Plastic design with HSS beams - The Steel Construction

1Webinar Series: Structural Design of High Strength SteelsSTROBE: Stronger Steels in the Built Environment EU RFCS Research Project 743504

Plastic design with HSS beams

Design requirements for the application of plastic design of beams made of high strength steel


Plastic global analysis

https://havitsteelstructure.com/steel-structure-detail/


Plastic Design in EC 3-1-1Cross-section requirements for plastic global analysis

• Class 1 cross-section

EC 3-1-1 – Section 5.6



• Class 1 cross-section


EC 3-1-1 / EC3-1-12:

Plastic global analysis can beapplied for conventionalstrength steel, not for high strength steel.

→ STROBE-Project

→ Effects of material non-linearity


Plastic global analysis• Allows for effects of material non-linearity when calculating action effects

Example: Formation of plastic collapse mechanism

EC 3-1-1 – Section 5.4.3




EC 3-1-1 – Section 5.4.3

• Realistic determination of load bearing capacity → More economic design




EC 3-1-1 – Section 5.4.3


• Stability of members has to be guaranteed EC 3-1-1 – Section 6.3.5




EC 3-1-1 – Section 5.4.3


• Stability of members has to be guaranteed

• A sufficient rotation capacity of the members has to be ensured

EC 3-1-1 – Section 6.3.5




• The member has Class 1 cross-sections:


Web

• Additional regulations referring to application of stiffeners, fastener holes, etc. 𝜀 =

235

𝑓𝑦, 𝑓𝑦 in

𝑁

𝑚𝑚2



• The member has Class 1 cross-sections:


FlangeWeb

• Additional regulations referring to application of stiffeners, fastener holes, etc. 𝜀 =

235

𝑓𝑦, 𝑓𝑦 in

𝑁

𝑚𝑚2


Definition of Rotation CapacityRotation Capacity

• Class 1 members of CSS show a sufficient Rotation Capacity → How is that defined?

• Experiments / Simulations / Approximation formula





• The background of EC 3-1-1 used R = 3 as requirement for Class 1

• Different systems require different rotation capacities R





• The background of EC 3-1-1 used R = 3 as requirement for Class 1

• Different systems require different rotation capacities R

High Strength Steels and Plastic Design

• Plastic global analysis is until now not allowed for steel grades over S460 to S700

→ HSS are assumed to have too poor rotation capacities

EC 3-1-12 – Section 2.1 about 5.4.3


Experimental InvestigationsExperimental rotation tests on beams: HSS beams can own sufficient rotation capacity

• 20 tests on I-shaped beams: 2 S355, 8 S690, 10 hybrid S690/S355

• Different slenderness properties (𝑐

𝑡) and lengths


0

100

200

300

400

500

600

0.0 0.1 0.2 0.3 0.4

Mo

men

t [k

Nm

]

Rotation [rad]

Mpl

ϕpl ϕrot




𝑡) and lengths

[mm]


0

100

200

300

400

500

600

0.0 0.1 0.2 0.3 0.4

Mo

men

t [k

Nm

]

Rotation [rad]

Mpl

ϕpl ϕrot




𝑡) and lengths

[mm]


0

100

200

300

400

500

600

0.0 0.1 0.2 0.3 0.4

Mo

men

t [k

Nm

]

Rotation [rad]

Mpl

ϕpl ϕrot




𝑡) and lengths

[mm]


0

100

200

300

400

500

600

0.0 0.1 0.2 0.3 0.4

Mo

men

t [k

Nm

]

Rotation [rad]

Mpl

ϕpl ϕrot




𝑡) and lengths

[mm]


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 1 2 3 4 5 6

M/M

pl[-

]

ϕ/ϕpl [-]

Mpl

ϕplϕrot




𝑡) and lengths

Ract = 4.3 > 3

[mm]


Numerical SimulationsNumerical simulations of beams: HSS beams can own sufficient rotation capacity

• Simulations of tests with FE-models including plastic material and damage criterion

0

100

200

300

400

500

600

700

800

900

0.00 0.05 0.10 0.15 0.20 0.25

Mo

men

t [k

Nm

]

Rotation [rad]

S109_Test

S109_FE

Mpl

ϕpl ϕrot

M-φ behaviour ✓




0

100

200

300

400

500

600

700

800

900

0.00 0.05 0.10 0.15 0.20 0.25

Mo

men

t [k

Nm

]

Rotation [rad]

S109_Test

S109_FE

Mpl

ϕpl ϕrot

M-φ behaviour ✓

Deformation and local buckling ✓




0

100

200

300

400

500

600

700

800

900

0.00 0.05 0.10 0.15 0.20 0.25

Mo

men

t [k

Nm

]

Rotation [rad]

S109_Test

S109_FE

Mpl

ϕpl ϕrot

M-φ behaviour ✓

Deformation and local buckling ✓

Crack initiation and growth ✓




• Parametric study: 780 Simulations

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10

M/

Mp

l[-

]

ϕ/ϕpl [-]

S690_MW_MW_25_050_025S690_MW_MW_25_050_050S690_MW_MW_25_050_075S690_MW_MW_25_050_100S690_MW_MW_25_075_025S690_MW_MW_25_075_050S690_MW_MW_25_075_075S690_MW_MW_25_075_100S690_MW_MW_25_100_025S690_MW_MW_25_100_050S690_MW_MW_25_100_075S690_MW_MW_25_100_100




• Parametric study: 780 Simulations

• Material: S500, S690

• 9 true stress strain curves per material

• 4 slenderness properties (𝑐

𝑡) web

• 3 slenderness properties (𝑐

𝑡)

• Homogeneous and hybrid 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10

M/

Mp

l[-

]

ϕ/ϕpl [-]

S690_MW_MW_25_050_025S690_MW_MW_25_050_050S690_MW_MW_25_050_075S690_MW_MW_25_050_100S690_MW_MW_25_075_025S690_MW_MW_25_075_050S690_MW_MW_25_075_075S690_MW_MW_25_075_100S690_MW_MW_25_100_025S690_MW_MW_25_100_050S690_MW_MW_25_100_075S690_MW_MW_25_100_100


Outcome of Parametric Study

0

2

4

6

8

10

12

14

16

0 2.5 5 7.5 10

Ro

tati

on

ca

pa

city

R [

-]

Flange slenderness c/(tε) [-]

Damage

No damage

R=3

Influence of slenderness properties on Rotation Capacity:



0

2

4

6

8

10

12

14

16

0 2.5 5 7.5 10

Ro

tati

on

ca

pa

city

R [

-]


Damage

No damage

R=3

0

2

4

6

8

10

12

14

16

0 20 40 60 80

Ro

tati

on

ca

pa

city

R [

-]

Web slenderness c/(tε) [-]

Damage

No damage

R=3




0

2

4

6

8

10

12

14

16

0 2.5 5 7.5 10

Ro

tati

on

ca

pa

city

R [

-]


Damage

No damage

R=3

0

2

4

6

8

10

12

14

16

0 20 40 60 80

Ro

tati

on

ca

pa

city

R [

-]


Damage

No damage

R=3


• Distinct influence of web slenderness



0

2

4

6

8

10

12

14

16

0 2.5 5 7.5 10

Ro

tati

on

ca

pa

city

R [

-]


Damage

No damage

R=3

0

2

4

6

8

10

12

14

16

0 20 40 60 80

Ro

tati

on

ca

pa

city

R [

-]


Damage

No damage

R=3


• Distinct influence of web slenderness

Rotation

Rotation capacity is sufficient for most cases

Stricter requirements for HSS are necessary


0

2

4

6

8

10

12

14

16

0 20 40 60 80

Ro

tati

on

ca

pa

city

R [

-]


Damage

No damage

R=3

0

2

4

6

8

10

12

14

16

0 2.5 5 7.5 10

Ro

tati

on

ca

pa

city

R [

-]


Damage

No damage

R=3

Design RequirementsExemplary Approach: Stricter Class 1 limits for HSS

60e

8e


Design ExampleDesigning a two-span beam with HSS using plastic design

S690bf = 120 mm tf = 12 mmhw = 225 mm tw = 10 mmaw = 3 mm

𝑷𝑬𝒅 = 𝟒𝟏𝟎 𝒌𝑵




Flange 𝑐

𝑡∙𝜀= 4.2 < 8→ Class 1*

Web 𝑐

𝑡∙𝜀= 21.7 < 60→ Class 1*





Flange 𝑐

𝑡∙𝜀= 4.2 < 8→ Class 1*

Web 𝑐

𝑡∙𝜀= 21.7 < 60→ Class 1*

𝑀𝑝𝑙 = 276.9 𝑘𝑁𝑚 < 𝑀𝐸𝑑 = 332.9 𝑘𝑁𝑚 (from elastic analysis)





Flange 𝑐

𝑡∙𝜀= 4.2 < 8→ Class 1*

Web 𝑐

𝑡∙𝜀= 21.7 < 60→ Class 1*

𝑀𝑝𝑙 = 276.9 𝑘𝑁𝑚 < 𝑀𝐸𝑑 = 332.9 𝑘𝑁𝑚 (from elastic analysis)

→ Plastic Design necessary





Flange 𝑐

𝑡∙𝜀= 4.2 < 8→ Class 1*

Web 𝑐

𝑡∙𝜀= 21.7 < 60→ Class 1*

𝑀𝑝𝑙 = 276.9 𝑘𝑁𝑚 < 𝑀𝐸𝑑 = 332.9 𝑘𝑁𝑚


𝑃𝑝𝑙𝑒𝑙 = 341 𝑘𝑁 (First order elastic analysis)





Flange 𝑐

𝑡∙𝜀= 4.2 < 8→ Class 1*

Web 𝑐

𝑡∙𝜀= 21.7 < 60→ Class 1*

𝑀𝑝𝑙 = 276.9 𝑘𝑁𝑚 < 𝑀𝐸𝑑 = 332.9 𝑘𝑁𝑚


𝑃𝑝𝑙𝑒𝑙 = 341 𝑘𝑁 (First order elastic analysis)

𝑃𝑝𝑙𝑝𝑙= 341 𝑘𝑁 + 74 𝑘𝑁 = 415 𝑘𝑁 > 410 𝑘𝑁



Design ExampleUsing S355:

S690 → S355bf = 120 mm → 135 mm tf = 12 mm → 15 mmhw = 225 mm → 300 mmtw = 10 mm → 12 mmaw = 3 mm → 4 mm

Flange 𝑐

𝑡∙𝜀= 4.2 < 8→ Class 1 → 3.7 < 9→ Class 1

Web 𝑐

𝑡∙𝜀= 21.7 < 60→ Class 1 → 24.1 < 72→ Class 1

𝑀𝑝𝑙 = 276.9 𝑘𝑁𝑚 → 274.4 𝑘𝑁𝑚 < 𝑀𝐸𝑑 = 332.9 𝑘𝑁𝑚


𝑃𝑝𝑙𝑒𝑙 = 341 𝑘𝑁 → 338 𝑘𝑁𝑚

𝑃𝑝𝑙𝑝𝑙= 341 𝑘𝑁 + 74 𝑘𝑁 = 415 𝑘𝑁→ 338 𝑘𝑁 + 74 𝑘𝑁 = 412 𝑘𝑁 > 410 𝑘𝑁



Design ExampleUsing S355:

S690 → S355bf = 120 mm → 135 mm tf = 12 mm → 15 mmhw = 225 mm → 300 mmtw = 10 mm → 12 mmaw = 3 mm → 4 mm

Flange 𝑐

𝑡∙𝜀= 4.2 < 8→ Class 1 → 3.7 < 9→ Class 1

Web 𝑐

𝑡∙𝜀= 21.7 < 60→ Class 1 → 24.1 < 72→ Class 1

𝑀𝑝𝑙 = 276.9 𝑘𝑁𝑚 → 274.4 𝑘𝑁𝑚 < 𝑀𝐸𝑑 = 332.9 𝑘𝑁𝑚


𝑃𝑝𝑙𝑒𝑙 = 341 𝑘𝑁 → 338 𝑘𝑁𝑚

𝑃𝑝𝑙𝑝𝑙= 341 𝑘𝑁 + 74 𝑘𝑁 = 415 𝑘𝑁→ 338 𝑘𝑁 + 74 𝑘𝑁 = 412 𝑘𝑁 > 410 𝑘𝑁


Rotation

S690

S355

Use of S355 instead of S690→ 50% more weight

Additional checks needede.g. Deformation limits


Conclusions

• Plastic Design - Realistic determination of load bearing capacity

→ Economic design


Conclusions


→ Economic design

• Rotation capacity depends on various influencing factors

• High strength steel can own sufficient rotation capacity


Conclusions


→ Economic design



• Limitations for plastic design with HSS are necessary


Conclusions


→ Economic design



• Limitations for plastic design with HSS are necessary

• Combination of plastic design and HSS → Even more economic design

• Using HSS in stead of CSS can lead to weight, carbon and cost savings

https://www.sweepstandard.org/


www.stb.rwth-aachen.de

Thank you for your attention.

Felix EybenM.Sc.

Mies-van-der-Rohe-Str. 152074 Aachen | GERMANY

+49 241 80-25182

[email protected]


https://www.archdaily.com/

Helen BartschM.Sc.

Mies-van-der-Rohe-Str. 152074 Aachen | GERMANY

+49 241 80-23595

[email protected]


Documents

Plastic design with HSS beams - The Steel Construction