Tabla 5.6 Fema

Chapter 2: General Requirement Requirements s

2.4. 2.4.4. 4.3. 3.1 1

Defo Deform rmat atio ionn-Co Cont ntro roll lled ed and and Forc ForceeControlled Behavior

The Type 1 curve depicted in Figure 2-3 is representative of ductile behavior where there is an elastic range (point 0 to point 1 on the curve) followed by a plastic range (points 1 to 3) with non-negligible residual strength and ability to support gravity loads at point 3. The plastic range includes a strain hardening or softening range (points 1 to 2) and a strength-degraded range (points 2 to 3). Primary component actions exhibiting this behavior shall be classified as deformation-controlled if the strain-hardening or strainsoftening range is such that e > 2g; otherwise, they shall be classified as force-controlled. Secondary component actions exhibiting Type 1 behavior shall be classified as deformation-controlled for any e/g ratio. The Type 2 curve depicted in Figure 2-3 is representative of ductile behavior where there is an elastic range (point 0 to point 1 on the curve) and a plastic range (points 1 to 2) followed by loss of strength and loss of ability to support gravity loads beyond point 2. Primary and secondary secondary component actions actions exhibiting this type of behavior shall be classified as deformation-controlled if the plastic range is such that e > 2g; otherwise, they shall be classified as forcecontrolled. The Type 3 curve depicted in Figure 2-3 is representative of a brittle or nonductile behavior where there is an elastic range (point 0 to point 1 on the curve) followed by loss of strength and loss of ability to support gravity gravity loads beyond point 1. Primary and secondary component actions displaying Type 3 behavior shall be classified as force-controlled C2.4 C2.4.4 .4.3 .3.1 .1

Defo Deform rmat atio ionn-Co Cont ntro roll lled ed and and Forc ForceeControlled Behavior

Acceptance criteria for primary components that exhibit Type 1 behavior are typically within the elastic or plastic ranges between points 0 and 2, depending on the performance level. Acceptance criteria for secondary elements that exhibit Type 1 behavior can b e within any of the performance ranges. Acceptance criteria for primary and secondary components exhibiting Type 2 behavior will be within the elastic or plastic ranges, depending on the performance level.

2-14

Acceptance criteria for primary and secondary components exhibiting Type 3 behavior will always be within the elastic range. Table C2-1 provides some examples of possible deformation- and force-controlled actions in common framing systems. Classification of force- or deformation-controlled actions are specified for foundation and framing components in Chapters 4 through 8. A given component may have a combination of both force- and deformation-controlled actions. Classification as a deformation-controlled action is not up to the discretion of the user. Deformation-controlled actions have been defined in this standard by the designation of m-factors or nonlinear deformation capacities in Chapters 4 through 8. In the absence of  component testing jus tifying Type 1 or Type 2 behavior, all other actions are to be taken as forcecontrolled.

Table C2-1

Examp amples les of Pos Possible  Deformation-Controlled and  Force-Controlled Actions 

Component

DeformationControlled Action

ForceControlled Action

Moment Frames  Beams • Columns • Joints

Moment (M) M --

Shear (V) Axial load (P), V V1

Shear Walls

M, V

P

Braced Frames • Braces • Beams • Columns • Shear Link

P --V

-P P P, M

Connections

P, V, M 3

P, V, M

Diaphragms

M, V2

P, V, M

1.

Shear may be a deformation-controlle d action in steel moment frame construction.

2.

If the diaphragm carries lateral loads from vertical seismic resisting elements above the diaphragm level, then M and V shall be considered force-controlled actions.

3.

Axial, shear, and moment may be deformation-controlled actions for certain steel and wood connections.

Seismic Rehabilitation Prestandard

FEMA 356

Chapter 2: General Requirements

Figure C2-1 shows the generalized force versus deformation curves used throughout this standard to specify component modeling and acceptance criteria for deformation-controlled actions in any of the four basic material types. Linear response is depicted between point A (unloaded component) and an effective yield point B. The slope from B to C is typically a small percentage (0-10%) of the elastic slope, and is included to represent phenomena such as strain hardening. C has an ordinate that represents the strength of the component, and an abscissa value equal to the deformation at which significant strength degradation begins (line CD). Beyond point D, the component responds with substantially reduced strength to point  E . At deformations greater than point  E , the component strength is essentially zero. The sharp transition as shown on idealized curves in Figure C2-1 between points C and D can result in computational difficulty and an inability to converge when used as modeling input in nonlinear computerized analysis software. In order to avoid this computational instability, a small slope may be provided to the segment of these curves between points C and D. For some components it is convenient to prescribe acceptance criteria in terms of deformation (e.g., θ or ∆), while for others it is more convenient to give criteria in terms of deformation ratios. To accommodate this, two types of idealized force vs. deformation curves are used in Figures C2-1 (a) and (b). Figure C2-1(a) shows normalized force (Q/QCE ) versus deformation (θ or ∆) and the parameters a, b, and c. Figure C2-1(b) shows normalized force ( Q/  QCE ) versus deformation ratio ( θ/θ y, ∆/∆ y, or ∆/h) and the parameters d, e, and c. Elastic stiffnesses and values for the parameters a, b, c, d, and e that can be used for modeling components are given in Chapters 5 through 8. Acceptance criteria for deformation or deformation ratios for primary members (P) and secondary members (S) corresponding to the target Building Performance Levels of Collapse Prevention (CP), Life Safety (LS), and Immediate Occupancy (IO) as shown in Figure 2-1(c) are given in Chapters 5 through 8.

FEMA 356

Figure C2-1

Seismic Rehabilitation Prestandard

Generalized Component Force-  Deformation Relations for Depicting  Modeling and Acceptance Criteria 

2-15

Chapter 5: Steel

5.5.2.2.2

Nonlinear Static Procedure

If the Nonlinear Static Procedure of Chapter 3 is used, the following criteria shall apply: 1. Elastic component properties shall be modeled as specified in Section 5.5.2.2.1. 2. Plastification shall be represented by nonlinear moment-curvature and interaction relationships for beams and beam-columns derived from experiment or analysis. 3. Linear or nonlinear behavior of panel zones shall be included in the mathematical model except as indicated in Section 5.5.2.2.1, Item 3.

The parameters Q and QCE  in Figure 5-1 are generalized component load and generalized component expected strength, respectively. For beams and columns, θ is the total elastic and plastic rotation of  the beam or column, θ y is the rotation at yield, ∆ is total elastic and plastic displacement, and ∆y is yield displacement. For panel zones, θ y is the angular shear deformation in radians. Figure 5-2 defines chord rotation for beams. The chord rotation shall be calculated either by adding the yield rotation, θ y, to the plastic rotation or taken to be equal to the story drift. Use of Equations (5-1) and (5-2) to calculate the yield rotation, θ y, where the point of contraflexure is anticipated to occur at the mid-length of the beam or column, respectively, shall be permitted.

In lieu of relationships derived from experiment or analysis, the generalized load-deformation curve shown in Figure 5-1, with parameters a, b, c, as defined in Tables 5-6 and 5-7, shall be used for components of  steel moment frames. Modification of this curve shall be permitted to account for strain-hardening of  components as follows: (a) a strain-hardening slope of  3% of the elastic slope shall be permitted for beams and columns unless a greater strain-hardening slope is  justified by test data; and (b) where panel zone yielding occurs, a strain-hardening slope of 6% shall be used for the panel zone unless a greater strain-hardening slope is  justified by test data.

Figure 5-2 Figure 5-1

Generalized Force-Deformation Relation  for Steel Elements or Components 

Definition of Chord Rotation 

Beams:

Columns:

FEMA 356

Seismic Rehabilitation Prestandard

θ y

θ y

 ZF  ye l b = ---------------6 EI b

 ZF  ye l c P = ----------------  1 – --------    6 EI c P ye  

(5-1)

(5-2)

5-13

Chapter 5: Steel

Q and QCE  are the generalized component load and generalized component expected strength, respectively. For flexural actions of beams and columns, QCE  refers to the plastic moment capacity, which shall be calculated using Equations (5-3) and (5-4):

t  p

= Total thickness of panel zone including doubler plates

θ θ y

= Chord rotation = Yield rotation

V CE  = Expected shear strength

Beams:

 Z  Q CE  = M CE  = ZF  ye

(5-3)

C5.5.2.2.2

(5-4)

Strain hardening should be considered for all components. The design professional is directed to FEMA 355D for information concerning nonlinear behavior of various tested connection configurations.

Columns: P Q CE  = M CE  = 1.18 ZF  ye  1 – --------   ≤  ZF  ye  P ye  

= Plastic section modulus

5.5.2.2.3

Nonlinear Static Procedure

Nonlinear Dynamic Procedure

For panel zones, QCE refers to the plastic shear capacity of the panel zone, which shall be calculated using Equation (5-5):

The complete hysteretic behavior of each component shall be determined experimentally.

Panel Zones:

The design professional is directed to FEMA 355D for information concerning nonlinear behavior of various tested connection configurations.

QCE  = V CE  = 0.55 F  ye d c t  p

(5-5)

where: d c

= Column depth

 E 

= Modulus of elasticity

F  ye

= Expected yield strength of the material

 I 

= Moment of inertia

lb

= Beam length

lc

= Column length

Strength

5.5.2.3.1

General

Component strengths shall be computed in accordance with the general requirements of Section 5.4.2 and the specific requirements of this section. Linear Static and Dynamic Procedures

The strength of elements of structural steel under flexural actions with negligible axial load present shall be calculated in accordance with this section. These actions shall be considered deformation-controlled. 1. Beams:

= Axial force in the member at the target displacement for nonlinear static analyses, or at the instant of computation for nonlinear dynamic analyses. For linear analyses, P shall be taken as QUF , calculated in accordance with Section 3.4.2.1.2

P ye

= Expected axial yield force of the member =  AgF   ye

Q

= Generalized component load

QCE  = Generalized component expected strength

5-14

Nonlinear Dynamic Procedure

5.5.2.3

5.5.2.3.2

 M CE  = Expected flexural strength P

C5.5.2.2.3

The expected flexural strength, QCE , of beam components shall be determined using equations for design strength,  M  p, given in AISC (1997) Seismic Provisions , except that φ shall be taken as 1.0 and F  ye shall be substituted for F  y. The component expected strength, QCE , of beams and other flexural deformation-controlled members shall be the lowest value obtained for the limit states of yielding, lateral-torsional buckling, local flange buckling, or shear yielding of the web.

Seismic Rehabilitation Prestandard

FEMA 356

Chapter 5: Steel

Table 5-6

Modeling Parameters and Acceptance Criteria for Nonlinear Procedures —S   tructural Steel  Components  Modeling Parameters Plastic Rotation Angle, Radians

Component/Action

Acceptance Criteria Plastic Rotation Angle, Radians

Residual Strength Ratio

Primary

Secondary

a

b

c

IO

LS

CP

LS

CP

9θy

11θy

0.6

1θy

6θ y

8θ y

9θy

11θy

4θy

6θy

0.2

0.25θy

2θ y

3θ y

3θy

4θ y

Beams —flexure a.

b 52 ---- f  -- ≤ -----------2 t  f  F   ye

and

418 h ----- ≤ -----------t w F   ye

b.

b 65 ---- f  -- ≥ -----------2 t  f  F   ye

or

640 h ----- ≥ -----------t w F   ye

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall be performed, and the lowest resulting value shall be used

c. Other Columns —flexure 2, 7 For P/P CL < 0.20

a.

b 52 ---- f  -- ≤ -----------2 t  f  F  ye and 300 h ----- ≤ -----------t w F 

9θy

11θy

0.6

1θy

6θ y

8θ y

9θy

11θy

4θy

6θy

0.2

0.25θy

2θ y

3θ y

3θy

4θ y

 ye

b 65 -- ≥ -----------b. d  ---- f  2 t  f  F  ye or

460 h ----- ≥ -----------t w F   ye

c. Other

5-40

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall be performed, and the lowest resulting value shall be used

Seismic Rehabilitation Prestandard

FEMA 356

Chapter 5: Steel

Table 5-6

Modeling Parameters and Acceptance Criteria for Nonlinear Procedures —S   tructural Steel  Components (continued)  Modeling Parameters Plastic Rotation Angle, Radians

Component/Action

Acceptance Criteria Plastic Rotation Angle, Radians

Residual Strength Ratio

Primary

Secondary

a

b

c

IO

LS

CP

LS

CP

 — 3 

 — 4 

0.2

0.25θy

— 5 

 — 3 

 — 6 

 — 4 

1θ y

1.5θy

0.2

0.25θy

0.5θy

0.8θy

1.2θy

1.2θy

For 0.2 < P/P CL < 0.50 a.

b 52 ---- f  -- ≤ -----------2 t  f  F   ye

and h 260 ----- ≤ -----------t w F   ye

b.

65 b ---- f  -- ≥ -----------2 t  f  F  ye or

h 400 ----- ≥ -----------t w F  ye c. Other Column Panel Zones

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall b e performed, and the lowest resulting value shall be used 12θy

12θy

1.0

1θy

8θy

11θy

12θy

12θy

0.2

0.01280.0003d 

0.03370.0009d 

0.02840.0004d 

0.03230.0005d 

0.043-0.0006d 

Fully Restrained Moment C onnections13  WUF12 

0.051-0.0013d  0.043-0.0006d 

Bottom haunch in WUF with slab

0.026

0.036

0.2

0.0065

0.0172

0.0238

0.0270

0.036

Bottom haunch in WUF without slab

0.018

0.023

0.2

0.0045

0.0119

0.0152

0.0180

0.023

Welded cover plate in WUF12 

0.056-0.0011 d  0.056-0.0011d 

0.2

0.01400.0003d 

0.03190.0006d 

0.04260.0008d 

0.04200.0008d 

0.056-0.0011 d 

Improved WUF-bolted web12 

0.021-0.0003d  0.050-0.0006d 

0.2

0.00530.0001d 

0.01390.0002d 

0.02100.0003d 

0.03750.0005d 

0.050-0.0006d 

0.2

0.0103

0.0312

0.0410

0.0410

0.054

Improved WUF-welded web

0.041

0.054

Free flange12 

0.067-0.0012d  0.094-0.0016d 

0.2

0.01680.0003d 

0.05090.0009d 

0.06700.0012d 

0.07050.0012d 

0.094-0.0016d 

Reduced beam section 12 

0.050-0.0003d  0.070-0.0003d 

0.2

0.01250.0001d 

0.03800.0002d 

0.05000.0003d 

0.05250.0002d 

0.07-0.0003d 

0.06

0.2

0.0075

0.0228

0.0300

0.0450

0.06

Welded flange plates a. Flange plate net section b. Other limit states

0.03 force-controlled

Welded bottom haunch

0.027

0.047

0.2

0.0068

0.0205

0.0270

0.0353

0.047

Welded top and bottom haunches

0.028

0.048

0.2

0.0070

0.0213

0.0280

0.0360

0.048

Welded cover-plated flanges

0.031

0.031

0.2

0.0078

0.0177

0.0236

0.0233

0.031

FEMA 356

Seismic Rehabilitation Prestandard

5-41

Chapter 5: Steel

Table 5-6

Modeling Parameters and Acceptance Criteria for Nonlinear Procedures —S   tructural Steel  Components (continued)  Modeling Parameters Plastic Rotation Angle, Radians

Component/Action

a

Acceptance Criteria Plastic Rotation Angle, Radians

Residual Strength Ratio

Primary

Secondary

b

c

IO

LS

CP

LS

CP

Partially Restrained Moment Connections Top and bottom clip angle9  a. Shear failure of rivet or bolt (Limit State 1)8 

0.036

0.048

0.200

0.008

0.020

0.030

0.030

0.040

b. Tension failure of horizontal leg of angle (Limit State 2)

0.012

0.018

0.800

0.003

0.008

0.010

0.010

0.015

c.

Tension failure of rivet or bolt (Limit State 3)8 

0.016

0.025

1.000

0.005

0.008

0.013

0.020

0.020

d. Flexural failure of angle (Limit State 4)

0.042

0.084

0.200

0.010

0.025

0.035

0.035

0.070

a. Shear failure of rivet or bolt (Limit State 1)8 

0.036

0.048

0.200

0.008

0.020

0.030

0.030

0.040

b. Tension failure of rivet or bolt (Limit State 2)8 

0.016

0.024

0.800

0.005

0.008

0.013

0.020

0.020

c.

Tension failure of split tee stem (Limit State 3)

0.012

0.018

0.800

0.003

0.008

0.010

0.010

0.015

d. Flexural failure of split tee (Limit State 4)

0.042

0.084

0.200

0.010

0.025

0.035

0.035

0.070

a. Failure in net section of flange plate or shear failure of bolts or rivets8 

0.030

0.030

0.800

0.008

0.020

0.025

0.020

0.025

b. Weld failure or tension failure on gross section of plate

0.012

0.018

0.800

0.003

0.008

0.010

0.010

0.015

Double split tee9

Bolted flange plate9 

Bolted end plate a.

Yield of end plate

0.042

0.042

0.800

0.010

0.028

0.035

0.035

0.035

b.

Yield of bolts

0.018

0.024

0.800

0.008

0.010

0.015

0.020

0.020

c.

Failure of weld

0.012

0.018

0.800

0.003

0.008

0.010

0.015

0.015

Composite top clip angle bottom 9

5-42

a. Failure of deck reinforcement

0.018

0.035

0.800

0.005

0.010

0.015

0.020

0.030

b. Local flange yielding and web crippling of column

0.036

0.042

0.400

0.008

0.020

0.030

0.025

0.035

Seismic Rehabilitation Prestandard

FEMA 356

Chapter 5: Steel

Table 5-6

Modeling Parameters and Acceptance Criteria for Nonlinear Procedures —S   tructural Steel  Components (continued)  Modeling Parameters Plastic Rotation Angle, Radians

Component/Action

Acceptance Criteria Plastic Rotation Angle, Radians

Residual Strength Ratio

Primary

Secondary

a

b

c

IO

LS

CP

LS

CP

Yield of bottom flange angle

0.036

0.042

0.200

0.008

0.020

0.030

0.025

0.035

d. Tensile yield of rivets or bolts at column flange

0.015

0.022

0.800

0.005

0.008

0.013

0.013

0.018

e. Shear yield of beam flange connection

0.022

0.027

0.200

0.005

0.013

0.018

0.018

0.023

0.0290.0002d bg 

0.15-0.0036d bg 

0.400

0.00730.0001d bg 

--

--

0.11250.0027d bg 

0.150.0036d bg 

0.15-0.0036d bg  0.15-0.0036d bg 

0.400

0.03750.0009d bg 

--

--

0.11250.0027d bg 

0.150.0036d b g

0.8

0.005

0.11

0.14

0.14

0.16

13θy

13θy

15θy

c.

Shear connection with slab12  Shear connection without slab12 

EBF Link Beam10, 11

1.6 M CE  a. e ≤ ------------------V C E 

0.15

0.17

2.6 M CE  b. e ≥ ------------------V C E 

Same as for beams.

.6 M CE  2.6 M CE  c. ------------------- < e < ------------------V CE  V CE  Steel Plate Shear Walls 1

Linear interpolation shall be used.

14θy

16θy

0.7

0.5θy

10θy

1.

Values are for shear walls with stiffeners to prevent shear buckling.

2.

Columns in moment or braced frames shall be permitted to be designed for the maximum force delivered by connecting members. For rectangular or square columns, replace bt  /2t  f  with b/t , replace 52 with 110, and replace 65 with 190.

3.

Plastic rotation = 11 (1-1.7 P/PCL) θy.

4.

Plastic rotation = 17 (1-1.7 P/PCL) θy.

5.

Plastic rotation = 8 (1-1.7 P/PCL) θy.

6.

Plastic rotation = 14 (1-1.7 P/PCL) θy.

7.

Columns with P/PCL > 0.5 shall be considered force-controlled.

8.

For high-strength bolts, divide values by 2.0.

9.

Web plate or stiffened seat shall be considered to carry shear. Without shear connection, action shall not be classified as secondary. If beam depth, d b > 18 inches, multiply m-factors by 18 /d b.

10. Deformation is the rotation angle between link and beam outside link or column. 11. Values are for link beams with three or more web stiffeners. If no stiffeners, divide values by 2.0. Linear interpolation shall be used for one or two stiffeners. 12. d is the beam depth; d bg is the depth of the bolt group. 13. Tabulated values shall be modified as indicated in Section 5.5.2.4.2, item 4.

FEMA 356

Seismic Rehabilitation Prestandard

5-43