Andrew SarawitAndrew Sarawit

Professor Teoman PeközProfessor Teoman Peköz

Sponsored by: Sponsored by:

Rack Manufacturers Institute Rack Manufacturers Institute

American Iron and Steel InstituteAmerican Iron and Steel Institute

CCORNELLORNELL U UNIVERSITYNIVERSITYSchool of Civil and Environmental EngineeringSchool of Civil and Environmental Engineering

Cold-Formed Steel Frame Cold-Formed Steel Frame and Beam-Column Designand Beam-Column Design

To verify or modify the RMI and the AISI provisions To verify or modify the RMI and the AISI provisions for frame designfor frame design

Column BasesColumn Bases Beam to Column ConnectionsBeam to Column Connections MembersMembers Cold-Formed Steel FramesCold-Formed Steel Frames FREEFREE Computer Programs Computer Programs

ObjectiveObjective

Project OutlineProject Outline

Cold-Formed Steel FramesCold-Formed Steel Frames

Two approaches are begin consideredTwo approaches are begin considered

1. Effective length approach (1. Effective length approach (KKxx > 1 > 1 ))

- Concentrically Loaded Compression Members- Concentrically Loaded Compression Members

- - Combined Compressive Axial Load and BendingCombined Compressive Axial Load and Bending

2. Notional load approach (2. Notional load approach (KKxx = 1 = 1 ) )

Effective Length Approach (KEffective Length Approach (Kxx>1)>1)

Concentrically Loaded Compression MembersConcentrically Loaded Compression Members

Approach 1Approach 1aa elastic elastic critical buckling load is determinedcritical buckling load is determined

by using the AISI torsional-flexural buckling provisionsby using the AISI torsional-flexural buckling provisions

Approach 1Approach 1bb elastic elastic critical buckling load is determinedcritical buckling load is determined

by performing an elastic buckling analysisby performing an elastic buckling analysis

u c nP P

Effective Length Approach (KEffective Length Approach (Kxx>1)>1)

Combined Compressive Axial Load and BendingCombined Compressive Axial Load and Bending

Approach 1Approach 1cc elastic elastic critical buckling load is determinedcritical buckling load is determined

by using the AISI torsional-flexural buckling provisionsby using the AISI torsional-flexural buckling provisions

Approach 1Approach 1dd elastic elastic critical buckling load is determinedcritical buckling load is determined

by performing an elastic buckling analysisby performing an elastic buckling analysis

1u u

c n b n

P M

P M

Notional Load Approach (KNotional Load Approach (Kxx=1)=1)

Approach 2Approach 2a a

Approach 2Approach 2bb

Approach 2Approach 2c c and a and a 10% reduced flexural 10% reduced flexural

stiffness analysis model is usedstiffness analysis model is used

( )

1u u

c n L b n

P M

P M

1 240

x x

x

K 1 168, 1 K 1.7

1 240, K 1.7

1 240

This can done by using a reduced flexural stiffness This can done by using a reduced flexural stiffness for all members and connections in the analysis modelfor all members and connections in the analysis model

* 0.9EI EI

*EI

Isolated Rotationally Isolated Rotationally

Restrained Sway ColumnRestrained Sway Column

1000

L

240L

P

P

60 in.L

The finite element method was used as the basis for The finite element method was used as the basis for evaluating the accuracy of the design approachesevaluating the accuracy of the design approaches

540 models were studied540 models were studied

- 3 material yield stresses (33, 55, 70 ksi)- 3 material yield stresses (33, 55, 70 ksi)

- 20 different rotational end-restraints - 20 different rotational end-restraints

GGAA ranging from 0 to 60 ranging from 0 to 60

GGBB ranging from 0 to ranging from 0 to

- 9 column sections- 9 column sections

C1 C2 C3

C7 C8 C9

C4 C5 C6

Study 1:Study 1:

Effective Length Approach Effective Length Approach

Approach 1Approach 1aa Approach 1Approach 1bb

u c nP PBuckling load

from AISI TFB Eq.

Buckling load

from FEM

Effective Length Approach Effective Length Approach

Approach 1Approach 1cc Approach 1Approach 1dd

Buckling load

from AISI TFB Eq.

Buckling load

from FEM1u u

c n b n

P M

P M

Notional Load Approach Notional Load Approach

1 240

Approach 2Approach 2aa Approach 2Approach 2bb

x x

x

K 1 168, 1 K 1.7

1 240, K 1.7

Notional Load Approach Notional Load Approach

Approach 2Approach 2aa Approach 2Approach 2cc

1 240 and * 0.9EI EI 1 240

972 pallet rack configurations 972 pallet rack configurations were studiedwere studied

2 load cases were considered2 load cases were considered

- 3 frame dimensions (bays x stories: 2x3, 6x3, 6x6)- 3 frame dimensions (bays x stories: 2x3, 6x3, 6x6)- 2 upright frame configurations - 2 upright frame configurations - 9 column sections - 9 column sections - 3 Material yield stresses (33, 55, 70 ksi)- 3 Material yield stresses (33, 55, 70 ksi)- 6 beam to column connection stiffnesses - 6 beam to column connection stiffnesses

Study 2:Study 2: Cold-Formed Steel Frames Cold-Formed Steel Frames

Gravity load case Seismic loads caseGravity load case Seismic loads case

Approach 1Approach 1aa Approach 1Approach 1cc

Gravity Load Case: Gravity Load Case: Effective Length Approach Effective Length Approach

u c nP P 1u u

c n b n

P M

P M

Approach 2Approach 2aa Approach 2Approach 2bb

Gravity Load Case: Notional Gravity Load Case: Notional Load Approach Load Approach

1 240 x x

x

K 1 168, 1 K 1.7

1 240, K 1.7

Approach 2Approach 2aa Approach 2Approach 2cc

Gravity Load Case: Notional Gravity Load Case: Notional Load Approach Load Approach

1 240 1 240 and * 0.9EI EI

Approach 1Approach 1cc

Seismic Load Case: Seismic Load Case: Effective Length Approach Effective Length Approach

1u u

c n b n

P M

P M

Approach 2Approach 2aa Approach 2Approach 2bb

Seismic Load Case: Notional Seismic Load Case: Notional Load Approach Load Approach

1 240 x x

x

K 1 168, 1 K 1.7

1 240, K 1.7

Approach 2Approach 2aa Approach 2Approach 2cc

Seismic Load Case: Notional Seismic Load Case: Notional Load Approach Load Approach

1 240 1 240 and * 0.9EI EI

Notional load approach agrees better with the finite Notional load approach agrees better with the finite element results than the effective length approach does element results than the effective length approach does

Notional Load Approach 2Notional Load Approach 2cc is recommended is recommended Use the effective length factors KUse the effective length factors K

xx = 1, K = 1, Kyy = 1, and K = 1, and K

tt = 0.8 = 0.8

Use the notional load parameter Use the notional load parameter = 1/240 = 1/240 A 10% reduced flexural stiffness analysis model is usedA 10% reduced flexural stiffness analysis model is used

- This can done by using a reduced flexural stiffness - This can done by using a reduced flexural stiffness

for all members and connections in the analysis model for all members and connections in the analysis model

ConclusionConclusion

* 0.9EI EI

*EI