design philosophy.pdf

7/30/2019 Design philosophy.pdf

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CSE 362 Design of Steel StructuresDesign philosophy, allowable stress design, design examples,limit stress design, comparison

Professor K.F. ChungProfessor K.F. Chung

Department of Civil and Structural EngineeringThe Hong Kong Polytechnic University

Hong Kong SAR, China

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Overall stability / equilibrium considerations / Linear elastic design

ACTION RESISTANCE

Section capacityAxial forces

Tension

Compression

where F is the applied forceA is the cross-sectional areaDesign is the design strength

Shear force

Bending moment

DesignA

F =

Design

A

F =

DesigntI

yAS =

DesignZ

M =

Allowable stress design


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F = 100 kN

DataDesign strength of mild steely,ASD = 165 N/mm

2

Consider

DesignAF =

A

FDesign

165

10x100

FA

3

Design

required =

Use a 25 x 25 mm square rod with the following cross-sectional area:

A = 625 mm2 Arequired = 606 mm2

Design of a tie

= 606 mm2

4

DataP = 10 kNDesign strength of mild steelDesign = 165 N/mm

2 or 0.6 x 275 N/mm2

Density of steel = 7850 kg/m3

Unit cost= $20 /kg

Assume no instability.

Truss 1

AB

C

P1.0 m

1.0 m

-P

P2+

LABLAC

Truss 2

A

B

C

P

1.0 m

1.0 m

+P

P2LABLAC

2.0 m

Truss 3

A

C

P

LABLAC

B

2

P+

2P

1.0 m

Design of a two-member truss


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Member Length (m) Total length (m) Force (kN)

Tensionmembers

AB 2.8

7.6

141

BC 2.0 200

CE 2.8 283

Compressionmembers

AD 4.0

10.8

100

BD 2.8 141CD 2.0 200

ED 2.0 200

2.0 m 4.0 m

P = 100 kN

P

2.0 m

-2P -P

-2P

+2P

P2+P2

P22+

A

BC

DE

2.0 m

Design of a cantilever truss

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(N/mm2)

Design = 275 N/mm2

t = 183 N/mm2 with load factor 1.5 tension

c = 100 N/mm2 compression due to buckling

Spare strength / reserved strength

PlasticElastic

Simplified stress-strain curve



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For S275 steel, the yield strength is 275 N/mm2. With a factor of safetyequal to 1.5, the design strength of the members under tension is

For those members under compression, buckling may occur, and hence,the design strength is further reduced to

c = 100 N/mm2 for I section

No reduction in the design strength for square hollow section incompression.

tensionmm/N1835.1

275 2t ==

SchemeS275 steel

Design strength (N/mm2)

Tension Compression

I Solid bar 183 100

II Joist 183 100

III Square hollow section 183 183


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Design for member under tension (Scheme I)

F = 283 kN (largest tension force in member CE)

t = 183 N/mm2

The cross sectional area, A, of the member required is

Arequired = F /t = 283 x 103 / 183

= 1546 mm2

Use 40 x 40 mm solid bar

Aprovided = 40 x 40

= 1600 mm2 > Areq = 1546 mm2

or the stress,= F / Aprovided= 283 x 103 / 1600

= 176.9 N/mm2


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F = 200 kN (largest compression force in members CD & ED)

c = 100 N/mm2


Arequired = F /c = 200 x 103 / 100= 2000 mm2

Use 45 x 45 mm solid bar

Aprovided = 45 x 45

= 2025 mm2 > Areq = 2000 mm2


= 98.8 N/mm2 Areq = 1546 mm2


= 174.7 N/mm2


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F = 200 kN (largest compression force in members CD & ED)

c = 100 N/mm2


Arequired = F /c = 200 x 103 / 100= 2000 mm2

Use 89 x 89 x 19.4 kg/m Joist

Aprovided = 24.9 cm2

= 2490 mm2 > Areq = 2000 mm2


= 80.3 N/mm2 Areq = 1546 mm

2


= 167.5 N/mm2


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F = 200 kN (largest tension force in member CE)

c = 183 N/mm2 (=t =y / 1.5)

No reduction for buckling is necessary.

The cross sectional area, A, of the member required isArequired = F /c = 200 x 10

3 / 183

= 1093 mm2

Use 90 x 90 x 3.6 SHS, 9.3 kg/m

Aprovided = 1240 mm2 > Areq = 1093 mm

2


= 161.3 N/mm2


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Scheme

Section designationMemberlength

(m)

*Weight

(kg)

Totalweight

(kg)

**Unitcost

($/kg)

Totalcost

($)DimensionsUnit

weight(kg/m)

IT

C

40 x 40 Solid bar

45 x 45 Solid bar

12.6

15.9

7.6

10.8

96

172268 30 8040

IIT

C

76 x 76 x 12.7 Joist

89 x 89 x 19.4 Joist

12.7

19.4

7.6

10.8

97

210307 15 4605

IIIT

C

90 x 90 x 5.0 SHS

90 x 90 x 3.6 SHS

13.3

9.3

7.6

10.8

102

101203 18 3654

* Minimum amount of materials (weight/tonnage) does NOT always meansmost economical design.

** The unit cost also includes cost of fabrication / welding / erection.

Design of a cantilever trussTwo section sizes

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Scheme One sectionsize

Two sectionsize

Ratio

One : Two

I 8790 (2.0) 8040 (2.2) 1.09 : 1.0

II 5355 (1.2) 4605 (1.3) 1.16 : 1.0

III 4410 (1.0) 3654 (1.0) 1.21 : 1.0

Scheme III is always preferred based on the above assumption and

data according to design strength unit cost (material / fabrication / welding / erection) availability of materials

Although there is saving of about 20% in using two section sizes,only one section size may be used in practice due to small quantity.The normal unit of purchase is one ton.



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As demonstrated in the above example Design of a truss, thefollowing data are very important:

section properties of members, such as cross-sectional area

design strength of materials under different types of internal forces- t tension- c compression (buckling ?)- s shear- b bending- tor torsion

partial safety factor for materials under different types of internalforces

unit cost of material / fabrication / welding / erection / time

Structural design

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Linear elastic design, i.e. all members of a structure operate withinthe linear elastic range of the stress-strain curve of the steelmaterial. Moreover, the structural response of all the membersoperate within the linear elastic range of the load-deformation curvesof the structure.

DataLoading, F obtained from loading allowance

Strength of material, fy obtained from tests or codesSafety factor, = 1.5 ~ 2.0

Design strength ft =

Section properties of the members, A

fy

Linearelasticrange

LOAD RESISTANCE

Applied stress Design strength

F/A ft = fy/

Allowable stress designWorking stress design, or permissible stress design


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Partial safety factors to allow for extreme situations

-f on loading G for permanent actions

Q for variable actions

Loads U.K. H.K. EuropeDead load (D)Imposed load (L)Wind load (W)

1.41.61.4

1.41.61.4

1.31.51.3

D + L + W 1.2 1.2 1.1

Dead load restraining upliftand overturning

1.0 1.0 1.0

-M on materials/resistance

Steel M = 1.0 or 1.05 (tension)

= 1.1 (local buckling)

= 1.2 (connection)

Concrete M = 1.5 (compression)

Partial safety factors for extreme situations

Limit state designUltimate limit state

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DataLoad = FPartial safety factor,f = 1.0 ~ 1.6Factored design load =f x F (increased)Strength of material = fy from tests or codes (y ormax)Partial safety factor,M = 1.0 ~ 1.5Section properties, A

Fullrange

LOAD RESISTANCE

Internal forces due toapplied load

Section capacityMember resistance

ftA = fyA /

ULS - strength (yielding, buckling, rupture)- stability against overturning & sway- fracture due to fatigue- brittle fracture

Ff M

Limit state designUltimate limit state


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Long term behaviour (not extreme situation) tends to happenduring the life time of the structure.

deflection / deformation (most common)

vibration, fatigue, corrosion & durability

From deflection, the design criterion is

Expected deflection < Limits of deflection

Compared to load/resistance calculation, the deflection is always veryapproximate. It is the order of magnitude other than the exact value moremeaningful.

Typical deflection limits

deflection due to unfactored imposed load

beams carrying plaster or other brittle finish

all other beams

180

Span

360

Span

200

Span

Limit state designServiceability limit state

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Allowable stress design Limit state design

Stress Cross-section capacity

Axial force F P = pyA

Shear force Fv P = pvAv

Bending moment M Mc = py S or 1.2 py Z

Interaction

yc pA

Fp =

[ ]vp

tI

yAS =

yb pzMp =

ypz

M

A

P+ 1

M

M

P

F

c

+

Allowable stress design vs Limit state design


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ASDDesign on the allowable

LSDDesign on the limit

One overall factor of safety on each loading type and load combinationon each material, failure mode and otherconstruction effects such as connection.

All the members of a structureoperate within the linearelastic range.

Design for failureSome materials may be yielded in service.

Deflection check Deflection check in serviceability limit state withdifferent set of partial safety factor (usually equal to1.0)

M

f

Allowable stress design vs Limit state design

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