CYCLIC BEHAVIOR OF DEEP SLENDER

WIDE-FLANGE STEEL BEAM-

UNDER COMBINED LATERAL

DRIFT AND AXIAL LOAD

A. Elkady1 and D. G. Lignos

2

ABSTRACT

During a seismic event, first-story

( drift demands coupled with -

selected

behavior of wide-flange beam-columns i

FEA simulations are used to evaluate: (a) the

flexural strength of the wide-flange beam-columns; (b) their -

a

-

web and flange slenderness ratios near the compactness limits of current seismic

design provisions. It is found that a deep slender wide flange column experiences more than two

times the axial shortening of a stocky wide flange column. -

wide-flange sections undergo

lateral loading current modeling recommendations

-

1PhD Candidate, Dept. of Civil Eng. and Applied Mechanics, McGill University, Montreal, Canada H3A 0C3

2Assistant Professor, Dept. of Civil Eng. and Applied Mechanics, McGill University, Montreal, Canada H3A 0C3

Elkady A, Lignos DG. Cyclic behavior of deep - -

axial load. Proceedings of the 10th

National Conference in Earthquake Engineering, Earthquake Engineering

Research Institute, Anchorage, AK, 2014.

Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

- -

Drift And Axial Load

A. Elkady1

and D. G. Lignos2

ABSTRACT During a seismic event, first-story columns in steel Special

- In

this paper, - -

flexural strength of the wide-flange beam-column -

- sections with web and flange slenderness ratios

- capping plastic rota -

-

Introduction

Deep wide-flange columns are typically used as part of steel buildings with perimeter special

moment frames (SMFs) in North America. These members are often selected over stocky

sections due to their high inertia-to-weight ratio. Deep slender wide-flange sections are

characterized by: 1) depths larger than 406 mm (i.e., 16 inches); and 2) compact webs and

λhd)based

on [1]. The high slenderness ratios of the webs and flanges imply weak resistance to twisting and

out-of-plane buckling in addition to susceptibility to local buckling failure modes.

Experimental data on the cyclic behavior of deep slender wide-flange beam-columns is

not presently available in the literature. Limited beam-column tests were conducted on either

small and/or stocky sections [2-4]. These tests demonstrated that stocky sections (i.e., h/tw<30

and bf/2tf<6) perform well even at high compressive axial load ratios of P/Py =0.8, where Py is

the axial yield strength of a steel column (Py is the product of the cross section gross area Agross

1PhD Candidate, Dept. of Civil Eng. and Applied Mechanics, McGill University, Montreal, Canada H3A 0C3

2Assistant Professor, Dept. of Civil Eng. and Applied Mechanics, McGill University, Montreal, Canada H3A 0C3

Elkady A, Lignos DG. - b -

axial load. Proceedings of the 10th

National Conference in Earthquake Engineering, Earthquake Engineering

Research Institute, Anchorage, AK, 2014.

and the yield stress Fy). Experimental studies on deep slender wide-flange beams [5, 6] have

demonstrated that these sections deteriorate fast in flexural stiffness due to web and

flange local buckling under cyclic loading.

This paper investigates the cyclic behavior of a range of wide-flange beam-columns

through detailed finite element (FE) analysis. These beam-columns are subjected to combined

lateral drift and axial load ratios. A typical first-story interior column is considered for this

investigation. The FE model simulates the rotational flexibility expected at the column's top end.

The FE results are used to evaluate and assess the following issues: (a) the cyclic deterioration in

flexural strength of beam-columns; (b) the pre-capping plastic rotation of beam-columns; and (c)

the axial shortening of a steel column when it is subjected to cyclic loading.

Member Sizes and Loading Protocols

A set of 40 wide-flange steel sections is selected for the FE study. The selected sections

represent a wide spectrum of web and flange slenderness ratios. The range of sections covers

those typically used as first-story columns of SMFs in low- and mid-rise buildings in North

America. The selected sections along with some of their main geometric properties are

summarized in Table 1. The web and flange slenderness ratios of 35 sections comply with the

compactness limits for highly ductile members (λhd) as specified by [1] even at high levels of

axial load ratio (i.e., P/Py=0.5). The remaining 5 sections (marked with asterisk), are compact

sections with web and flange slenderness ratios that comply with the compactness limits

specified for moderately ductile members (λmd). It should be noted that for highly ductile

members, the compactness limits for the flange slenderness is 7 and the compactness limit for the

web slenderness is 43, at P/Py=0.5.

Table 1.Summary of wide-flange steel sections used in the FE study.

Section bf /2tf h/tw ry [mm] Cw [mm

6] J [mm

4]

W36

W36x650 2.48 16.0 104 3.0E+14 2.5E+08 W36x527 2.96 19.6 102 2.2E+14 1.4E+08 W36x439 3.48 23.1 100 1.7E+14 8.0E+07 W36x359 4.16 28.1 99 1.5E+14 5.9E+07 W36x280 5.29 35.6 97 9.8E+13 2.2E+07 W36x230 6.54 41.4 95 7.6E+13 1.2E+07 W36x135* 7.56 54.1 60 1.8E+13 2.9E+06

W33

W33x387 3.55 23.7 96 1.2E+14 6.2E+07 W33x318 4.23 28.7 94 9.6E+13 3.5E+07 W33x263 5.03 34.3 93 7.6E+13 2.0E+07 W33x221 6.20 38.5 91 6.0E+13 1.2E+07 W33x201 6.85 41.7 90 5.3E+13 8.7E+06 W33x118* 7.76 54.5 59 1.3E+13 2.2E+06

W30

W30x391 3.19 19.7 93 9.8E+13 7.2E+07 W30x326 3.75 23.4 91 7.7E+13 4.3E+07 W30x261 4.59 28.7 90 5.8E+13 2.3E+07 W30x211 5.74 34.5 89 4.5E+13 1.2E+07 W30x148 4.44 41.6 58 1.3E+13 6.0E+06 W30x90* 8.52 57.5 53 6.4E+12 1.2E+06

W27 W27x539 2.15 12.1 93 1.2E+14 2.1E+08 W27x336 3.19 18.9 88 6.1E+13 5.5E+07 W27x258 4.03 24.4 85 4.3E+13 2.6E+07

Table 1. (continue) Summary of wide-flange steel sections used in the FE study.

Section bf /2tf h/tw ry [mm] Cw [mm

6] J [mm

4]

W27 W27x194 5.24 31.8 84 3.0E+13 1.1E+07 W27x161 6.49 36.1 82 2.3E+13 6.3E+06 W27x84* 7.78 52.7 53 4.8E+12 1.2E+06

W24

W24x370 2.51 14.2 83 5.0E+13 8.4E+07 W24x279 3.18 18.6 81 3.4E+13 3.8E+07 W24x250 3.49 20.7 80 2.9E+13 2.8E+07 W24x192 4.43 26.6 78 2.1E+13 1.3E+07 W24x146 5.92 33.2 76 1.5E+13 5.6E+06 W24x131 6.70 35.6 75 1.3E+13 4.0E+06 W24x68* 7.66 52.0 47 2.5E+12 7.9E+05

W21

W21x201 3.86 20.6 77 1.7E+13 1.7E+07 W21x147 5.44 26.1 75 1.1E+13 6.4E+06 W21x122 6.45 31.3 74 8.8E+12 3.7E+06 W21x73 5.60 41.2 46 2.0E+12 1.2E+06

W16

W16x100 5.29 23.2 64 3.2E+12 3.4E+06 W16x77 6.77 29.9 62 2.3E+12 1.6E+06 W16x57 4.98 33.0 41 7.1E+11 9.2E+05 W16x45 6.23 41.1 40 5.3E+11 4.6E+05

* Compact λmd) sections

In order to thoroughly evaluate the FE results, the selected 40 wide-flange sections are

divided into 8 sets based on their flange and web slenderness (see Fig. 1). From this figure, sets

numbered 1, 2, and 3 represent compact sections with low, moderate, and high web and flange

slenderness ratios, respectively. Set 4 represents the 5 compact () sections (see Fig. 1).

(a) (b)

Figure 1. Wide flange sections categorized by (a) web and (b) flange slenderness ratios.

The set of 40 sections is subjected to cyclic lateral loading combined with different levels

of constant compressive axial load ratio. The lateral loading protocol implemented in the FE

study is the symmetric SAC protocol [7]. This protocol is combined with different levels of

constant compressive axial loads: 0%, 20%, 35%, and 50% Py. The axial load (20% and higher)

is representative of that applied to a first-story interior column of a steel SMF. These levels of

compressive axial loads are based on observations from nonlinear response history analyses of

perimeter SMFs of archetype buildings with heights ranging from 2 to 20 stories [8, 9].

q “ Y -X” SYM

refers to the symmetric SAC protocol, and X is the level of axial load as a percentage of Py.

10 20 30 40 50 60Web Slenderness, h/t

w

Set W2 Set W3 Set W4Set W1

43.032.522.0

compact sections

hd

compact sections

md

2 3 4 5 6 7 8 9Flange Slenderness, b

f/2t

f

Set F4Set F2 Set F3Set F1

3.9 7.05.5

compact sections

md

compact sections

hd

Additionally, a monotonic lateral loading case with no axial load, MON-00, is also conducted.

Finite Element Modeling

A typical first-story column is modeled ABAQUS-FEA/CAE [10] as shown in Fig. 2a. The

column has a length, L, of 4.6 meters (15 feet) with a fully-fixed support at one end (i.e. fixed

support) and partially-fixed support at the other end (i.e. flexible support). These boundary

conditions simulate the variation of the moment gradient observed in first-story columns during

an earthquake once plastification occurs at the column base. The simulated boundary conditions

are a better representation of the boundary conditions of first-story columns than the ones used in

previous exploratory FE studies for the same purpose [3, 11, 12]. The flexible support is

’

required rotational stiffness such that the inflection point of the column before flexural yielding

is at 75% of the column height, measured from the column base. Typically, this preset location

of the inflection point is expected in first-story columns while they remain elastic. Once yielding

occurs at the column base, the location of the inflection point changes and hence its movement

needs to be monitored. This is achieved by first monitoring the normal stresses at several

sections along the column length. These stresses are then used to calculate and construct the

moment gradient along the column in order to trace the position of the inflection point.

(a) (b)

Figure 2. (a) Boundary conditions of the FE model; and (b) external forces acting on the

deformed first-story column.

As illustrated in Fig. 2b, the moment at the column base can be calculated using Eqn. 1,

where Vbase is the first order shear force at the base, Li is the distance between the column base

and the inflection point, P is the applied axial load, and δ is the displacement at the column's top

end. All the variables in Eqn. 1 are known during the analysis except Li (i.e. location of inflection

Ux=Restrain

Uy=Restrain

Uz=Restrain

Rx=Restrain

Ry=Restrain

Rz=Restrain

Ux=Restrain

Rx=Restrain

Ry=Restrain

Rz=Restrain

Flexible

Beam

Fixed Support

Flexible Support

180"

Lbrace

Ux=Restrain

Uy=Guide

Ry=Restrain

Rz=Restrain

Ux=Restrain

Lateral Support

Vbase

P

Mbase

PMFlexible

L

Li

δ

Inflection

Pointδ

Li

L

θ

point), which is calculated as discussed in the previous paragraph.

base base i iM V L P L / L (1)

The column is laterally supported at a distance Lbrace measured from the column base.

The length Lbrace is taken as the minimum of Lb,HD and Lp as given by Eqns. 2 and 3, where Lb,HD

is the minimum length between points that are braced against lateral displacement for h

members [1] and Lp is the maximum laterally unbraced length required to avoid lateral

torsional buckling for the yielding limit state in steel beams [13]. This is done in order to

investigate the effect of plastic hinging on the overall column performance without considering

the possibility of lateral torsional buckling throughout the member. The latter is currently

investigated by a separate FE study. In all cases, the length Lbrace was controlled by Lp.

0 086b,HD y yL . r E / F (2)

1 76p y yL . r E / F (3)

The column is meshed using 1"x1" 4- q “ 4 ”

global geometric imperfections are introduced to the model by scaling and superimposing the

’ G

with ASTM [14] limits. The approach to introduce such imperfections has been discussed in

detail in a companion paper [12]. Residual stresses was shown to be insignificant based on the

same study [12]; hence they are not considered as part of the FE model discussed herein.

The nonlinear cyclic behavior of the column is simulated using the nonlinear

isotropic/kinematic hardening material model in ABAQUS. A modulus of elasticity E=208000

MPa (30165 ksi) and an expected yield stress of Fy=383 MPa (55.5 ksi) is considered to

represent typical ASTM A992 Gr.50 steel (Fy=345MPa). The additional four parameters, used to

define the cyclic hardening properties of the material model, are as follows: C=6895 MPa (1000

ksi), γ=25, Q∞=172 MPa (25 ksi), and b=2. These

tests conducted by Krawinkler et al. [15] and MacRae et al. [2]. These parameters are

independent of the loading history and axial load demand that a steel column is subjected to [12].

The aforementioned FE modelling approach has been validated against past experimental data

- tests [2] as discussed in [12].

Results and Discussion

This section summarizes the results based on the FE analysis of the 40 sections shown in Table

1. Emphasis is placed on the following issues: (a) the cyclic deterioration in flexural strength of

the steel columns; (b) the pre-capping plastic rotation of steel beam-columns; and (c) the column

axial shortening.

Cyclic Deterioration in Flexural Strength

Fig. 3 shows the simulated peak strength response at the column base (normalized by the plastic

strength, Mp) measured at a range of chord rotations, θ: 1, 2, 3, 4, and 5% rads. From this figure,

it is evident that the applied axial load and the section cross sectional slenderness affect both the

level of cyclic strain hardening and the rate of cyclic deterioration in flexural strength of a steel

column. Fig. 3a shows that, in the absence of axial load, cyclic strain hardening (expressed by

the ratio of the maximum moment to plastic moment, Mmax/Mp) can reach a factor of 2.0 for

highly compact sections (i.e. Sets W1 and F1). This is primarily attributed to: 1) the large

number of small inelastic cycles within the symmetric SAC protocol; and 2) the absence of axial

load. Generally, the level of cyclic strain hardening decreases when the applied axial load

increases. The same observation holds true when the web and flange slenderness ratios increase

(see Table 2).

In the absence of axial load (see Fig. 3a), all the sections are able to maintain their plastic

bending strength at 4% chord rotation. When the applied axial load increases (see Figs. 4b to 4d),

the rate of cyclic deterioration in flexural strength of steel columns increases. For an applied

axial load larger than 20% Py, seismically compact sections, with high web and flange

slenderness ratios (i.e., 32.5<h/tw<43 and 5.5<bf/2tf<7), approach zero flexural strength before

reaching a 4% chord rotation. At 50% Py (see Fig. 4d), almost all the cross sections reach a zero

flexural strength before reaching a 4% chord rotation.

(a) SYM-00 (b) SYM-20

(c) SYM-35 (d) SYM-50

Figure 3. Normalized peak strength response of steel columns at different chord rotations.

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

Chord Rotation, [rad]

M/M

p

Set W1

Set W2

Set W3

Set W4

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

Chord Rotation, [rad]

M/M

p

Set W1

Set W2

Set W3

Set W4

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

Chord Rotation, [rad]

M/M

p

Set W1

Set W2

Set W3

Set W4

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

Chord Rotation, [rad]

M/M

p

Set W1

Set W2

Set W3

Set W4

Another way to assess the cyclic performance of the steel beam-columns, analyzed as

part of this paper, is to examine if they can sustain 80% of their full plastic flexural strength at

4% chord rotation. This assessment is consistent with the way that fully restrained beam-to-

column connections are evaluated in terms of flexural resistance according to [1]. The average

values of the chord rotation at 80% Mp for each section set are summarized in Table 2. This table

indicates that deep slender wide-flange beam-columns close to the compact limits for highly

ductile members as per [1] (i.e. Sets F3 and W3) reached 80% of their plastic bending moment,

Mp, at chord rotations less than 4% rads even at low axial load ratios (P/Py=0.2).

Table 2. Summary of average chord rotations at 80% Mp and average levels of cyclic strain

hardening, Mmax/Mp.

Chord Rotation at

80% Mp [% rad]

Cyclic Strain

Hardening, Mmax/Mp

P/Py [%] 00 20 35 50 00 20 35 50

Sets based on

flange slenderness

F1 bf/2tf<3.9 >5 >5 4.2 2.6 1.9 1.6 1.4 1.2

F2 3.9<bf/2tf<5.5 >5 4.5 2.5 1.1 1.5 1.2 1 0.8

F3 5.5<bf/2tf<7 >5 3.3 1.3 <1 1.4 1.1 0.9 0.6

F4 bf/2tf >7 >5 1.5 <1 <1 1.2 0.9 0.6 NA

Sets based on web

slenderness

W1 h/tw<22 >5 >5 4.4 3.1 1.9 1.6 1.4 1.2

W2 22<h/tw<32.5 >5 >5 3.2 1.4 1.6 1.3 1.1 0.9

W3 32.5<h/tw<43 >5 3.3 1.3 <1 1.4 1.1 0.9 0.6

W4 h/tw >43 >5 1.5 <1 <1 1.2 0.9 0.6 NA

Pre-Capping Plastic Rotation

The pre-capping plastic rotation is commonly used by structural engineers to model structural

components as part of steel frame buildings in order to conduct a nonlinear static and/or dynamic

analysis to evaluate their seismic performance. The PEER/ATC [16] modeling recommendations

for steel columns (modeling option 1) use the pre-capping plastic rotation θp, in addition to other

strength and deformation parameters, to construct a monotonic "backbone" curve that bounds the

behavior of a steel component as shown in Fig. 4a. For the PEER/ATC [16] modeling option 1,

θp is computed based on the multivariate regression equations developed by [6]. These equations

were obtained from extensive calibrations in which the parameters of the backbone curve were

matched to cyclic experimental data from steel beams with 20<h/tw<55 and 4<bf/2tf<8. The pre-

capping plastic rotation calculated using PEER/ATC [16] “θp, ATC-Option1”

compared to the θp, values as predicted by the FEA. For both the cyclic and monotonic loading

cases, θp is defined as the difference between the capping rotation (at maximum flexural strength)

and the yield rotation (at plastic flexural strength) as shown in Figs. 4b and 4c. It should be noted

that in the case of cyclic loading, the capping rotation is deduced based on the cyclic envelope

curve as shown in Fig. 4b.

(a) (b) (c)

Figure 4. Definition of the pre-capping plastic rotation; (a) PEER/ATC [16], modeling option

1; (b) FEA cyclic loading; (c) FEA monotonic loading.

Figs. 5a and 5b show the θp, ATC-Option1 versus the pre-capping plastic rotation as

predicted by the FEA when the column is subjected to the loading cases MON-00 (noted as θp,

MON-00) and SYM-00 (noted as θp, SYM-00), respectively. For monotonic loading, the θp, ATC-

Option1 values match the θp, MON-00 values for low compactness sections (i.e., 32.5<h/tw<43

and 5.5<bf/2tf<7). However, for highly and moderately compact sections (i.e., h/tw<32.5 and

bf/2tf<5.5), the values of θp, ATC-Option1 are lower than the corresponding ones from θp, MON-

00. This is primarily attributed to the fact that θp, ATC-Option1 is calculated from equations that

are based on calibrations against cyclic and not monotonic data. Normally, the capping rotation

moves towards the yield rotation in such case compared to the monotonic one [6, 16].

In the case of cyclic loading, values of θp, ATC-Option1, by definition, are expected to be

larger than θp, SYM-00 values. However, this is not the case for set W1 as shown in Fig. 5b. The

same observation holds true for set F1. This is attributed to the cyclic strain hardening observed

in highly compact sections due to the delayed formation of flange and web local buckling. Also,

sets W1 and F1, represent sections with h/tw<22 and bf/2tf<3.9; this range of web and flange

slenderness is outside the valid range of the Lignos and Krawinkler [6] regression equations.

(a) (b)

Figure 5. Plastic rotation as calculated per PEER/ATC [16] versus the

plastic rotation predicted by the FE analysis: (a) MON-00; and (b) SYM-00.

-0.05 0 0.05Chord Rotation, [rad]

Mom

ent

[kN

.m]

p

Cyclic data

Mono. Backbone

-0.05 0 0.05

-5

0

5

Chord Rotation, [rad]M

om

ent

[kN

.m]

p

Cyclic data

Envelope curve

Mmax

0.05 0.1 0.150

1

2

3

4

Chord Rotation, [rad]

Mo

men

t [k

N.m

]

Mp

Mmax

p

0 0.05 0.1 0.15 0.20

0.05

0.1

0.15

0.2

p MON-00 [rad]

p A

TC

-Op

tio

n1

[ra

d]

Set W1

Set W2

Set W3

Set W4

0 0.05 0.10

0.02

0.04

0.06

0.08

0.1

p SYM-00 [rad]

p A

TC

-Op

tio

n1

[ra

d]

Set W1

Set W2

Set W3

Set W4

Axial Shortening

Steel columns subjected to inelastic lateral cyclic drift ratios experience axial shortening

primarily due to web local buckling. The level of axial shortening increases in the presence of

high compressive axial loads. The issue of axial shortening has been reported by MacRae et al.

[2] after conducting tests on 1.10m tall cantilever columns with 250UC73 sections (equivalent to

W10x49). Based on this data, MacRae et al. [17] developed empirical equations to predict the

column axial shortening as a function of the applied axial load level, P/Py and the cumulative

inelastic drift, ΣθH.

Fig. 6 shows the axial shortening ∆a, as a percentage of the column length, versus the

cumulative inelastic drift ΣθH for all the column sections that were analyzed as part of this paper.

The axial shortening, ∆a, is deduced by monitoring the axial displacement of the column's top

end. At any loading stage, the cumulative inelastic drift, ΣθH, is defined as the sum of absolute

peak drift values for all cycles following the yield drift (i.e. inelastic cycles). It should be noted

that at the second 4% drift cycle of the SYM protocol, the average value of the cumulative

inelastic drift, for all sections, is 0.7. This value for cumulative inelastic drift, ΣθH=0.7, is used

next as reference value for assessing the column axial shortening.

(a) SYM-00 (b) SYM-20

(c) SYM-35 (d) SYM-50

Figure 6. Axial shortening versus cumulative inelastic drift ratio.

0 0.5 1 1.5 2 2.50

5

10

15

20

25

Cummulative Inelastic Drift [rad]

Axia

l D

ispla

cmen

t [%

]

Set W1

Set W2

Set W3

Set W4

0 0.5 1 1.5 2 2.50

5

10

15

20

25

Cummulative Inelastic Drift [rad]

Axia

l D

ispla

cmen

t [%

]

Set W1

Set W2

Set W3

Set W4

0 0.5 1 1.5 2 2.50

5

10

15

20

25

Cummulative Inelastic Drift [rad]

Axia

l D

ispla

cmen

t [%

]

Set W1

Set W2

Set W3

Set W4

0 0.5 1 1.5 2 2.50

5

10

15

20

25

Cummulative Inelastic Drift [rad]

Axia

l D

ispla

cmen

t [%

]

Set W1

Set W2

Set W3

Set W4

Fig. 6a shows that, at 0% Py and ΣθH=0.7, the level of axial shortening is below 2% of the

total column length for all the seismically compact sections. This is attributed to the occurrence

of web/flange local buckling at chord rotations larger than 4% when subjected to zero axial load

(i.e., SYM-00). When an axial load of 20% Py is applied, a significant increase in column axial

shortening is observed (see Fig. 6b). At 20% Py and ΣθH=0.7, highly compact sections (i.e.,

h/tw<22 and bf/2tf<3.9) experience an average ∆a equal to 3% compared to 7% for low

compactness sections (i.e., 32.5<h/tw<43 and 5.5<bf/2tf<7). The column axial shortening

increases while the applied column axial load increases (see Figs. 6c and 6d). However, for axial

load ratios P/Py >35%, a further increase in axial load level has a minor effect on the column

axial shortening. This agrees with MacRae et al. [17] findings that axial shortening does not

increase after a critical axial load level.

Summary and Conclusions

The cyclic behavior of a range of wide-flange steel beam-columns was investigated

through detailed finite element (FE) analysis. The beam-columns are subjected to the SAC

symmetric lateral loading protocol, as well as, different levels of constant compressive axial

load. The main findings of the FE analysis are summarized as follows:

At 0% Py axial load, wide-flange sections with h/tw<22 and bf/2tf<3.9 experience high

levels of cyclic strain hardening. The maximum moment Mmax reaches about 1.9Mp

compared to 1.4Mp for sections with 32.5<h/tw<43 and 5.5<bf/2tf<7.

At P/Py = 20%, slender wide-flange beam-columns with 32.5<h/tw<43 and 5.5<bf/2tf<7

reach 80% of their plastic strength at chord rotations less than 4% rads.

Except for the load case SYM-50, highly compact wide-flange sections with h/tw<22 and

bf/2tf<3.9 are able to maintain 80% of their plastic bending resistance at chord rotations

larger than 4% rads.

The pre-capping plastic rotation based on PEER/ATC [16], modeling option 1, is shown

to be adequate for predicting the monotonic behavior of sections with 32.5<h/tw<43 and

5.5<bf/2tf<7. However, it is underestimated for sections with h/tw<32.5 and bf/2tf<5.5.

The pre-capping rotation based on PEER/ATC [16], modeling option 1, is underestimated

for sections with h/tw<22 and bf/2tf<3.9 undergoing the SYM-00 loading case.

At 20% Py and ΣθH=0.7 (corresponding to the second 4% drift cycle), highly compact

wide-flange sections with h/tw<22 and bf/2tf<3.9, experience an average axial shortening

∆a of 3% of the column length compared to 7% for slender sections with 32.5<h/tw<43

and 5.5<bf/2tf<7. At axial load levels P/Py>35%, the increase in axial shortening is minor.

It should be noted that the results presented here are dependent on the applied loading

protocols and the selected beam-column boundary conditions. The authors currently evaluate the

behavior of the same set of beam-columns for other lateral and axial loading protocols. The

findings from the extensive analytical study summarized herein will also be complemented by a

series of full-scale experiments on deep wide-flange beam-columns.

Acknowledgments

Council of Cana G

expressed i

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