Concentrically Braced Frames

Design of SeismicResistant Steel Building Structures Concentrically Braced Frames 

Reference: Michael D. Engelhardt with the support of the  American Institute of of Steel Construction. Construction.

Concentrically Braced Frames

•

Description and Types of Concentrically Braced Frames

• •

Basic Behavior of Concentrically Braced Frames AISC Seismic Provisions for Special Concentrically Braced Frames

Concentrically Braced Frames

•

Description and Types of Concentrically Braced Frames

• •

Basic Behavior of Concentrically Braced Frames AISC Seismic Provisions for Special Concentrically Braced Frames

Concentrically Braced Frames (CBFs) Beams, columns and braces arranged to form a vertical truss. Resist lateral earthquake forces by truss action. Develop ductility through inelastic action in braces. - braces yield in tension - braces buckle in compression Advantages - high elastic stiffness Disadvantages - less ductile than other systems (SMFs, EBFs, BRBFs) - reduced architectural versatility

Types of CBFs

Single Diagonal

Inverted V- Bracing

X- Bracing

V- Bracing

Two Story X- Bracing

Concentrically Braced Frames

•

Description and Types of Concentrically Braced Frames

• •

Basic Behavior of Concentrically Braced Frames AISC Seismic Provisions for Special Concentrically Braced Frames

Inelastic Response of CBFs under Earthquake Loading

Inelastic Response of CBFs under Earthquake Loading

Tension Brace: Yields (ductile)

Compression Brace: Buckles (nonductile)

Columns and beams: remain essentially elastic

Inelastic Response of CBFs under Earthquake Loading

Compression Brace (previously in tension): Buckles (nonductile)

Tension Brace (previously in compression): Yields (ductile)

Columns and beams: remain essentially elastic

Brace Behavior Under Cyclic Axial Loading P Tension

Shortening

! Elongation

Compression !

P

Brace Behavior Under Cyclic Axial Loading P

1. Brace loaded in compression to peak compression capacity (buckling).

!

1

PCR

P

Brace Behavior Under Cyclic Axial Loading P

1. Brace loaded in compression to peak compression capacity (buckling). 2. Continue loading in compression. Compressive resistance drops rapidly. Flexural plastic hinge forms at midlength (due to P-! moment in member).

! 2

1

PCR

plastic hinge  "

P

Brace Behavior Under Cyclic Axial Loading P

1. Brace loaded in compression to peak compression capacity (buckling). 2. Continue loading in compression. Compressive resistance drops rapidly. Flexural plastic hinge forms at midlength (due to P-! moment in member).

3

!

2

1

PCR

3. Remove load from member (P=0). Member has permanent out-of-plane deformation.

Brace Behavior Under Cyclic Axial Loading P

4.

4

Brace loaded in tension to yield.

Py

3

!

2

1

PCR

P

Brace Behavior Under Cyclic Axial Loading P 4

Py

3 5 2

1

PCR

!

4.

Brace loaded in tension to yield.

5.

Remove load from member (P=0). Member still has permanent out-ofplane deformation.

Brace Behavior Under Cyclic Axial Loading P 4

Py

3 5 2

4.

Brace loaded in tension to yield.

5.

Remove load from member (P=0). Member still has permanent out-ofplane deformation.

6.

Brace loaded in compression to peak compression capacity (buckling). Peak compression capacity reduced from previous cycle.

6 1

PCR

P

Brace Behavior Under Cyclic Axial Loading P 4

Py

3 5 7

2

6 1

PCR

4.

Brace loaded in tension to yield.

5.

Remove load from member (P=0). Member still has permanent out-ofplane deformation.

6.

Brace loaded in compression to peak compression capacity (buckling). Peak compression capacity reduced from previous cycle.

7.

Continue loading in compression. Flexural plastic hinge forms at midlength (due to P-! moment in member).

!

P

Experimental Behavior of Brace Under Cyclic Axial Loading W6x20 Kl/r = 80

!

P

Experimental Behavior of Brace Under Cyclic Axial Loading W6x16 Kl/r = 120

!

P

Experimental Behavior of Braced Frame Under Cyclic Loading

Developing Ductile Behavior in CBFs General Approach

• Design frame so that inelastic behavior is restricted to braces. !

!

Braces are "fuse" elements of frame. Braces are weakest element of frame. All other frame elements (columns, beams, connections) are stronger than braces.

• Choose brace members with good energy dissipation capacity and fracture life (limit kL/r and b/t).

Developing Ductile Behavior in CBFs General Approach

• Design brace connections for maximum forces and deformations imposed by brace during cyclic yielding/buckling

Developing Ductile Behavior in CBFs General Approach

• Design beams and columns (and column splices and column bases) for maximum forces imposed by braces

Developing Ductile Behavior in CBFs General Approach

• Design braces based on code specified earthquake forces. • Design all other frame elements for maximum forces that can be developed by braces.

Maximum Forces Developed by Braces Braces in Tension - Axial Force: !

P P For design:

Pmax = Py

Take Pmax = R y  F y  Ag 

!

Maximum Forces Developed by Braces Braces in Compression - Axial Force !

P !

For design:

Presidual =

Take lesser of

0.3 Pcr 

Pmax = 1.14 P n ( P n = Ag  F cre - Ch. E)

Pmax

Pmax = RyFyAg

Take Presidual = 0.3 P max 

P

P max is expected Compression Strength

Maximum Forces Developed by Braces Braces in Compression - Bending Moment: Plastic Hinges

P

P M

M

For "fixed" end braces: flexural plastic hinges will form at mid-length and at brace ends. Brace will impose bending moment on connections and adjoining members.

For design: Take Mmax = 1.1 R y  F y  Z brace (for critical buckling direction)

Maximum Forces Developed by Braces Braces in Compression - Bending Moment:

P

P Plastic Hinge

P

P

For "pinned" end braces: flexural plastic hinge will form at mid-length only. Brace will impose no bending moment on connections and adjoining members. Must design brace connection to behave like a "pin"

Maximum Forces in Columns and Beams To estimate maximum axial forces imposed by braces on columns and beams: Braces in tension: Take P = R y  F y  Ag  Braces in compression: Take P = 1.14 P n or P = 0.3 P max  whichever produces critical design case

Example

! 

Find maximum axial compression in column. Tension Braces: Take P = R y  F y  Ag  Compression Braces: Take P = 0.3 P max 

Example

R y  F y  Ag 

! 

0.3 P n R y  F y  Ag 

Column Axial Compression = [ ! (R y  F y  Ag  ) cos !  +! (0.3 P max ) cos ! ] + P gravity  0.3 P n

(sum brace forces for all levels above column) R y  F y  Ag 

0.3 P n

Example

! 

Find maximum axial tension in column. Tension Braces: Take P = R y  F y  Ag  Compression Braces: Take P = 0.3 P max 

Example

0.3 P max 

!  R y  F y  Ag 

0.3 P max 

Column Axial Tension = [ ! (R y  F y  Ag  ) cos !  + ! (0.3 P max ) cos !  ] - P gravity 

R y  F y  Ag 

0.3 P max 

(sum brace forces for all levels above column) R y  F y  Ag 

Example Find maximum axial compression in column. Tension Brace: Take P = R y  F y  Ag  ! 

Compression Brace: Take P = 0.3 P max 

Example

0.3 P max  R y  F y  Ag 

! 

Column Axial Compression = (R y  F y  Ag  ) cos !  + (0.3 P 0.3 P max ) cos !  + P gravity 

Note Based on elastic frame analysis: Column Axial Force = P gravity 

Example Find maximum bending moment in beam. Tension Brace: Take P = R y  F y  Ag  ! 

Compression Brace: Take P = 0.3 P max 

Example

! 

R y  F y  Ag 

0.3 P max 

Example

Compute moment in beam resulting from application of concentrated load at midspan of ( R y  F y  Ag - 0.3 P max ) sin !  and add moment due to gravity load

( R y  F y  Ag - 0.3 P max ) sin ! 

Note Based on elastic frame analysis: Moment in beam

0

Example Find maximum axial tension and compression that will be applied to gusset plate. ! 

Tension Brace: Take P = R y  F y  Ag  Compression Brace: Take P = 1.14P max 

Example L

wgravity = (1.2 + 0.2 SDS) D + 0.5L

! 

R y  F y  Ag 

0.3 P max 

Beam-to-column connections: simple framing

Example Forces acting on beam: L

wgravity = (1.2 + 0.2 SDS) D + 0.5L

( R y  F y  Ag + 0.3 P max ) cos ! 

( R y  F y  Ag - 0.3 P max ) sin ! 

Example Check gusset yield, gusset net section fracture, gusset block shear fracture, local beam web yielding, etc.

R y  F y Ag 

Check gusset buckling, beam web crippling, etc.

1.14 P n or 0.3P max 

Concentrically Braced Frames

•

Description and Types of Concentrically Braced Frames

• •

Basic Behavior of Concentrically Braced Frames AISC Seismic Provisions for Special Concentrically Braced Frames

2010 AISC Seismic Provisions Section F2

Special Concentrically Braced Frames (SCBF)

Section F1

Ordinary Concentrically Braced Frames (OCBF)

Section F2 Special Concentrically Braced Frames (SCBF) F2.1

Scope

F2.2

Basis of Design

F2.3

Analysis

F2.4

System Requirements

F2.5

Members

F2.6

Connections

 AISC Seismic Provisions – SCBF

F2.2 Design Basis

Special concentrically braced frames (SCBF) are expected to provide significant inelastic deformations primarily through brace buckling and yielding of the brace in tension.

 AISC Seismic Provisions – SCBF

F2.3 Analysis • The required strength of the columns, beams and connections in SCBF shall be based on the load combinations in the applicable building code that include amplified seismic load. • The seismic load effect shall be taken as the the larger force from •  An analysis in which all the braces are assumed to resist forces corresponding to their expected strength in compression or tension •  An analysis in which all braces in tension are assumed to resist forces corresponding to their expected strength and all the braces in compression are assumed to resist their expected post yield buckling strength. • Braces shall be determined in compression or tension neglecting the effects of gravity loads.

 AISC Seismic Provisions – SCBF

F2.3 Analysis •  Analysis shall consider both directions of frame loading • It is permitted to neglect flexural forces from seismic drift • The required strength need not exceed the least of the following: • The forces determined using load combinations stipulated by the applicable building code including the amplified seismic load, applied to the building in which all the compression braces have been removed. • The forces corresponding to resistance of the foundation due to overturning uplift • Forces determined from a non-linear analysis

F2.4 System Requirements F2.4a Lateral Force Distribution Along any line of bracing, braces shall be deployed in alternate directions such that, for either direction of force parallel to the bracing, at least 30 percent but not more than 70% of the total horizontal force along that line is resisted by braces in tension.

F2.4 System Requirements F2.4a Lateral Force Distribution Deploy braces so that about half are in tension (and the other half in compression)

All braces in tension (or compression) NG

OK 

 AISC Seismic Provisions - SCBF

F2.4 System Requirements F2.4b V-Type and Inverted V-Type Bracing

Both flanges of the beam must be braced at the point of intersection of the braces unless the beam has sufficient out of plane strength and stiffness to ensure stability.

Beams shall be braced to satisfy the requirements for moderately ductile members in Section D1.2a.

 AISC Seismic Provisions - SCBF

F2.4 System Requirements F2.4c K-Type Bracing

K-Type Braces are not Permitted for SCBF

 AISC Seismic Provisions - SCBF

F2.5b Members – Diagonal Bracing F2.5b Slenderness

Bracing members shall have:

KL r

! 200

Shall conform to the requirements for highly ductile members in Section D1.1 Built up members for bracing shall conform to Section F2.5b (2).

 AISC Seismic Provisions - SCBF

F2.5b Members – Diagonal Bracing F2.5b Slenderness plastic hinge  "

P

Braces: form plastic hinge during buckling With high b/t's - local buckling and possibly fracture may occur at plastic hinge region

 AISC Seismic Provisions - SCBF SCBF

F2.5b Members – Diagonal Bracing F2.5b (3) Area The brace effective net area shall not be less than the brace gross area. Where reinforcement on braces is used the following requirements apply: i. Strength of reinforcement shall be at least that of brace. ii. The connections of the reinforcement shall have sufficient strength to develop the expected reinforcement strength.

Objective: yield of gross section of brace prior to fracture of net section sec tion

Example gusset plate double angle bracing member

Check double angle bracing member for limit state of net section fracture

P u = R y  F y  Ag  Required axial tension strength of brace for limit state of fracture of the net section

P u = R y  F y  Ag  Critical Net Section  Ae = U An  Ae 2t

> 2t

 AISC Seismic Provisions - SCBF

F2.6 Connections –Bracing F2.6c (2) Compressive Strength

The required compressive strength of bracing connections shall be at least 1.1 R y  P n

P n = Ag  F cr  of bracing member (per Chapter E of AISC Main Specification)

1.1 R y  P n

Check: - buckling of gusset plate - web crippling for beam and column