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



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� 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


� "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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� 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

Documents

Basis of Structural Design Structures