lessen of steel design

8/9/2019 Lessen of Steel Design

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Eurocode 3-1-1: 2.2.2.2 (3)

The self-weight of the structure may, in most

cases, be calculated on the basis of the nominal

dimensions and mean unit masses.

Eurocode 3-1-1: 2.3.2.4 (6)

The self-weight of any unrelated structural or

non-structural elements made of different

construction materials should be treated as

different permanent actions.

Self-weights calculationSelf-weights calculation

Calculating the self-weight of the following floor constructionCalculating the self-weight of the following floor construction

Floor constructions of commercial building

consists of

50 mm sand/cement screed (tasoituslaasti)

150 mm normal weight reinforcement concrete

slab

12 mm plaster(gypsum mortar) ceiling


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Materials Density γγγγ

[kN/m3]

concrete (see ENV 206)

Lightweight (varies with density class) 9 - 20

normal weight *24

heavyweight >28

reinforced and prestressed concrete;

unhardened concrete

+1

mortar

cement mortar 19 - 23

gypsum mortar; lime mortar 12 - 18

lime-cement mortar 18 - 20


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Component Density

(kN/m3)

Thickness

(m)

Load intensity= density

×××× thickness (kN/m2)

Screed 20

(19 - 23)

0,05 20 ×××× 0,05 = 1,0

Slab 24 0,15 24 ×××× 0,15 = 3,6

Plaster 15(12 - 18)

0,012 15 ×××× 0,012 = 0,2


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A building in Helsinki with duo pitched roof,calculating the snow load distributions.

αααα 1 24

αααα 2 36

s = µ·sks = µ·sk


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αααα [0° 15°] [15° 30°] [30° 60°] ≥≥≥≥

60°

µµµµ1 0.8 0.8 0.8(60 - αααα)/30 0.0

µµµµ2 0.8 0.8 + 0.6(αααα-15)/30 1.1(60-αααα)/30 0.0

µµµµ 2.24 0.8 0.6

24 15−( )

30⋅+:= µµµµ 2.24 0.98

µµµµ 1.36 0.8 60 36−( )

30⋅:= µµµµ 1.36 0.64

µµµµ 1.24 0.8

µµµµ2.36

0.88µµµµ 2.36 1.1

60 36−

30⋅:=


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0.980.98 0.640.64

0.5x0.8=0.40.5x0.8=0.4

0.80.8

0.880.88

0.5x0.64=0.320.5x0.64=0.32

The characteristic snow load on the ground sk is

2.0 kN/m2. The possible snow loads on the roof

are:

0.98x2=1.960.98x2=1.96 0.64x2=1.280.64x2=1.28

0.4x2=0.80.4x2=0.8

0.8x2=1.6

0.8x2=1.6

0.88x2=1.760.88x2=1.76

0.32x2=0.640.32x2=0.64

In most cases it may be conservatively assumed

that maximum snow load intensity is applieduniformly across the full width


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Persistent and transient design situations for

verifications other than those relating to fatigue

(fundamental combination)

Σγ G.j Gk.j + γ Q.1Qk.1 + Σγ Q.j Ψ0.iQk.i (1)

Accidental design situation

Σγ G.A Gk.j + Ad + Ψ1.1 Qk.1 + ΣΨ2..iQk.i (2)

For building structures, as a simplification, (1)

can be replaced by whichever of the following

combination gives the larger value:

Σγ G.j Gk.j + γ Q.1Qk.1

Σγ G.j Gk.j + 0.9Σγ Q.j Qk.i

Combination of actions for ultimate limit designCombination of actions for ultimate limit design


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Three combinations of actions are defined:

Rare combination

ΣGk.j + Qk.1 + ΣΨ0.iQk.i (1)

Frequent combinationΣGk.j + Ψ1.1 Qk.1 + ΣΨ2..iQk.i (2)

Quasi-permanent combinations

ΣG

k.j+ΣΨ2..i

Qk.i

(3)

For building structures, as a simplification, (1)

can be replaced by whichever of the following

combination gives the larger value:

ΣGk.j + Qk.1

ΣGk.j + 0.9Σ Qk.i

Combination of actions for serviceability limit designCombination of actions for serviceability limit design


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Eurocode 3-1-1: 2.3.2.3 (5)

For continuous beams and frames, the same

design value of the self-weight of the structure

may be applied to all spans, except of cases

involving the static equilibrium of cantilevers

Load combinationsLoad combinations

Write the critical load combination for continuous beam with

permanent load and imposed load

Write the critical load combination for continuous beam withpermanent load and imposed load

Eurocode 3-1-1: 2.3.2.4 (3)

Variable actions should be applied where they

increase the destabilizing effects but omitted

where they would increase the stabilizing

effects


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Load combination 1: maximum bending in span 1

Load combination 1: maximum bending in span 1


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Load combination 2: maximum bending in span 2Load combination 2: maximum bending in span 2


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Span LSpan L

SpacingSpacing

SpacingSpacing

snow load ssnow load s

purlinspurlins

purlinpurlin

purlinpurlin

Sheeting gSheeting gSheeting gSheeting g


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Write load combinations for ultimate limit state

Basic load combination ruleBasic load combination rule

Point load and

distributed load

Point load and

distributed load

Two variable loadingsTwo variable loadings


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Combination

Case aCase a


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Final critical load combinationFinal critical load combination

Case bCase b


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Load combinationLoad combination

aa

bb

1.35 g⋅ 1.5 q F+( )⋅+

1.35 g⋅ 0.9 1.5⋅ q F+( )⋅+

F is assumed to be variable load in

this example and can be added to q

F is assumed to be variable load in

this example and can be added to q


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Final critical load combinationFinal critical load combination

Case aCase a

Case bCase b

M max max M max_a M max_b,( )


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aa

Determine the maximum

bending moment in Member 1

Determine the maximum

bending moment in Member 1

11

22

the moment of inertia of member

1 and 2 are the same

the moment of inertia of member

1 and 2 are the same

L = hL = h

1.35 g⋅ 1.5 s⋅+ snow load dominatessnow load dominates


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bb 1.35 g⋅ 1.5⋅+ wind load dominateswind load dominates


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cc 1.35 g⋅ 1.35 s W+( )⋅+


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The final critical load will be the one with the maximum

bending moment from the following figures

The final critical load will be the one with the maximum

bending moment from the following figures

aa

bb

cc


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General

• Applied to ultimate Limit State

Design

• Benefits of classifying cross-sections

– guide selection of globe analysis – determine the design criteria of

member

• Rules that guide the classification

– Width-to-thickness ratio – yield strength

– loading: bending, compression, bending+compression

• Based on normal stress. Shear buckling is considered separately indesign rules


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outstand flangeoutstand flangenormal stress


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loading cases: bending or compression


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(d)

(c)

(b)(a)

Simply supported onall four edges

t

L

b

Simply supported

edge

Free

edge

b

L

1

2

3

4

5

1 2 30 4 5

Plate aspect ratio L / b

Buckling coefficient k

b

L FreeExact

k = 0.425 + (b/L)2

0.425

( )2

2

2

112

−=

b

t k cr

σ

width to thickness ratio


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Class 1Class 2

Class 3

Euler Buckling Stress

0,5 0,6 0,9

1

1,0 λ p

N f p

u

y

= σ

==

k 4.28

/5.0

σ

λ t b

cr

( )2

2

2

112

−=

b

t k cr

σ

Np = σu / f y


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Outstand

Internal

Web

Flange

Web

Internal

Flange

(a) Rolled I-section (b) Hollow section

Flange

(c) Welded box section

InternalOutstand

InternalWeb

Internal: webs of open beams, flanges of boxes

Outstand: flanges of open section, legs of angles


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a. Webs: (internal elements perpendicular to axis of bending)

tw twd

tw d tw

tf

hdAxis of

Bending

d = h-3t (t = tf = tw)

ClassWeb subject to

bending

Web subject to

compression

Web subject to bending

and compression

Stressdistribution in

element(compression positive)

+ f y

f y -

d h

+ f y + f y

f y - f y -

d h hdαd

when α > 0,5:d/t w < 396ε/(13α − 1)when α < 0,5:

d/t w < 36ε/α

_

_

1 d/t w < 72ε _ d/t w < 33 ε _

d/tw < 83 ε _ d/t w < 38ε _ 2

when α > 0,5:d/t w < 456ε/(13α − 1) _ when α < 0,5:d/t w < 41,5ε/α _

Stress

distribution inelement

(compression positive)

+ f y

f y -

+ f y

+ f y

ψ f y -

d/2

d/2h

+

d h d h

3 d/t w < 124 ε _ d/t w < 42 ε _

when ψ > −1:d/t w < 42ε/(0,67 + 0,33ψ) _

when ψ < −1: _

d/t w < 62ε/(1 − ψ) (− )ψ

ε = f y/235f y

ε

235 275 355

1 0,92 0,81

_


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b. Internal flange elements: (internal elements parallel to axis of bending)

axis of

bending

b tf t f b

tf

b

b tf

Class TypeSection in bending

Section in compression

Stress distribution

in element andacross section

(compression

positive)

+-

f y

- +

+-

f y

- +

1

Rolled hollow section

Other

(b - 3t f )/ t f

b / t f


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33/34

ε= √235/355 = 0.8136

Welded profile, flange

9ε = 7.3 10ε = 8.1 14ε = 11.4

Web

33ε = 26.8 38ε = 30.9 42ε = 34.2


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(a) Class 4 cross-sections - axial force

Gross cross-section

Gross cross-section

Centroidal axis of

gross cross-section

Centroidal axis ofgross cross-section

Centroidal axis ofeffective cross-section

Non-effective zones

Non-effective zone

Non-effective zone

Centroidal axis

Centroidal axisCentroidal axis of

effective section

e N

eM

e M

Centroidal axis ofeffective section

lessen of steel design

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