Basic Concepts in Ductile Detailing of Steel Structures EAC 2013 Michael D. Engelhardt University of Texas at Austin

Overview of Presentation What is Ductility ? Why is Ductility Important ? How Do We Achieve Ductility in Steel Structures ? Ductility in Seismic-Resistant Design

Ductility = inelastic deformation capacity What is Ductility ? Ductility: The ability to sustain large inelastic deformations without significant loss in strength. Ductility = inelastic deformation capacity Ductility: - material response - structural component response (members and connections) - global frame response

F Δ Ductility F Fyield Δ

How is ductility developed in steel structures ? F Δ Ductility = Yielding F Loss of load carrying capability: Instability Fracture Δ

Why is Ductility Important? Permits redistribution of internal stresses and forces Increases strength of members, connections and structures Permits design based on simple equilibrium models Results in more robust structures Provides warning of failure Permits structure to survive severe earthquake loading

Why Ductility ? Permits redistribution of internal stresses and forces Increases strength of members, connections and structures Permits design based on simple equilibrium models Results in more robust structures Provides warning of failure Permits structure to survive severe earthquake loading

General Philosophy for Earthquake-Resistant Design Objective: Prevent loss of life by preventing collapse in the extreme earthquake likely to occur at a building site. Objectives are not to: - limit damage - maintain function - provide for easy repair Design Approach: Survive earthquake by providing large ductility rather than large strength

H Δ H Helastic Available Ductility Required Strength 3/4 *Helastic MAX

H Δ H Helastic Observations: We can trade strength for ductility MAX

H Δ H Helastic Observations: Ductility = Damage 3/4 *Helastic MAX

H Δ H Helastic Observations: The maximum lateral load a structure will see in an earthquake is equal to the lateral strength of the structure 1/4 *Helastic MAX

How Do We Achieve Ductility in Steel Structures ?

Ductile Limit States Must Precede Brittle Limit States Achieving Ductile Response.... Ductile Limit States Must Precede Brittle Limit States

Example P P gusset plate double angle tension member Ductile Limit State: Gross-section yielding of tension member Brittle Limit States: Net-section fracture of tension member Block-shear fracture of tension member Net-section fracture of gusset plate Block-shear fracture of gusset plate Bolt shear fracture Plate bearing failure in double angles or gusset

double angle tension member P P Example: Gross-section yielding of tension member must precede net section fracture of tension member Gross-section yield: Pyield = Ag Fy Net-section fracture: Pfracture = Ae Fu

P P Pyield  Pfracture Ag Fy  Ae Fu double angle tension member The required strength for brittle limit states is defined by the capacity of the ductile element Pyield  Pfracture Ag Fy  Ae Fu Steels with a low yield ratio are preferable for ductile behavior = yield ratio

double angle tension member P P Example: Gross-section yielding of tension member must precede bolt shear fracture Gross-section yield: Pyield = Ag Fy Bolt shear fracture: Pbolt-fracture = nb ns Ab Fv

Pyield  Pbolt-fracture double angle tension member P P The required strength for brittle limit states is defined by the capacity of the ductile element Pyield  Pbolt-fracture The ductile element must be the weakest element in the load path

P P Example: Bolts: 3 - 3/4" A325-X double shear double angle tension member P P Example: Bolts: 3 - 3/4" A325-X double shear Ab = 0.44 in2 Fv = 0.563 x 120 ksi = 68 ksi Pbolt-fracture = 3 x 0.44 in2 x 68 ksi x 2 = 180k Angles: 2L 4 x 4 x 1/4 A36 Ag = 3.87 in2 Pyield = 3.87 in2 x 36 ksi = 139k

Pyield  Pbolt-fracture double angle tension member P P Pyield  Pbolt-fracture Pyield = 139k Pbolt-fracture = 180k OK What if the actual yield stress for the A36 angles is greater than 36 ksi? Say, for example, the actual yield stress for the A36 angle is 54 ksi.

Pyield  Pbolt-fracture Pyield  Pbolt-fracture double angle tension member P P Pyield  Pbolt-fracture Pyield = 3.87 in2 x 54 ksi = 209k Pbolt-fracture = 180k Pyield  Pbolt-fracture Bolt fracture will occur before yield of angles non-ductile behavior

P P Pyield  Pbrittle Stronger is not better in the ductile element double angle tension member P P Pyield  Pbrittle Stronger is not better in the ductile element (Ductile element must be weakest element in the load path) For ductile response: must consider material overstrength in ductile element

P P Pyield  Pbrittle Pyield = Ag RyFy double angle tension member P P Pyield  Pbrittle The required strength for brittle limit states is defined by the expected capacity of the ductile element (not minimum specified capacity) Pyield = Ag RyFy Ry Fy = expected yield stress of angles

Ductile Limit States Must Precede Brittle Limit States Achieving Ductile Response.... Ductile Limit States Must Precede Brittle Limit States Define the required strength for brittle limit states based on the expected yield capacity of ductile element The ductile element must be the weakest in the load path Unanticipated overstrength in the ductile element can lead to non-ductile behavior. Steels with a low value of yield ratio, Fy / Fu are preferable for ductile elements

Connection response is generally non-ductile..... Achieving Ductile Response.... Connection response is generally non-ductile..... Connections should be stronger than connected members

Be cautious of high-strength steels Achieving Ductile Response.... Be cautious of high-strength steels

Ref: Salmon and Johnson - Steel Structures: Design and Behavior General Trends: As Fy Elongation (material ductility) Fy / Fu Ref: Salmon and Johnson - Steel Structures: Design and Behavior

Be cautious of high-strength steels Achieving Ductile Response.... Be cautious of high-strength steels High strength steels are generally less ductile (lower elongations) and generally have a higher yield ratio. High strength steels are generally undesirable for ductile elements

Achieving Ductile Response.... Use Sections with Low Width-Thickness Ratios and Adequate Lateral Bracing

M q Effect of Local Buckling on Flexural Strength and Ductility Mp  Increasing b / t

Mp Moment Capacity Ductility Plastic Buckling Inelastic Buckling 0.7 My Elastic Buckling hd p Width-Thickness Ratio (b/t) r Ductility

Mp Moment Capacity Ductility Plastic Buckling Inelastic Buckling 0.7 My Elastic Buckling Slender Element Sections hd p Width-Thickness Ratio (b/t) r Ductility

Mp Moment Capacity Ductility Plastic Buckling Inelastic Buckling 0.7 My Elastic Buckling Noncompact Sections hd p Width-Thickness Ratio (b/t) r Ductility

Mp Moment Capacity Ductility Plastic Buckling Inelastic Buckling 0.7 My Elastic Buckling Compact Sections hd p Width-Thickness Ratio (b/t) r Ductility

Mp Moment Capacity Ductility Plastic Buckling Inelastic Buckling 0.7 My Elastic Buckling Highly Ductile Sections (for seismic design) hd p Width-Thickness Ratio (b/t) r Ductility

Local buckling of noncompact and slender element sections

Local buckling of moment frame beam with highly ductile compactness (  < hd ) .....

Local buckling of a shear yielding EBF link with highly ductile compactness (  < hd ) .....

Effect of Local Buckling on Ductility For highly ductile flexural response: b f t h w Example: W-Shape

Beam Flanges Beam Web Highly Ductile Compactness:

Lateral Torsional Buckling Lateral torsional buckling controlled by: Lb = distance between beam lateral braces ry = weak axis radius of gyration Beam lateral braces Lb Lb

Effect of Lateral Torsional Buckling on Flexural Strength and Ductility: M  M q Mp Increasing Lb / ry

Effect of Lateral Buckling on Ductility For highly ductile flexural response: For Fy = 50 ksi:

Recognize that buckling of a compression member is non-ductile Achieving Ductile Response.... Recognize that buckling of a compression member is non-ductile

Pcr P d P Pcr d

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

How Do We Achieve Ductile Response in Steel Structures ? Ductile limit states must precede brittle limit states Ductile elements must be the weakest in the load path Stronger is not better in ductile elements Define Required Strength for brittle limit states based on expected yield capacity of ductile element Provide connections that are stronger than members Avoid high strength steels in ductile elements Use cross-sections with low b/t ratios Provide adequate lateral bracing Recognize that compression member buckling is non-ductile

How Do We Achieve Ductile Response in Steel Structures ?

Ductile Detailing for Seismic Resistance High Ductility Steel Systems for Lateral Resistance: Special Moment Frames Special Concentrically Braced Frames Eccentrically Braced Frames Buckling Restrained Braced Frames Special Plate Shear Walls

Ductile Detailing for Seismic Resistance Choose frame elements ("fuses") that will yield in an earthquake. Detail "fuses" to sustain large inelastic deformations prior to the onset of fracture or instability (i.e. , detail fuses for ductility). Design all other frame elements to be stronger than the fuses, i.e., design all other frame elements to develop the capacity of the fuses.

Special Moment Frame (SMF) Ductile fuse: Flexural yielding of beams

Inelastic Response of a Special Moment Frame Fuse: Flexural Yielding of Beams Detail beam for ductile flexural response: no high strength steels low b/t ratios (highly ductile ) beam lateral bracing (per seismic req'ts)

Inelastic Response of a Special Moment Frame Design all other frame elements to be stronger than the beam: Connections Beam-to-column connections Column splices Column bases Column buckling capacity Column flexural capacity

Special Concentrically Braced Frame Ductile fuse: tension yielding of braces.

Inelastic Response of an SCBF Tension Brace: Yields (ductile) Compression Brace: Buckles (nonductile)

Inelastic Response of CBFs under Earthquake Loading Compression Brace (previously in tension): Buckles (nonductile) Tension Brace (previously buckled in compression): Yields (ductile) Connections, columns and beams: designed to be stronger than braces

An X-braced CBF with wide flange braces that have buckled in-plane. Note that depending on the orientation of the bracing member and the end connection details, braces may buckle either in-plane or out-of-plane.

Eccentrically Braced Frames (EBFs) Ductile fuse: Shear yielding of links Eccentrically Braced Frames (EBFs) are braced frames, consisting of beams, columns, and braces. Unlike conventional concentrically braced frames, an intentional eccentricity is introduced in EBFs, so that the brace-beam-column centerlines do not meet at a single point. The framing is arranged so as to isolate a short segment of beam at one of each brace. This isolated beam segment is called a "link." EBFs are designed so that inelastic action occurs within the links. The links, in turn, can be designed and detailed to provide very high levels of ductility. The braces, columns and beam segments outside of the links are designed to remain essentially elastic, by designing these elements to be stronger than the links. A well designed EBF can combine high stiffness in the elastic range (similar to a concentrically braced frame), with high ductility in the inelastic range (similar to a moment resisting frame). Because of the high elastic stiffness of an EBF, beam and column sizes are generally much smaller than in a moment resisting frame.

Link Link

Inelastic Response of an EBF

Braces, beam segments outside of link, columns, connections: designed to be stronger than link

Buckling-Restrained Braced Frames (BRBFs) Ductile fuse: Tension yielding and compression yielding of Buckling Restrained Braces

Buckling- Restrained Brace: Steel Core + Casing

Buckling- Restrained Brace: Steel Core + Casing Steel jacket Mortar Debonding material Section A-A

Inelastic Response of BRBFs

Tension Brace: Yields Compression Brace: Yields

Compression Brace: Yields Tension Brace: Yields Connections, columns and beams: designed to be stronger than braces

Special Plate Shear Walls (SPSW) Ductile fuse: Tension field yielding of web panels

Inelastic Response of a SPSW Development yielding along tension diagonals Shear buckling Columns, beams and connections: designed to be stronger than web panel

Ductile Fuses: Special Moment Frames: Beams: Flexural Yielding Special Concentrically Braced Frames: Braces: Tension Yielding Eccentrically Braced Frames: Links: Shear Yielding Buckling Restrained Braced Frames: Braces: Tension and Compression Yielding Special Plate Shear Walls: Web Panels: Tension Field Yielding

Summary Ductility = Inelastic Deformation Capacity Ductility Important in all Structures Ductility Key Element of Seismic Resistance

Summary Achieving Ductility - Simple Rules......... avoid high strength steels use sections with low b/t's and adequate lateral bracing design connections and other brittle elements to be stronger than ductile members For seismic-resistant structures: Follow AISC Seismic Provisions