron and steel
steel
Very highstrength
prestressing
wires
Aluminium alloy (dural)
Brittle
NA
Brittle
Large
ductility
Moderate
ductility
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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
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