Seismic Design of Steel Column-Tree Moment-Resisting Frames -...

STRUCTURALSTEELEDUCATIONALCOUNCIL

TECHNICAL INFORMATION & PRODUCT SERVICE

APRIL 1997

Seismic Design ofSteel Column-Tree

Moment-Resisting Frames

by

Abolhassan Astaneh-Asl, Ph.D., P.E.Department of Civil and Environmental Engineering

University of California, Berkeley

©Copyright Abolhassan Astaneh-Asl, 1997

Seismic Design of Steel Column-tree Moment-Resisting Framesby Abolhassan Astaneh-Asl

This report presents information and tips on seismic behavior and design of steel column-tree moment-resisting frames used in building structures. In column-tree moment-resistingframes, short stubs of girders are welded to the column in the shop and then the middleportion of the girder spans are bolted to the column trees in the field. Thus, the system is afield bolted-shop welded structural system. The emphasis of the report is on the seismicbehavior and design of special ductile steel column-tree moment-resisting frames. Asummary of relevant research and applicable code provisions is provided followed bydesign procedures that can be used to design steel column-tree moment-resisting frames.The appendix to the report provides a numerical example on seismic design of a typicalconnection of a steel column-tree moment-resisting frame. The example utilizes theconcepts and recommendations presented in the report.

First Printing, April 15, 1997Figures by Abolhassan Astaneh-Asl unless otherwise indicated.

COPYRIGHT © 1997 by Abolhassan Astaneh-Asl209 Vernal Drive, Alamo, California 94507, Fax and Phone: (510) 946-0903All Rights Reserved

Neither this document nor any part of it may be reproduced, translated or transmitted inany form or by any means, mechanical or electronic, including photocopying, scanning, orby any information storage and retrieval system without written permission of the authorand copyright owner: Abolhassan Astaneh-Asl. The Structural Steel Educational Councilis hereby granted the right to print or reproduce this document in any number in its as-isform prior to January 1, 2003.

The information presented in this publication is for general information only. Theinformation should not be used or relied upon for any specific application withoutcompetent professional examination and verification of its accuracy, suitability, andapplicability by a licensed professional engineer or architect. The publication of the materialcontained herein is not intended as a representation or warranty on the part of theStructural Steel Educational Council, or of any other person or agency named herein, thatthis information is suitable for any general or particular use or of freedom frominfringement of any patent or patents. Anyone making use of this information assumes allliability arising from such use. The information provided in this report on seismic design ofcolumn-tree systems is based on data available on behavior of components of the system.At this writing no test data on the behavior of column tree system as a whole system could•be located.

AC OWI EOCME TS

The publication of this report was made possible in part by the support of the StructuralSteel Educational Council (SSEC). The author wishes to thank all Council members fortheir support and comments. Particularly, written comments provided by Council membersDavid Berrens, Patrick Hasset, Rudy Hofer, James J. Putkey, and Jamie Winans werevery valuable and are sincerely appreciated.

The support provided by a number of agencies to the author's research on the subject ofthis report at the Department of Civil and Environmental Engineering of the University ofCalifornia, Berkeley has been essential in collecting and developing many technologiespresented and used in this report. In particular, the support of the Kajima Corporation ofJapan and the California Universities for Research in Earthquake Engineering (CUREE),in the form of a CUREE/Kajima Research grant to the author, was essential to initiate theresearch on this subject and gather information on it over the last five years.

The author, at present, is a member of the Structural Steel Educational Council ofCalifornia, Research Council on Structural Connections, Earthquake EngineeringResearch Institute, American Society of Civil Engineering, Structural Stability ResearchCouncil and the Council on Tall Buildings and Urban Habitat. The opinions expressed inthis report are solely those of the author and do not necessarily reflect the views of theUniversity of California, Berkeley where the author is a professor of civil andenvironmental engineering, the Structural Steel Educational Council or other agencies andindividuals whose names appear in this report.

SEISMIC DESIGN OFSTEEL COLUMN-TREEMOMENT-RESISTING FRAMES

by Dr. ABOLHASSAN ASTANEH-ASL, P.E.ProfessorDepartment of Civil and Environmental EngineeringUniversity of California, Berkeley

CONTENTS

ACKNOWLEDGMENTS / Page ii

TABLE OF CONTENTS / Page iii

NOTATIONS / Page iv

1. INTRODUCTION / Page 1

2. SEISMIC BEHAVIOR OF BOLTED STEEL MOMENT CONNECTIONS/ Page 11

3. CODE PROVISIONS ON BOLTED STEEL MOMENT-RESISTING FRAMES / Page 13

4. SEISMIC DESIGN OF BOLTED MOMENT-RESISTING FRAMES / Page 15

REFERENCES/Page 25

APPENDIX/Page 27

111

NOTATIONS

A

AbAg

AgfpAgtAgvAg,q,AntAnp

Anv

^npAn •qoa

b

bcfbfd

dbdcdhdsdld2E

Fb

FvfpFvFvpFupFyg

FuFy

h

= area of cross section= area of one bolt= gross area

= gross area of one flange plate

= gross area subject to tension= gross area subject to shear= gross area of web plate subjected to shear= net area subject to tension= net area of plate= net area subject to shear

= net area of one flange plate

= net area of web plate= distance from center of column to center of girder splice= width ofunstiffened element in calculating b/t ratios= width of the column flange= width of flange= overall depth of girder= diameter of bolt= depth of the column

= diameter of bolt hole= depth of panel zone

= arm for calculatingplastic section modulus= arm for calculatingplastic section modulus= modulus of elasticity= shear strength of bolt

= minimum specified yield stress of the plates= nominal slip critical shear resistance (Table J3.6 of the AISC Spec., 1994)= minimum specified yield stress of plate= minimum specified tensile strength of the plates= realistic minimum specified yield stress of the material. For dual yield

point A36, the higher yield value should be used in this context.= minimum specified ultimate strength of the material= minimum specified yield stress of the material

= length of plate

iv

IX

KsKs2LLp

LspMbsMbMngMnsMpbMpgMps

Ms

= moment of inertia of girder

= initial rotational stiffness of splice= rotational stiffness of splice including bolt slippage (for drift analysis)

= length of span; center-to-center of columns= actual length of splice plate= eft. length of splice plate= Lp/2 for bolted-bolted and Lp/4 for welded-bolted splices= moment in the splice due to factored load= moment capacity of bolts= net section ultimate moment capacity= plastic moment capacity of the net section of the plates = Fy d Anp= moment capacity causing bearing yielding = 2.4FupdbNt= plastic moment capacity of the girder= ZxFy= plastic moment capacity of the splice plates= Agfp dFy= factored moment in the girder splice

Mslip = moment that can cause slippage in the connection FvAb N dM(service, corm) = moment in the connection due to application of service ioadsM(service, splice) = moment in the splice due to application of service loads

Mp•pMun•,pmnN

PnPuPyqt

tcftp

tftwV

Vb

VnVpzVsVux•p

VwVyVyx•

Zxfl

asp

= plastic moment capacity of the web plates= Ag,n, d,,•, Fy/4= ultimate moment capacity of the web plates --- Anw d,,•, Fu/4

= stiffness ratio =Kc/(EI/L)= number of bolts= number of bolts

= nominal resistance of flange plate in block shear failure as given below:= axial tension or compression force in the column panel zone= axial tension yield capacity of column= uniformly distributed gravity load on the girder= thickness of the plate or flange.= thickness of the coIumn flange= total thickness of the panel zone= thickness of flange= thickness of web= shear in the splice due to factored load combinations= shear acting on the bolts= nominal shear capacity of panel zone= shear capacity of panel zone= factored shear in the girder splice= ultimate shear capacity of net area of web Plate = 0.6AnwFu= shear capacity of weld line= shear yield capacity of web plates= shear yield capacity of web Plate = 0.6 AgwFy= plastic section modulus of the girder cross section= ratio of plastic moment of splice to plastic moment of girder= elongation of splice plate

•b•n

Os¥

= resistance reduction factor for yielding =0.90

= resistance reduction factor for fracture of bolts = 0.75

= resistance reduction factor for fracture =0.75

= limit ofb/t ratio for elastic local buckling given in the AISC-LRFD Spec., 1994)

= rotation of splice= stiffness ratio =KsV(EI/L)

vi

1. INTRODUCTION

1.1. Introduction

One of the most common types of steel structural system is the moment resisting framingsystem shown in Figure 1.1. Depending on their ductility, steel moment resisting framesare divided into two categories of "Special" and "Ordinary". Figure 1.2 shows typicalbehavior of Special and Ordinary moment-resisting frames under lateral load. Specialmoment-resisting frames are designed to have higher ductility and be able to deforminelasticly during earthquakes. Such inelastic ductile deformations increases damping andreduces stiffness of the structure resulting in smaller seismic forces generated in thestructure. As a result, current codes allow special moment resisting frames to be designedfor smaller seismic forces than similar but ordinary moment frames.

t / // / I

/ / /

/ I I/ / /

I I I

FORCE

Elastic

E

Ordina• Moment Fmn•

*A

Special Frame

O I•

DISPLACEMENT

Figure 1.1. A Typical SteelMoment Frame

Figure 1.2. Behavior of Special andOrdinary Moment-resisting Frames

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Aprfl 1997 I

Prior to the 1994 Northridge earthquake, field-welded moment frames were very popularwith structural engineers and steel fabricators in California. This was due to theireconomy and relative ease of design. Frequently, in seismic areas, a standard field-weldedmoment connection shown in Figure 1.3 was specified and built. However, the 1994Northridge caused damage to a number of field-welded steel moment frames using thedetail shown in Figure 1.3. Other recent earthquakes such as the 1995 Kobe-Japan and the1992 Landers-California have also caused similar damage although in only a fewstructures. More information on the damage to field-welded steel moment frames can befound in References, (Youssefet al, 1995), (SAC, 1995) and (AIJ, 1995).

Since the 1994 Northridge earthquake, a number of studies have been completed or areunderway to understand the causes of the damage, to establish consequences of thedamage (Astaneh-Asl, 1995a), (Astaneh-Asl, 1996) and to develop remedies for thedamaged as well as undamaged field-welded moment frames (SAC, 1995). Many factorshave been identified as possible cause of Northridge damage to steel field weldedconnections. The main culprits at this writing appear to be the type of moment frame,configuration of field-welded connections, stress concentrations due to back-up bars andaccess holes, material properties of steel produced in the past two decades, quality controland inspection of field welds and characteristics of the ground motion.

i

i

i;

Figure 1.3. The Pre-Northridge Moment Frame Connection

The research efforts undertaken after the 1994 Northridge earthquake so far have notyielded a single standard and economical detail that eliminates the problem of field-welded moment connections. In the meantime, design and construction of safe andeconomical steel structures in seismic areas had to continue. Some structural engineershave chosen other material or other structural systems such as braced frames or shear wallsystems. Others have used improved versions of field-welded moment frame connectionsthat have been developed and tested after the Northridge earthquake (SAC, 1995). Yet anumber of structural engineers have used shop-welded andfield-bolted moment framessuccessfully (Astaneh-Asl, 1995b).

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Ap#11997 2

One of the very efficient shop-welded and field bolted systems is the column-tree system.In a column-tree system short segments of the girders or a built-up short girder, usuallytwo to four feet long, are welded to the columns in the shop. Then, after the column-trees are erected in the field, the middle segment of the girder is bolted to the ends of theshort girder stubs. Figure 1.4 shows examples of special ductile column-tree moment-resisting frames.

•,ELOeOLTEO 1 • cotu•mEE*,UOEB / _? I •OMENT - FIELD BOLTED

SPLICES BRACED

FRAME

m • • COL UMN'TR EE

I I . ' - MOMENT

FRAME

Figure 1.4. Typical Column-Tree Moment-Resisting Frames(a) Perimeter Frame and; (b) Planar Frame

The column-tree system discussed in this report is a shop-welded, field-bolted steelstructure. The shop welding of the girder stubs to the columns provides for high qualityand economical welding as well as easy inspection. The field bolting of girder splicesresults in the economy, ease of field erection, possibility of year-round construction almostindependent of the weather conditions. In addition, quality control and inspection ofshop-welded and field bolted connections are easier than the field-welded connections.

In construction projects where field-welding and field inspection are too costly or cannotbe done easily, the use of column-tree system can be more economical than the otherstructural systems that require field-welding. In Japan, perhaps due to the high cost oflabor, and the fact that shop-welding is mostly automated, column-tree frames werealmost the only steel moment-resisting systems until in recent years the detail shown inFigure 1.3 started appearing in Japan (Takanashi, 1994).

1.2. Types of Column-Tree Moment-Resisting Frames Based on Configuration

Various forms of column tree framing system have been used in the past in the UnitedStates and elsewhere. Column-tree systems can be used in planar frames, perimeterframes or as a space moment-resisting frame as shown in Figure 1.4.

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Ap/fl 1997 3

1.3. Types of Column-Tree Moment-Resisting Frames Based on Splice Details

The splice connection of the column-trees to girders can be fully bolted, welded andbolted or fully welded as shown Figure 1.5.

Location of Details

•_.•TC• (Full Penetration Shop Weld)

- • - - / " / - Girder Stub/ / / - H.S. Field Bolts

/ / //-Flange Splice Plate/ • / J • •op Welds (Fillet Welt

Shims •' ii: /-One or Two Web Plates

ii** /,. One or Two Rows ofShop Welds J ii · /High Strength Bolts

i i : : l : - =i i

Shim is Required

. (•Jj• tO Adiust El·vet 'i°n

SHOP-WELDED AND FIELD-BOLTED

(Full Penetration Shop Weld)

* / F•"°"•'raer•tub/ / / ' Flange Splice Plate

/ //I ; ® :: · toAdjust Elevetaion

Shims• i · ! · /- Web Splice Plate .,: :: ** •'- H.S. Bolts.!!- /

.-, [[i i m B m z · i · i m j

: [h•

SHOP-WELDED AND FIELD-BOLTED


Short Girder Stub

Sj- -;

Erection Clip " • i · '

• : : .--

, (e• .".

SHOP- AND FIELD-WELDED


' / ': s;;oTG,•e,s•

/ / ,4/- Field Welds (Fill;:o:elwd;ds (Fillet Weld)//¥! ,w>' / :: · ' •- Flange Splice Plate

:: · ; n e or Two Web Splice Plate(sFiad we,ds -,• ::.:::e:: · •/'One or Two Rows of

• . _ High Strength Bolts:: ·I •"--Field Welds (Fillet Weld)

Shop Welds (Fillet Weld): I•1•

( d )SHOP- AND FIELD-WELDED

Figure 1.5. Example Connections of Column-Tree Moment Frames


1.4. Types of Column-Tree Moment-Resisting Frames Based on Ductility

Similar to any steel moment frame, depending on their ductility the column-tree momentresisting frames can be divided into two categories of "special" and "ordinary" asdiscussed in the following sections.

1.4.a Special Ductile Moment Resisting Frames

The connections and the members of Special Column-tree Moment-resisting Frames aredesigned such that premature brittle local buckling and fracture of the structural membersand the connections are prevented. As a result, the special MRFs behave in a ductilemanner. Figure 1.2 shows behavior of special and ordinary moment frame under lateralload. In general, ordinary moment frames tend to be stiffer and stronger but less ductilethan the special moment-resisting frames for the same application.

In special MRFs, to achieve high ductility, the damage should be in the form of slippage,yielding of steel, delayed and limited inelastic local buckling within the girder connectionsor plastic hinges. Fracture in any part that can impair the gravity-load carrying systemshould be avoided. This type of behavior categorizes the system as a ductile system.

Nader and Astaneh-Asl (1992) based on their studies of seismic behavior of steelstructures, recommended that in special moment-resisting frames the connections shouldhave a rotational ductility of at least 0.03 radian. This limit appears to be accepted by theprofession in the aftermath of the Northridge earthquake (SAC, 1995). In addition, theauthor (Astaneh-Asl, 1995) has suggested that the cumulative inelastic cyclic rotationcapacity of a ductile moment connection should be at least 0.15 radian. This lattercriterion is suggested to ensure sufficient low-cycle fatigue life for the connection.

When a framing system can be categorized as special moment-resisting frame, thereduction factor Rw used in seismic design is given as 12 by the current seismic designcodes (UBC-94).

1.4.b. Ordinary Moment-Resisting Frames

If a steel moment-resisting frame does not meet the requirements of the special momentresisting frame (SMRF), then the frame is not expected to behave in a ductile manner andit is categorized in the seismic design codes as an ordinary moment resisting frame(OMRF). Ordinary MltYs still need to have sufficient rotational ductility to make themeligible to be designed using a reduction factor of Rw equal to 6. Again there is no well-established value of the required ductility supplied for Ordinary MRF's. It is suggested(Astaneh-Asl, 1995) that, in the absence of more reliable value, the connections of

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, April 1997 5

Ordinary MRF's should have a rotational ductility of at least 0.02 radian. The cumulativecyclic rotational capacity is suggested to be at least 0.10 radian.

When a framing system cannot be categorized as special moment-resisting frame andtherefore is categorized as ordinary moment resisting frame, the reduction factor R,, usedin seismic design is given as 6 by the seismic design codes (UBC-94). The reductionfactor for ordinary moment-resisting frames is half of the reduction factor for specialmoment-resisting frames. As a result, the design seismic forces for the same building usingordinary moment frames will be twice the design seismic forces if special moment framesare used. Therefore, it is economically sensible and safer to use special ductile momentframes instead of ordinary moment frames.

1.5. Types of Column-Tree Moment-Resisting Frames Based on Stiffness

Based on stiffness, steel MRFs are divided into the three categories of Rigid (FullyRestrained, FR), Semi-rigid (Partially Restrained, PR) and Flexible (Simple) (AISC,1994), (Astaneh-Asl, 1995). The parameter frequently used to define the relativerotational stiffness of a girder and its connections is the stiffness parameter mdefined as:

Kc (1.1)m= (_•)

where Kc is the rotational stiffness of the connection, and (El/L) is bending stiffness ofthe girder. L is the span. For column-tree systems where the length of the beam stubwelded to the column is less than 15% of the span length, the flexibility of the rigid splicedoes not have significant effects on the overall stiffness of the span. Therefore, during thedesign phase, to ensure that the column-tree is a rigid frame, the length of the girder stubsshould be less than 15% of span and the rotational stiffness of the splice satisfies thefollowing equations for each category of the frames.

Rigid: y z 18 (1.2a)

Semi-rigid: 0.5 > y z 18 (1.2b)

Flexible: 7 < 0.5 (1.2c)

where; 7 represents relative rotational stiffness of the splice and the girder. ¥ is given by:

Ks (1.3)

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Apn? 1997 6

Therefore, if length of girder stub is less than 15% of the span, the parameters ¥above equations are very close and approximately can be assumedTherefore,

Ksm•y= E(_•)

In the above equation, Ks is the rotational stiffness of the girder splice.

and m into be the same.

(1.4)

Figure 1.6 shows the above three regions of the moment-rotation behavior based on therelative rotational stiffness of the connection and the girder in the frame. The abovecategorization is solely based on the elastic rotational stiffness of the connections and thegirders in a single span. In seismic design, however, the plastic moment capacity of theconnections and the girders should also be considered in categorizing the span. Tocategorize a column-tree moment resisting frame as rigid or semi-rigid, one should includethe relative bending strengths of the girders and splices defined by ct:

ct= MpsMpg

(1.4)

where, MPs and Mpg are plastic moment capacities of the splice and girder, respectively.

•, =Mpc/Mpg

1.o

0.2

Semi-rigid

I t

m=Ks/(EI/L)

Figure 1.6. Regions of Semi-rigid and Flexible Behavior

In traditional moment frame where connection of girder to column is at the face ofcolumn, incorporation the effects of stiffness of the girder and the splice connections, thedefinitions of rigid and semi-rigid column-tree frames can be refined to include the effectsof the enhanced and given as follows:

Rigid: m >__ 18 and cz > 1.0 1.5a)

Seismic Design of Steel Column-Tres Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Apt# 1997 7

Semi-rigid: either 0.5 > m > 18 or tx < 1.0 (1.5b)

Flexible: m < 0.5 (1.5c)

The definitions of terms in the above equations are shown in Figure 1.7. Notice that mand tx are defined for each span. Usually, in moment resisting frames there are variousspan lengths, L, and moment capacities Mps and Mpg throughout the frame. It issuggested that in design, the values of m and cz be the average value of m and tx for thespans of the mid-height story of the frame.

T Y

Splice .__..I

Moment /

17-L

Typical Moment Frame Column-Tree Frame

Figure 1.7. Behavior of Typical Moment Frame and Column-Tree Moment-ResistingFrame

Traditionally, column-tree systems were rigid frames. In these frames the spliceconnection of the girder is designed to be stronger than the connected beams. As a result,after erection, the splice does not play a major role in seismic performance of the frame.To utilize the splice to control and improve seismic performance, semi-rigid versions ofthe column-tree moment resisting frame system was proposed by A. Astaneh-Asl (1988,1991). In the proposed semi-rigid column-tree the bolted connection of the girder,located away from the column, is made semi-rigid. By using semi-rigid connections,stiffness, strength, ductility and energy dissipation capacity can be easily manipulated andadjusted to reduce seismic forces, to limit displacements to acceptable levels and toimprove seismic performance.

A recent study of standard rigid and the proposed semi-rigid column-tree systems(McMullin et al, 1993) has shown that the semi-rigid column-tree system is a potentiallyreliable and economical seismic resisting structural system.

One of the main advantages of a semi-rigid column-tree system over the standard rigidsystem is that the bolted semi-rigid connection, located at the girder splice, can act as a


fuse and protect the welded connections at the face of columns from being subjected tolarge moments. In addition, the use of semi-rigid connections can increase damping,elongate the period of vibration, reduce stiffness to a desirable level and can result in areduction of seismic forces and displacements.1.7. Categories Based on the Moment Capacity of the Connected Members

Depending on the relative bending moment capacities of columns and girders, a moment-resisting frame is categorized as Strong-Column/Weak Beam or Strong-Beam / WeakColumn.

The strong column-weak beam frames are used very frequently and many structuralengineers believe that these systems have superior seismic behavior to that of the weakcolumn-strong beam frames. Most current codes (UBC, 1994) also promote the use of thestrong column-weak beam philosophy. Recent studies have shown that the steel MRFsthat develop hinges in the girders (strong column-weak beam design) can be more stablethan the frames that have column hinges (strong beam-weak column).

In the strong column-weak beam frame, the moment capacity of the beams in a joint is lessthan the moment capacity of the columns. Therefore under combinations of gravity andlateral loads, plastic hinges are expected to form in the beams. In the strong beam-weakcolumn design, plastic hinges are expected to form in the columns.

One of the advantages of the column-tree system is that by selecting an appropriatemoment capacity for the splice of the girder, the splice will act as a moment fuse andprevent large moments from developing at the face of the colum.

Seismic Design of Steel Column-Tree Moment-Reeisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, April 1997 9

2. SEISMIC BEHAVIOR

OF STEEL COLUMN-TREE MOMENT-RESISTING FRAMES

2.1. Introduction

Seismic behavior of a column-tree special moment-resisting frame is expected to be ductileand satisfy code expectations of ductility. Unlike pre-Northridge field-welded momentframes, in column-trees, the designer has a very strong tool to control and reduce seismicbehavior of the frame. This tool is the girder splice. The girder splices can be designed tobe sufficiently ductile and have a prescribed bending moment capacity. In such design,during the earthquakes, the girder splices will act as ductile "fuses" and limit themagnitude of forces including bending moment that can be developed in the frame.Depending on bending strength and rotational stiffness of the girder splice, the column-tree frame will behave as a rigid or a semi-rigid moment resisting system. In thefollowing some information on expected seismic behavior of rigid and semi-rigid column-tree systems is provided.

2.2. Expected Seismic Behavior of RIGID Column-Tree Moment Frames

As discussed in Chapter One, in order for a column-tree moment frame to be categorizedas rigid, the following two conditions should be satisfied:

m>18 and; (2.1)

_ ].o (2.2)

The first condition depends on relative rotational stiffness of the girder and the splicewhile the second condition depends on relative bending strength of girder and the splice.

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Ap#11997 l l

If the above conditions are met, then the column-tree splices are stiffer and stronger thanthe girders. This means that the resulting column-tree moment resisting system willbehave as a traditional ductile frame. The plastic hinges are expected to form at the face ofcolumns while girder splices are expected to remain elastic. Therefore, in this case, thesplices do not act as fuses, but, they are merely erection splices enabling the frame to befabricated as a shop welded-fieM bolted steel frame.

In bolted splices, it is expected that some small amount of slippage will occur during majorearthquakes. The slippage is beneficial and acts as a friction device and isolator todissipate the energy and to reduce seismic forces. Laboratory shaking table tests andanalytical studies (Nader and Astaneh-Asl, 1992, and 1996) have indicated that theselimited connection slippage do not result in noticeable increase in drift during theearthquakes.

2.3. Expected Seismic Behavior of SEMI-RIGID Column-Tree Moment Frames

If in a column tree either one of Equations 2.1 and 2.2 above is not satisfied, the frame canbe categorized as semi-rigid (partially restrained). Technically, for a column-tree momentframe to be considered semi-rigid, one of the following conditions need to be met:

· m >18 and 0.2<(•<1.0 (2.3)

18 > m >0.5 and ct>0.2 (2.4)

Seismic behavior of steel rigid and semi-rigid column-tree moment frames have beenstudied in recent years (Astaneh-Asl, 1991), (McMullin et al.), (McMullin and Astaneh-Asl, 1996). The studies indicate that in general semi-rigid column-tree moment framesare expected to perform as good or better than rigid frames. To obtain a ductile andefficient semi-rigid frame that will not be too flexible for non-seismic loads, it is suggestedthat the rigidity and strength of semi-rigid frame splice connections be at least 70% of thecorresponding values for a rigid connection. This can be expressed in the form ofsatisfying the following criteria:

18> m >(0.7)18 and 0.7<(z<l.0 (2.5)

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Ap#11997 ] 2

3. CODE PROVISIONS

RELEVANT TO STEELCOLUMN-TREEMOMENT FRAMES

3.1. Introduction

Seismic design codes have a number of provisions applicable to moment frames. Theseprovisions were discussed in a Steel Tip report (Astaneh-Asl, 1995). In this chapter, asummary of applicable provisions in the Uniform Building Code (ICBO, 1994) to designof special column-tree moment-resisting frames is provided. The information isapplicable to rigid frames.

3.1. Provisions in UBC on Bolted Special Steel Moment Frames

The Uniform Building Code, UBC-94, has the following provision regarding strength ofgirder-to-column connections in special moment-resisting frames (SMRF), includingcolumn-tree special moment-resisting frames.

Sec. 2211.7.1.1 Required strength. The girder-to-column connection shall beadequate to develop the lesser of the following:

1. The strength of the girder in flexure.2. The moment corresponding to development of the panel zone shear strength as

determined from Formula (11-1).EXCEPTION: Where a connection is not designed to contribute flexural resistance at the joint, it

need not develop the required strength if it can be shown to meet the deformation compatibilityrequirements of Section 1631.2.4.(Reproduced from the 1994 Uniform Building Code©, copyright©1994 with the permission of thepublisher, the International Conference of Building Officials.)

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Aprf11997 13

The Formula (11-1) in Part 2 above is given as the following in UBC-94:

3bet2_V--- 0.S5Fydctp [1+ d bdct ] (Formula 11-1 of UBC-94) (3.1)

The EXCEPTION in the above UBC provision is primarily for shear and semi-rigidconnections that are not considered in design as part of the lateralload resisting system.Section 1631.2.4 of the UBC-94 (ICBO, 1994) has the following provisions on the issue:

Sec. 1631.2.4 Deformation compatibility. All framing elements not required by designto be part of the lateral-force-resisting system shall be investigated and shown to beadequate for vertical load-carrying capacity when displaced 3(Rw/8) times thedisplacement resulting from the required lateral forces. P A effects on such elementsshall be accounted for. For design using working stress methods,. ..... "

(Reproduced from the 1994 Uniform Building Code©, copyright© 1994 with the permission of the•ublisher, the International Conference of Building Officials.)

The first and second printing of the Uniform Building Code (ICBO, 1994) in its Section2211.7.1.3 has provisions permitting the use of "Alternate" connections which includesbolted special moment-resisting frame connections. In the aftermath of the 1994Northridge earthquake and damage to welded special moment frame connections, theICBO Board of Directors on September 14, 1994 approved the following emergencycode change.

Reference (Building Standards, 1994) made modifications to the 1994 Uniform BuildingCode and stated that:" Connection configurations utilizing welds or high-strength boltsshall demonstrate, by approved cyclic test results or calculation, the ability to sustaininelastic rotation and develop the strength criteria in Section 2211.7.1.1 (of UBC-94)considering the effects of steel overstrength and strain hardening."

Seismic Design o! Steel Column-Tree Moment-Resisting Frames © by Abolhaesan Astaneh-Asl, Steel Tips, April 1997 14

4. SEISMIC DESIGN OFSTEEL COLUMN-TREEMOMENT-RESISTINGFRAMES

4.1. Introduction

Seismic design of rigid column-tree MRFs is similar to seismic design of welded MRFs.First, seismic lateral loads need to be established following the governing code. Second,seismic forces in combination with gravity loads are applied to a realistic model of thestructure and by analyzing the structure component forces and nodal displacements arecalculated. Finally, the components (i.e. girders, column, girder-to-column connectionsand girder splices) are designed to carry the applied loads. In addition, like any frame thelateral drifts are calculated and checked to ensure that the drift is less than allowablevalues.

4.2. Design Considerations

The first step in design of a column-tree system is to decide the location of girder splices.The girder splices can be placed at the location of point of inflection of the girder undergravity load only. This point is at a distance of span/10 to span/8 from the centerline of thecolumn. In addition, with current transportation limitations, it is suggested that the splicesbe placed such that the total width of the column trees does not exceed 8 feet.

To take advantage of column-tree systems, the connection of the girder splice is suggestedto be entirely bolted, Figure 1.5(a), or shop-welded and field-bolted, Figure 1.5(b). Thereare many advantages to having bolted splices. Slippage of bolts is a very reliable source ofinelasticity and energy dissipation in steel structures. If slippage occurs under service load,it may create problems with serviceability of the structure and cause cracking of the brittlenon-structural elements. However, if slippage occurs under controlled conditions duringearthquakes, in many cases, the slippage of bolts can improve seismic performance.

The main components of a column-tree moment flame are: (a) girder splices, (b) girders,(c) welded connection of girders to columns, (d) columns, (e) panel zones and; (f) base


plates. In the following issues related to seismic design of these components arediscussed.

4.3. Criteria for Design of Components of Column-tree Frames

The girder splices are suggested to be designed to satisfy the following:

1. The plastic moment capacity of the girder splice does not need to be greater than theplastic moment capacity of the girder.

. The plastic moment capacity of the splice, Mp•, should be equal or greater than thelarger of: (a) the calculated applied moment at the location of the splice or 1-(2a/L)times the plastic moment capacity of the girder.

3. The girder splices should be designed to have a ductile rotational capacity of 0.03radians.

. The girder splice should be designed such that the yield capacity of the gross area ofthe plates in the splice govern. Other failure modes such as net section failure or boltfailure should have larger capacity than the yield capacity.

5. The connection of girder stub to column should have the strength equal or greater thanthe girder.

6. The panel zone in the column should have a shear strength of 1.2 times the shear dueto Mp of the girders connected to the panel zone.

7. The girders and columns should have b/t ratios satisfying the requirements of thegoverning code for special ductile moment-resisting frames.

The fixed base plates should be designed to develop 1.2 Mp of the column. The pinnedbase plates should be designed to develop a rotation of at least 0.03 radians.

4.4. Design of Girder Splice

The first step in seismic design of any connection is to identify failure modes (or limitstates). Then, to arrange the failure modes such that ductile and more desirable failuremodes govern.

The possible failure modes of the typical girder splice connections shown in Figure 4.1arel

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Ap#l 1997 16

L .J•, ¥ J •- ¥ -) • I y l ; hr' "

Ductile Ductile Ductile/brittle BrittleSlippage Failure Failure FailureMode Modes Modes Modes

Figure 4.1. Failure Modes of Top and Bottom Flange Plate Connections

Ductile Failure Modes:

a. Slippage of the flange boltsb. Yielding of the gross area of the top and bottom flange platesc. Bearing yielding of the bolt holes in the girder flanges and the flange platesd. Yielding of the gross area of the girder

Failure Modes with Limited Ductility:

e. Local buckling of the top and bottom flange platesf. Local buckling of the girder flangesg. Shear yielding of the column panel zone

Relatively Brittle Failure Modes:

h. Fracture of edge distance or bolt spacing in flange splice platesi. Block shear failure of flange splice platesJ. Shear fracture of flange boltsk. Fracture of flange plate welds (in bolted-welded splices)1. Fracture of net areas of the flange splice platesm. Block shear failure of girder flangesn. Fracture of edge distance or bolt spacing in flanges of the girdero. Yielding of the gross area of the web splice plate due to combined shear and

bendingp. Shear fracture of web boltsq. Fracture of net area of web splice plate or girder webr. Fracture of net area of girder.

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, April 1997 ] 7

The failure modes in the above list are given in the order of their desirability. Slippage offlange bolts followed by yielding of the flange plates are the most desirable failure modes(first two failure modes in the above list). The fracture of net area of the girder ( the lastitem in the above list) is the least desirable failure mode.

4.4.a. Slippage of Flange Bolts

In incorporating slippage into seismic design, the question is when is the appropriate timefor a moment connection to slip? In establishing appropriate slip moment capacity, Mslip,the following items need to be considered:

. The bolted connection should not slip under the service loads. To be conservative, theslip moment greater than 1.25 times the moment in the connection due to service (notfactored) loads is suggested.

2. The bolted connection should slip during moderate and strong earthquakes to reducethe stiffness, to increase ductility and to dissipate energy. On the basis of experienceand intuition, it is suggested here that the slip moment be smaller than 0.8 times theplastic moment capacity of the splice.

Combining the above two suggestions, the equation to establish slip moment is:

1.2SM(service ' splice) -< Mslip < 0.8 Mps (4.])

4.4.b. Yielding of Gross Area of Top and Bottom Flange Splice Plates

To increase ductility of the connection, yielding of flange splice plates should be thegoverning failure mode. To achieve this, moment capacity of splice can be limited suchthat when splice plate moment reaches plastic moment value, the moment in the girderconnection to the column does not exceed plastic moment of the girder. In doing so,yielding of the splice plates acts as a fuse to protect the welded connection of the girder tocolumn. Figure 4.2 shows the relationship between the plastic moments of the splice andthe girder.

a

I-

Mpg

Mpg=Mps+Va

V=2Mps/(L-2a) + q(L-2a)/2

Figure 4.2. Free-Body Diagram of Span

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Apt# 1997 18

To have desirable behavior of splice acting as a fuse, the following criterion is suggested:

Mps < Mpg-Va (4.2)

Which with reference to Figure 4.2, can be written as:

2aMps < (1--•-) Mpg (4.3)

In addition to above criterion, it is suggested that the moment capacity of splice plates begreater than 1.25 times the bending moment calculated by the analysis. This means:

Mps > 1.25 Ms (4.4)

4.4.c. Bearing Yielding of Bolt Holes in Girder Flange and Splice Plates

Bearing yielding of the bolt holes is beneficial in reducing seismic response during extremeevents. It is suggested that in seismic design the following criterion be used:

Mpb > 1.25 Mps (4.5)

4.4.d. Yielding of Gross Area of Girder

This failure mode occurs when a plastic hinge forms in the girder. The equation toestablish plastic moment capacity of the girder is:

Mpg =FyZx (4.6)

4.4.e. Local Buckling of the Flange Splice Plates

Buckling of splice plates occurring late during the earthquake can be tolerated. To avoidearly buckling of flange splice plates, it is suggested that the slenderness of the plate, theKL/r ratio, not exceed 20. This means that the free length of splice plate divided by itsthickness should not exceed 11. The free length of splice plate is the distance between thefirst rows of bolt on each side of splice as shown in Figure 4.3.

I

• - - Free Length of PI

r ,

• ' " ' = = = = ;I®,,®

o ' , ' , .

®,, ·

,o

[


Figure 4.3. Free Length of Splice Plate4.4.f. Local Buckling of the Girder Flanges

Local buckling can be categorized as ductile or brittle depending on how rapidly thelocally buckled area deteriorates during cyclic loading. Available cyclic test results indicatethat steel members wlth high b/t ratios, say higher than 3,r given in the AISC Specifications(AISC, 1994), tend to form local buckling in a very sharp configuration, develop relativelylarge lateral displacements and fracture through the sharp tip of the locally buckled areasalter a few inelastic cycles. Cyclic local buckling in this manner should be consideredbrittle. The value of Xr suggested for the flanges of the girders in special moment-resisting frames is 95 / On the other hand, members with a b/t ratio less than those

specified by the AISC Seismic Provisions (AISC, 1993) tend to develop local bucklingat•er a relatively large number of inelastic cyclic deformations (usually more than 10 to 15cycles of inelastic behavior before local buckling). The limit for the b/t ratio for theflanges of the girders currently given in the AISC Seismic Provisions (AISC, 1993), is52 / .

4.4.g. Shear Yielding of the Column Panel Zone

The Uniform Building Code permits limited yielding of the panel zones in special momentframes (UBC, 1994). The provisions of UBC state that the panel zone shear may becalculated by using 80 percent of the moment capacity of the connected girders. Sincesome cracks have been observed in the panel zone in the aftermath of the 1994 Northridgeearthquake, it is suggested that to protect the panel zone against extensive yielding, it issuggested that the panel zone shear capacity be at least equal to the shear that can bedelivered to the panel zone by plastic moments of the girders:

VPz > (4.7)d

where d is the depth of girder

The Uniform Building Code (UBC, 1994) provides the following equation for design ofpanel zone:

r. = 0.ssJ*y a, t [ 1 + - -23b•f t•

dbd t ] ( 4 . 8 )

As an alternative, until the cause of panel zone fractures is established and a realisticdesign equation is developed (or the above equation is validated), the author suggests theuse of equations that are given in the AISC-LRFD Specification (AISC, 1994). Theequations are given for panel zone design when the effect of panel zone deformation on

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Apd11997 20

frame stability is not considered in the analysis. The equations from AISC-LRFDSpecifications (AISC, 1994) are:

For Pu < 0.4 P y ; Vn-•(0.60Fydctp) (4.9a)

F o r P u > 0 . 4 P y ; Vn-•b (0.60Fydctp)(1.4- P u / P y ) (4.9b)

4.4.h. Fracture of Edge Distance or Bolt Spacing in Flange Splice Plates

Fracture of edge distance by itself may not be catastrophic, but during cyclic loading acrack within the edge distance can jump the bolt hole and fracture the entire width of theplate or girder flange. On the basis of the limited information currently available on thecyclic behavior of bolt edge distances, it is suggested that in special moment frames boltedge distances should not be less than 1.5 times the diameter of the bolt and preferably 2.0times the diameter. In most bolted connections, there is sufficient width of plate or flangeto accommodate easily an edge distance equal to twice the bolt diameter. The boltspacing, due to automation of drilling or punching is usually specified as 3 inches. In theabsence of any report of failure of bolt spacing during earthquakes or in laboratory tests,it appears that 3 inch spacing is satisfactory.

4.4.i. Block Shear Failure of Flange Splice Plates

To ensure that this relatively brittle failure mode does not occur before the plates yield, thefollowing condition is suggested:

Pn > 1.25 4) Mp (•p•i•) / d (4.10)

When FuAnt > 0.6FuAnv; Pn = 0-6FyAgv + FuAnt (4.11 a)

When FuAnt < 0.6FuAnv; Pn = 0.6FuAnv + FyAgt (4.1 lb)

4.4.j. Shear Fracture of Flange Bolts

This failure mode can occur when after slippage of the bolts and some beating yielding, theapplied moment is totally carded by the shear strength of the bolts. To encourage yieldingof steel before bolt shear failure, the following criterion is suggested:

*bFbAb N d >-d•Mps (4.12)

4.4.k. Fracture of the Welds Connecting the Splice Plates to Girder Flanges

The welds on splice plates are usually fillet welds and should be designed to develop 1.25times axial yield capacity of the plates.

Seismic Design of Steel Column-Tree Moment-Resisting Frames O by Abolhassan Astaneh-Asl, Steel Tips, April 1997 21

4.4.1. Fracture of Net Area of the Flange Splice Plates

The splice plates should be designed such that the fracture of plates does not occur beforeyielding of the girder. The following criterion is suggested:

> q>Mps (4.13)

4.4.m. Block Shear Failure of Girder Flanges

Earlier in Section 4.4.i the issue of block shear failure of flange plates was discussed. Forblock shear failure of the flange itself the same discussion and equations as in Section 4.4.iapply.

4.4.n. Fracture of Edge Distance or Bolt Spacing in Flanges of the Girder

Earlier in Section 4.4.h this issue was discussed for plates. The same discussion andrecommendations apply to the girder flanges.

4.4.0. Yielding of Gross Area of Web Splice Plate

Failure modes of shear connections have been studied in recent years and reliable designprocedures are available (AISC, 1994; Astaneh-Asl et al., 1989). The philosophy used indeveloping design procedure for shear plate connections has been to force yielding of steelto occur before fracture of the net area, bolts or welds (Astaneh-Asl et al., 1989).

The web plates in the splice of a column-tree are subjected to a combination of shear andbending. To check this failure mode, the following interaction equation is suggested:

_<1.oq•Vywp p

(4.14)

4.4.p. Fracture of Web Bolts

Web bolts are subjected to a combination of shear and bending moment. It is suggestedthat for a ductile behavior the strength of the bolts be greater than the strength of theplates. To achieve this, the bolts should be designed for an eccentric shear as shown inFigure 4.3. For the design of bolt groups subjected to eccentric shear, the procedures andtables given in Volume II of the AISC-LRFD Manual (AISC, 1994) can be used.

4.4.q. Fracture of Net Area of Web Plate

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Apn? 1997 22

This failure mode if occurs can have catastrophic consequences due to the fact that thespan can collapse. To prevent this failure mode from occurring before the yield failureoccurs, the following criterion can be used.

V )2+( Ve )2 < 1.0 (4.15)(*nVun ' --*nMu% -

4.4.r. Fracture of Net Area of the Girder

This failure mode is not acceptable. It is suggested that the ultimate bending capacity of

the net section of the girder be more than 1.25Mps, where Mps is the plastic momentcapacity of the girder splice plates.

qbn Mng > qb Mps (4.16)

where Mng, the ultimate moment capacity of the net area of the girder can becalculated as:

Mng = (Zx-N d htf) Fu (4.17)

4.4.s Check Welds Connecting the Girder to Column:

The full penetration welds connecting the girder flanges to column face should be done

using material and complying with the procedures that result in ductile welds. More

information on this can be found in Reference (SAC, 1995).

The fillet welds connecting the web of the girder to the column flange are suggested to be

designed for a force equal to 1.25 times shear capacity of the web of the girder:

qbnVw > 1.25 qb (0.6Fy)(tw d) (4.18)

4.5. Establishing Stiffness of the Girder splice Connection

To establish rotational behavior of a typical column-tree splice connection, the spliceconnection can be modeled as a rotational spring in the elastic analysis of the column-treeframe. The rotational stiffness of the spring can be established as:

Ks = Ms= Ms = Ms E d (4.19)0s Aw / (d/2) 2Lsp Fy

The above rotational stiffness represents initial elastic stiffness of the splice and can beused in elastic analysis of the column-tree frames to obtain design forces. Also, the above

Seismic Design of Steel Column-Tree Moment-Resisting Frames O by Abolhassan Astaneh-Asl, Steel Tips, Aprg 1997 23

value of rotational stiffness may be used in establishing m values in categorizing the frame.However, if more accurate calculation of displacements, particularly drift values underfactored loads, is desired, the flexibility of the connection due to slippage of bolts shouldbe included. The following equation is suggested for establishing rotational stiffness ofconnection including slippage:

Ms Ms Ms (4.20)Ks2 = Os = (Asp + 1/16")/(d/2) = (Lsp Fy/E + 1/16")/(d/2)

It should be added that throughout this report the emphasis was placed on seismic design.However, the final design of connection will be governed by load combinations includingthe wind load. Following the design philosophy and concepts presented in this report, thedesigner should ensure that bolted connections are designed as slip-critical to resist theservice loads without slip. Such approach will ensure that the connections will not slipduring the service wind and small to moderate earthquakes. However, the bolt slip duringthe major earthquakes can be ben'eficial in dissipating energy in the form of friction,elongating the period of the structure as well as isolating the connections and cutting offthe flow of seismic energy into the structure.

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Apd11997 24

AH, (1995), "Reconnaissance Report on Damage to Steel Building Structures Observedfrom the 1995 Hyogoken-Nanbu (Hanshin/Awaji) Earthquake", Report, ArchitecturalInstitute of Japan, (in Japanese with English summary), May.

AISC (1994), Manual of Steel Construction- Load and Resistance Factor Design, 2ndEdition., 2 Volumes, American Institute of Steel Construction, Chicago

Astaneh-Asl, A., (1989), "Demand and Supply of Ductility in Steel Shear Connections,"Journal of Constructional Steel Research., Vol. 14, No. 1.

Astaneh-Asl, A., (1993), "The Innovative Concept of Semi-rigid Composite Beam",Proceedings, Structures Congress, ASCE, Irvine, April.

Astaneh-Asl, A., (1994), "Seismic Behavior and Design of Steel Semi-rigid Structures",Proceedings, Fkst Int. Workshop and Seminar on Behavior of Steel Structures in SeismicAreas, 26 June-1 July, Romania.

Astaneh-Asl, A., (1995), "Seismic Design of Bolted Steel Moment-Resisting Frames",Steel Tips Report, Structural Steel Educational Council, Moraga, CA, July.

Astaneh-Asl, A., Call, S.M., and McMullin, K. M. (1989), "Design of Single Plate ShearConnections," Engineering Journal Am. Institute of Steel Construction, Vol. 26, No. 1.

Astaneh-Asl, A., and Nader, M. N., (1990),"Experimental Studies and Design of Steel TeeShear Connections," J. of Structural Engineering ASCE, Vol. 116, No. 10, October.

Astaneh-Asl, A. and Nader M., (1991), "Cyclic Behavior of Frames with Semi-rigidConnections, in Connections in Steel Structures II, Elsevier Applied Science.

Astaneh-Asl, A., Nader, M.N. and Harriott, J. D., (1991) "Seismic Behavior and DesignConsiderations in Semi-Rigid Frames", Proceedings, AISC, 1991 National SteelConstruction Conference, Washington, D. C., June.

Astaneh-Asl, A., Nader, M. N. and Malik, L., (1989),"Cyclic Behavior of Double AngleConnections," J. of Structural Engineering ASCE, Vol. 115, No. 5.

Becker, R., Naeim, F. and Teal, E., (1993), "Seismic Design Practice for Steel Buildings",Steel Tips Report, Stmctural Steel Educational Council, Moraga, CA, July.

Building Standards, (1994), "ICBO Board Approves Emergency Structural DesignProvision", Journal, September- October Issue.

Seismic Design of Steel Column-Tres Moment-Resisting Frames O by Abolhassan Astaneh-Asl, Steel Tips, April 1997 25

Englekirk, R., (1994), '•Steel Structures, Controlling Behavior Through Design",, JohnWiley and Sons Inc..

Guh, T. J., Astaneh, A., Harriott, J. and Youssef, N. (1991) "A Comparative Study of theSeismic Performance of Steel Structures with Semi-Rigid Joints", Proceedings, ASCE-Structures Congress, 91, Indianapolis, April 29-May 1, pp. 271-274.

ICBO, (1994), "The Uniform Building Code", Volume 2, The International Conference ofBuilding Officials, Whittier, CA.

Kulak, G. L., Fisher, J. W., and Struik, J. H. A., (1987) "Guide to Design Criteria forBolted and Riveted Joints", Second Edition, John Wiley and Sons, New York.

McMullin, K., Astaneh-Asl, A., Fenves, G. and Fukuzawa, E., "Innovative Semi-RigidSteel Frames for Control of the Seismic Response of Buildings", Report No. UCB/CE-Steel-93/02., Dept. of Civil and Env. Engineering, University of California, Berkeley.

Nader M. N. and Astaneh-Asl, A., (1991) "Dynamic Behavior of Flexible, Semi-Rigid andRigid Steel Frames", Journal of Constructional Steel Research Vol. 18, PP 179-192.

Nader, M. N. and Astaneh-Asl , A., (1996)" Seismic Behavior of Semi-rigid SteelFrames", J. of Structural Engineering ASCE, No. ST7, July.

Porter K. A. and A. Astaneh-Asl, (1990), "Design of Single Plate Shear Connections withSnug-tight Bolts in Short Slotted Holes," Report No. UCB/SEMM-90/23, Department ofCivil Engineering, University of California, Berkeley, December.

SAC Joint Venture, (1995), "Interim Guidelines: Evaluation, Repair, Modification andDesign of Welded Steel Moment Frame Structures", Report FEMA 267, FederalEmergency Management Agency, Washington D.C. August.

Youssef, N. F. G., Bonowitz, D. and Gross John L., " A Survey of Steel Moment-Resisting Frame Buildings Affected by the 1994 Northridge Earthquake", Report No.NISTIR 5625 National Institute of Standards and Technology, Washington D.C., April.

Index of Steel Tips PublicationsThe following is a list of available Steel Tips. Copies will be sent upon request. Some are invery limited quantity.

· Seismic Design of Special Concentrically Braced Frames· Seismic Design of Bolted Steel Moment Resisting Frames· Structural Details to Increase Ductility of Connections· Slotted Bolted Connection Energy Dissipaters· Use of Steel in the Seismic Retrofit of Historic Oakland City Hall· Heavy Structural Shapes in Tension° Economical Use of Cambered Steel Beams· Value Engineering & Steel Economy· What Design Engineers Can Do to Reduce Fabrication Costs· Charts for Strong Column Weak Girder Design of Steel Frames· Seismic Strengthening with Steel Slotted Bolt Connections· Seismic Design of Steel Column-Tree Moment-Resisting Frames


APPENDIXA NUMERICAL EXAMPLE

A.1. A Numerical Example

Design a rigid moment connection of a column-tree flame. The connection is for twoW24x68 girders connected to the flange side of a W14x132 column. The steel used ingirders and column is A572 Gr. 50. The bolts are 7/8' diameter ASTM A325-N andwelds are E70xx. The connection in this example is assumed to be for the 4th. floor of a 7-story moment frame that was used by Roy Becker in his Steel Tips issue (Becker et al.,1993).

Given:A 7-story steel column-tree frame. Assumed service loads are as follows:Roof: Dead Load = 67 psf, Live Load =20 psf.Typical Floor: Dead Load = 85 psf, Live Load =50 psf.Partition Load: 15 psfon all floors.

OI

-•- Q o el:; o • - -

c:C rn c: o o

-•- =E tn ri: [= -•-

¢

CID

Q cie ca c• o

-.• ?-E- car' •_•_ •- __

bnar

i_ 3@30'-0' i

Figure A. 1. The Structure

©Seismic Design of Steel Column-Tree Moment-Resisting Frames by Abolhassan Astaneh-Asl, Steel Tips, Ap#l 1997 27

;'! / Flange Splice Plate

,i / / H.S. Field Bolts

. . . . . . . . . . . . . . . . . ' . . . . . . " . •. i . . . 11t . . . . . . . . . . . . . . . ·

,.s. ,o,,

..................... I . . . . . . . . : •': ....................

W24x6 · • . i W24x6 , W24x6 '!!"• W24x6 . . . . . . ._ i! . . . . . . . ,' ; • . . . . . . . !i . . . . . . .

i

! y W14x13

i

i

J

a=3'-7"i

i

i

Figure A.2. Column-Tree Joint

M, Moment

-422 k-ft / -636 k-ff

I•' +2o4 k-tt

/J

J

V, Shear

Figure A. 3.

tAssumed Bending and Shear Diagram for 4th Floor Girders

The factored shear and bending moment in the connection are shown in the above figure.The lefi side connection of the joint, which has the largest forces, is designed in thisexample. The same connection will be used for the right side of the joint.

Maximum factored shear in the connection: Ru= 64 kipsMaximum factored bending moment in the connection: Mu = 636 •kipsNo significant axial load exists in the girder.Factored axial load in the column: Nu= 300 kips (needed for panel zone check).

The bending moment acting on the connection due to service loads (un-factored) obtainedfrom analysis:

M(service ' conn.)= 242 fi-kips (due to combination of gravity and seismic loads)

The bending moments and shear forces acting on the splice, at a distance of 43 inches ("a"distance in Figure A. 2) from the centerline of the column are:

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Aptfl 1997 28

Maximum factored shear in the girder splice: Vs= 55.4 kipsMaximum factored bending moment in the girder splice: Ms = 422 ft-kipsNo significant axial load exists in the girder splice.

The bending moment acting on the girder splice due to service loads (un-factored)obtained from analysis:

M(service' splice)= 161.5 f•-kips (due to combined service gravityand service seismic loads)

The above service moment will be used in the design of girder splice bolts to ensure thatthe splice does not slip under the service loads.

The properties of the girders and the column in the joint are:

Girder: W24x68, Fy=50, Fu=65 ksi, Span=30 f•, d= 23.73 in., A=20.1 in2

tw= 0.415 in. bf = 8.965 in., tf = 0.585 in, Ix-- 1830 in4, Zx = I77 in. 3

Column: W14x132, Fy =50, Fu=65 ksi, Height=l 1'-6", d=14.66 in., A=38.8 in2

tw= 0.645 in., bf = 14.725 in., tf =1.030 in, Ix= 1530 in4, Zx = 234 in. 3Solution:

1. Establish plastic moment capacity of the girder:Mp =ZxFy = 177x50= 8,850 k-in.

2. Check local buckling of the girder flanges:?

b/t= 8.965/(2x0.585)=7.66'__<52=7.35 Say O.K.qFy

3. Strong column-weak beam concept checked and is satisfied

4. Establish size of the flange plates of the girder splice:2a

Mps _< (1 - -•-) Mpg

Mps < (1-2x43"/360)(8,850) = 6,735 in-kipsMps > 1.25 MsMps > 1.25x 422x12= 6,330Use A36 steel (with minimum Fy of 36 ksi and design plates for a momentof 6,330 in-kips. Try 3/4' plate:Ag = Mps/(Fyd)= 6,330/[36(23.73+0.75)]--7.2 inch

Try: PL 10"x3/4" A36 for flange splices of the girder

5. Check net section failure of the splice plates

q•nMns > {Mps0.75(10-2)(3/4)(58)(23.73)> (0.9)(10x0.75)(36)(23.73+.75)

Seismic Design of Steel Column-Tres Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Aprf11997 29

6,194 > 5,949 O.K.

6. Check net-section fracture of the girder:

qbn Mng > qb Mps

qbn (Z h - N d htf) Fu > qb Mps

0.75[177in3-2xlx0.585 (23.73-.585)](65)> (0.9)(10x0.75)(36)(23.73+.75)7308 > 0.9x6,609 O.K.

7. Establish number of the flange bolts:

qbb(VbAbN)(d) > 1.25qbMp

0.75(48)(0.601)(N)(23.73) > 1.25(5,949)

N > 14.6; Try_: 14 7/8"dia A325N flange bolts

St,ms : : . 7'215 ?/8'a,a A325t•Boh -• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . [I •nc• •o i . . . . . . . . . . . . . . . . • ; ft : : : : : . , ,

c . . . . . ; ir

W14x•32.

Ji

e=3'-• a=3..7,' ,

W24x68

: : : - . _ - _ - : - _ . 1 _ - , ,

• . J[_ s' W24x68

' l : • l . s ' . . . . . . .i i ' L . ; .• i • i . . ,

I 5 . ' • T '• 6@3---'; •1.5"

, _ L I

' ! ! '

i i

14.s'l

Figure A.4. Girder Splice

8. Check bearing capacity of the bolts:

MPb > 1.25 Mps

2.4(58ksi)(0.75")(7/8")(14)(23.73) > 1.25 (6,609)

30,348 k-in > 8,271 O.K.

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Ap/fl 1997 3 0

9 Check buckling offiangeplate: 11.5 < 20 O.K.

10. Check to ensure that the bolts do not slip under the service loads:

1.25M(service ' splice) < Mslip < 0.8Mps1.25 (161.5x12) < (14 bolts)(10.2 kipsPoolt)(23.73") < 0.8(6,609)

2,423 _< 3,388 < 5,287 O.K.

11. Check edge distances:

Using a bolt gage of 4.5 inches c/c on the flanges, Figure A.4, provides 2.75 inches ofedge distance for splice plates and girder, large enough to satisfy AISC(1994)requirements.

12. Check panel zone yielding:

where

VPz >_ • Mpgd

Vn = 0.55Fydctp[ 1-•dbdctp ]

3x14.725xl.032Vn = 0.55x50x14.66x0.645[ 14

23.73x14.66x0.645Vn= 314 kips < 2(8,550)/23.73= 721.

Therefore, doubler plates are needed:

t=__ 0.645(721/314)-0.645 = 0.88" Use 7/8" doubler plate.

] =314 kips

Or, change the colum size or use stronger colum material if it results in moreeconomical design.

If instead of above UBC-94 equation, the equation given in the AISC-LRFDSpecifications (AISC, 1994) are used, the following will result:

Pu= column axial = 300 kips 1940

Since Pu <_ 0.4 P y ; then Vn---•( 0.60Fydct ).

Vn = qb p =0.9(0.6)(50)(14.66)(0.645)=255 kips < 721 kips

t_= 0.645(721/255)-0.645 = 1.17" Use 1-1/4" doubler plate.

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Apr# 1997 31

Or, change the column size or use stronger column material if iteconomical design

13. Design web shear connection

results in more

The loads acting on the web plate are shown in the following figure:

J i

IJ

Figure A. 5. Loads Acting on the Web Connection

The web plate are subjected to a combination of shear V and bending moment Ve. Tocheck this failure mode, the following interaction equation is used:

< 1.o4)Vywp p

V=2Mps/(L-2a)+q(L-2a)/2 (see Figure 4.2)V=2x6,609/(360-2x43)+ (2.4 k/fiJ12)(360-2x43)/2= 76 kips

Try PL 7"x3/8"xl'-3"

76 . )2 =0.53_< 1.0]2+[ 76x2

[ 0.9(3/8)(15)(0.6x36) 0.9(3/8)(152)(36)/4

14. Fracture of web bolts

The web splice bolt group is subjected to an eccentric shear. The shear is equal to 76 kipsand eccentricity is 2 inches, see Figure A. 5. To design the bolts, the tables in Volume II ofthe AISC-LRFD Manual (AISC, 1994) are used. The results:

Use 5 7/8' dia A325N bolts

15. Fracture of net area of web plate

To check this failure mode the following equation is used:( V -2- Ve )2•4-•, 1 +1'• M..,• < 1.0

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Ap•f11997 32

V(• (t)(h- Ndh)(O.6F.))2+(ep (O(h2/4-ndh 4 -ndh d2)(Fy))2 < 1.0.

76 2 76x2" 2 0.66(0.75(3/8)(15 - 5xl")(O.6x58)) +(0.75(3/8)(15•/4 - l"x2x3 - 1 "x2x6 )(58)) =

< 1.0 O.K.

16. Check welds connecting the girder to column:

The full penetration welds connecting the girder flanges to column face should be done

using material and complying with the procedures that result in ductile welds. More

information on this can be found in Reference (SAC, 1995).

The fillet welds connecting the web of the girder to the column flange are designed

following the criterion. The length of fillet welds is 20 inches.

q)nVw 2 1.25 4) (0.6Fy) tw d

0.75 (0.6x70ksi)(2)(20")(0.707D) _>1.25x 0.9(0.6x50)x 0.415x23.73

D&0.37" Use 3/8' fillet welds E70xx

1 7. Establish rotational stiffness of the connection:

Ms Ms Ms E d

Ks =O s - Asp 7 (d/2) = 2Lsp Fy

KS "-5948x29,000x23.73

2x20x36= 2,842,500 kip-inch/radians

m=Ks / (EI/L) = 2,842,500/(29,000X1830/360)=19.2 > 18 O.K.

Therefore, the flame can be categorized as rigid since m is greater than 18.

To calculate rotational stiffness that includes the effects of bolt slippage:

Ks2 = M-''-•s = Ms = MsOs (Asp + 1/16")/(d/2) (Lsp Fy/E + 1/16")/(d/2)

Ks2 =5,948(23.73/2)

20x36/29,000 + 1/16"- 808,000 kip-inch/radians

The above value of rotational stiffness can be modeled into computer analysis program asstiffness of a rotational spring. Such analysis can result in better calculation of drifts.

Seismic Design of Steel Column-Tree Moment-Resisting Frames © by Abolhassan Astaneh-Asl, Steel Tips, Apn11997 33

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