Engineering Structures 25 (2003) 229–239www.elsevier.com/locate/engstruct

Evaluation of maximum strength and optimum haunch length ofsteel beam-end with horizontal haunch

Naoki Tanaka∗

Kajima Technical Research Institute, Kajima Corporation 19-1, Tobitakyu 2-Chome, Chofu-shi, Tokyo 182-0036, Japan

Received 23 July 2002; accepted 13 August 2002

Abstract

Since the 1995 Hyogoken-Nanbu Earthquake, the use of horizontally haunched beams has been increasing to prevent brittlefractures of beam flanges in the vicinity of steel-beam-to-boxed-column connections of moment-resisting frames. The author hasalready proposed a design method based on experimental studies. This method produces ductile beam-to-column connections,because it predicts the fracture mode and an optimum haunch length by comparing a beam’s local buckling strength with that offracture perpendicular or diagonal to the beam-axis. However, strength-formulas for local buckling used in the method have recentlybeen amended, so the design method needs to be revised and its applicability verified. The revised design method has been appliedto test results of twenty-nine horizontally haunched beam specimens designed by the author and other researchers to confirm itseffectiveness. Results show that the revised method closely matches the test results. Furthermore, it produces more accurate fracturemodes and optimum haunch lengths, except where the haunches incorporate stiffeners. A formula for the optimum haunch lengthis also proposed. A rough value of the optimum haunch length is about 25 to 35% of the beam depth. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Horizontal beam haunch; Local buckling strength; Diagonal rupture strength

1. Introduction

In the 1995 Hyogoken-Nanbu earthquake, there weremany cases of damage to beam flanges, including brittlefractures of both base metals and welded parts in thevicinity of steel-beam-to-square-hollow-column (S.H.C.)moment-resisting connections. Among the causes of thefractures was inadequate bending strength of the beamweb. According to the Architectural Institute of Japan(A.I.J.) [1], bending strength deteriorates largely due toaccess holes for welding the beam and out-of-planebending of the flange of the S.H.C. connected to thebeam web. This concentrates the bending stress in theflange, leading to a brittle fracture. To relieve the highstresses and thus prevent brittle fracture, use of horizon-tally haunched beams as shown in Fig. 1 has increasedin Japan. The haunch increases the beam-flange area.

∗ Tel.: +81-424-89-8439; fax:+81-424-89-7110.E-mail address: naokit@kajima.com (N. Tanaka).

0141-0296/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0141-0296(02)00146-3

However, the FEMA reports [2], summarized by theSAC project in response to the 1994 Northridge earth-quake, did not recommend this horizontal haunch mainlybecause of fabrication cost. This may reflects differencesin the manner of a frame design, a fabrication or weldingetc. in both countries. Results of tests carried out by theauthor [3–5] using 12 beam-type specimens demon-strated the effectiveness of the horizontal haunch. How-ever, it also indicated that a short haunch length couldlead to diagonal fractures passing through a point justabove the access hole to the start point of the haunch,as shown in Photo 1, while a long haunch can causeearly buckling at the beam end, resulting in lowerstrength. Therefore, the author proposed a method ofproviding an optimum haunch length by comparingbeam strength of local buckling with that of rupture per-pendicular or diagonal to the beam axis. In this method,the local buckling strength is obtained from Kato’s for-mulas [6], but it has recently been revised to moreclosely match the latest experimental results [7,8]. Otherresearches have recently provided many test results onhaunched beams. This has required correction of the

230 N. Tanaka / Engineering Structures 25 (2003) 229–239

Nomenclature

B beam-widthb half width of beam with no haunch (b=B/2)bh half width of widened part of haunchb/tf width-to-thickness ratio of beam flangeD beam depth(D�tf) / tw width-to-thickness ratio of beam webE Young’s modulus�F length of rupture line of beam�h length of haunch of beam�opt optimum haunch length of beamld haunch length ratio of beam (ld � �h /D)lopt optimum haunch length ratio of beam (lopt � �opt /D)Mp full plastic moment of beamMd diagonal rupture strength of beam (converted to beam-end value)MLB local buckling strength of beamMLa local buckling strength of beam at start point of haunch (converted to beam-end value)MLb local buckling strength of beam at beam endMGENmax maximum strength of beam at start point of haunch (converted to beam-end value)MENDmax maximum strength of beam at beam endm� coefficient for gradient of bending (m� � � / (���h))Pd rupture strength of beam flangeS coefficient of local buckling strength at start point of haunchS� revised S considering connection condition of beam web to column flangeS�END revised S� when used at beam endsfy yield point of beam flangeswy yield point of beam websfB maximum stress of beam flangeswB maximum stress of beam webtf thickness of beam flangetw thickness of beam webq declaiming angle of diagonal rupture line

Fig. 1. Horizontal haunched beam subjected to bending moment.Photo 1. Diagonal rupture of beam flange.

231N. Tanaka / Engineering Structures 25 (2003) 229–239

method and confirmation of its applicability in modelingthe latest test results.

This paper presents the refined method in detail andits applicability.

2. Maximum strength diagram (M.S.D.)

2.1. Decision of maximum strength of a beam by aM.S.D.

Five beam strength criteria are considered for thehaunched beam. One is diagonal rupture strength, calledFd-Line; naming the “Line” is why the strength variesas with haunch length. The others include local bucklingstrength at the start point of the haunch (called La-Line),local buckling strength at the beam end (called Lb-Line),maximum beam strength at the start point of the haunch(called FGENmax-Line) and maximum beam strength at thebeam end (called FENDmax-Line).

Fig. 2 is a M.S.D. showing the relationships amongthe five strength criteria and the beam’s haunch length.The strengths are normalized by the full plastic momentof the beam (Mp) and are converted to values at the beamend. The abscissa is the ratio of haunch length to beamdepth (named haunch length ratio; ld). The minimumstrength given by Eq. (1) on the M.S.D. is the maximumstrength of the beam to determine the fracture mode. Iflocal buckling at the start point of the haunch is favor-able, an optimum haunch length could be that where theFd-Line and La-Line intersect.

Mmax � MIN(Md, MLa, MLb, MGENmax, MENDmax) (1)

where Md is diagonal rupture strength, MLa is local buck-ling strength at the start point of the haunch, MLb is localbuckling strength at the beam end, MGENmax is maximumbeam strength at the start point of the haunch, andMENDmax is maximum beam strength at the beam end. Inthe calculation, Md, MLb and MENDmax neglected web

Fig. 2. Maximum strength diagram (M.S.D.).

bending strength in the safety judgment because it ismuch smaller than that of the flange. This is due to theaccess holes in the web and out of plane deflection of thecolumn flange connected to the beam web. Web strengthshould be included where there are no access holes.MLa and MGENmax use the web strength because it carriesbeam bending moment at the start point of the haunch.The strengths are calculated as follows.

2.1.1. Diagonal rupture strength (Fd-Line)Strength against diagonal rupture for the beam flange

shown in Fig. 3 employs Eq. (2), which Kurobane [9]proposed by applying von Mises’s yield criterion to amaximum strength, and reported that it closely modelsthe test results.

Pd2�1 � sin2qsfb

�3�Ftf (2)

where q is declaiming angle of rupture line, �F is lengthof rupture line, and sfB is maximum stress of beamflange. Therefore, the beam rupture strength (Md) isobtained from Eq. (3), which multiplies the diagonal rup-ture strength of the beam-flange calculated from Eq. (2)by the distance between the centers of both beamflanges, and neglects web bending strength.

Md � 2�1 � 2sin2qsfB

�3�Ftf(D�tf) m� (3)

m� ��

���h

(4)

where m� is a coefficient relating to the gradient of bend-ing moment used for conversion to a value at the beamend, and �h is haunch length.

2.1.2. Local buckling strengthStrength against local buckling, MLB is obtained from:

MLB � S�·MP (5)

Fig. 3. Diagonal rupture of beam flange.

232 N. Tanaka / Engineering Structures 25 (2003) 229–239

where is full plastic moment of a beam and S� is therevised S considering the condition of the beam webconnection obtained from Eqs. (6) and (7).

For beam web welded: S� � 1.08S (6)

For beam web bolted: S� � 1.06S (7)

where S is a coefficient of local buckling strengthobtained from:

For SS400, SN400:1S

� 0.4896l2f � 0.0460l2

w (8)

� 0.7606

For SN490:1S

� 0.2868l2f � 0.0588l2

w � 0.7730 (9)

where lf � �sfy

Ebtf

, lw � �swy

E·

D�2tf

tw, sfy is yield

point of a beam flange, swyis yield point of a beam web,b / tf is width-to-thickness ratio of a beam-flange, (D�tf) / tw is width-to-thickness ratio of a beam-web, D isbeam depth, b=B/2, B is beam width, tf is beam-flangethickness, tw is beam-web thickness, E is Young’sModulus, and SS400, SN400, SN490 are steel grades.

2.1.2.1. Local buckling strength at start point of haunch(La-Line) Eq. (10) gives the local buckling strength (MLa) at the start point of the haunch by using Eq. (4)and Eq. (5). The width-to-thickness ratio at the startpoint of the haunch is used for S�.

MLa � S�m�Mp (10)

2.1.2.2. Local buckling strength at beam-end (Lb-Line)This strength (MLb) uses Eq. (11). S�END is obtained

from Eq. (6) to Eq. (9) by using the width-to-thicknessratio at the beam end, where the web strength is not con-sidered.

MLb � S�END(B � 2bh) tfsfy(D�tf) (11)

where bh is half the width of the added part of thehaunch, as shown in Fig. 3.

2.1.3. Maximum beam strength at start point ofhaunch (FGEN max-Line)

MGENmaxis the strength when the beam brakes perpen-dicular to the beam axis at the start point of the haunch.This is given by:

MGENmax �sfB

sfy

m�Mp (12)

2.1.4. Maximum beam strength at beam-end (LEND max-Line)

The strength when the beam breaks at the beam endis given by:

MENDmax � (B � 2bh) tfsfB(D�tf) (13)

This comprises no web bending strength.

2.2. Outline of design procedures

First, we assume a haunch length for a given beam.Based on the author’s research [3–5], this is 30–40% ofthe beam depth. This enables us to calculate Fd-Line,La-Line and FGENmax-Line. The intersection of Fd-Lineand La-Line could give an optimum haunch length. Next,a temporary haunch width is decided within the widthof the connected column, which gives us Lb-Line andFENDmax-Line. Further, we need to adjust the haunchwidth by considering where the local buckling occursand the haunch-end stress. For the latter decision, theauthor recommends that it should not exceed the yieldstress, because this extreme stress could deteriorate thewelded part of the beam end and accelerate earlybrittle fracture.

3. Comparison of test results with M.S.D.

3.1. Outline of specimens

The twenty-nine specimens tested are listed in Tables1 and 2. Table 1 shows member types, mechanicalproperties, etc., while Table 2 shows haunch details,strength properties and failure modes. The author createdthe names of test series.

Specimen configurations are shown in Fig. 4. Allspecimens were cyclically loaded up to the ultimatestate. The BC-, S- and RB-series were carried out by theauthors [3–5], T-series by Sugimoto [10,11], and SN-series by Sakamoto [12] and Yokoyama [13]. Specimensshown in columns (3) to (5) of Table 1 (except for RB-series, which uses a concrete-filled circular column) con-sist of H-shaped beams and rectangular hollow columns.The mechanical properties are listed in (7) to (11) ofTable 1. For the specimen with the inner diaphragm, thebeam flange was welded directly to the column and otherspecimens were welded to the outer or through dia-phragm, where CO2 gas-shield arc welding wasemployed using conventional access holes. For BC-ser-ies except for specimen BB5, the beam web was connec-ted to the column flange by welding, as shown in (6) ofTable 1. The other series used high-strength bolts(H.T.B.s). Column (12) of Table 2 shows how a haunchis made. For BC-, SB- and RB-series it was cut out ofplate, while for the other series trapezoid-like steel plateswere welded to the beam flange. For BC- and SB-series,the haunch width was designed so that the beam-endstress was restrained within the yield stress when thestrength reached S�Mp. The same method was used forT-series except that S�Mp was replaced by the designated

233N. Tanaka / Engineering Structures 25 (2003) 229–239T

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1.10

415

1628

71.

205.

0Fr

actu

re

WB

-1R

ibw

elde

d28

015

037

.518

254.

561.

013

1.17

01.

114

5658

631.

446.

5L

ocal

buck

ling

WB

-2R

ibw

elde

d30

025

062

.518

254.

561.

013

1.17

01.

137

5658

631.

627.

5L

ocal

buck

ling

WB

-2R

Rib

wel

ded

300

250

62.5

1825

4.56

1.01

31.

170

1.13

756

5863

1.62

8.1

Loc

albu

cklin

g

SN-J

––

00

2800

5.6

0.99

41.

214

1.21

398

7208

1.42

7.4

Frac

ture

SN-H

1R

ibw

elde

d25

035

070

2800

5.6

0.88

51.

270

1.20

083

4905

1.59

6.5

Loc

albu

cklin

gSN

-H2

Rib

wel

ded

290

350

7028

005.

60.

870

1,27

01.

182

8250

121.

626.

3L

ocal

buck

ling

SN-H

3R

ibw

elde

d34

035

070

2800

5.6

0.82

51.

190

1.13

889

9625

1.47

5.6

Loc

albu

cklin

gSN

-L2

Rib

wel

ded

290

500

100

2800

5.6

0.84

71.

210

1.18

277

5524

1.73

6.2

Loc

albu

cklin

gSN

-L3

Rib

wel

ded

290

250

5028

005.

60.

885

1.20

61.

182

8580

041.

557.

1L

ocal

buck

ling

SN-M

1R

ibw

elde

d31

535

070

2800

5.6

0.87

01.

207

1.17

482

5012

1.63

6.7

Loc

albu

cklin

g

235N. Tanaka / Engineering Structures 25 (2003) 229–239

Fig. 4. Configuration of specimens. (a) BC-series, (b) SB-series, (c) RB-series, (d) T-series, (e) WB-series, and (f) SN-series.

maximum strength. For RB-series, it was designed sothat rupture at the beam end was prevented when thebeam flange buckled locally at the start point of thehaunch. The haunch for WB- and SN-series wasdesigned so that the beam yielded at the same time atboth the beam end and the start point of the haunch. Thisis not clear for S-series. The primary parameters includehaunch length for BC-, SB- and WB-series; span lengthfor RB- and S-series; and a haunch width for T- andSN-series.

3.2. Necessity of haunch and deformation capacities

Test and analytical results are summarized in Table2, which shows maximum strengths and deformationcapacities of specimens, etc. Local buckling strengths,as shown in the column (19) and (20) of Table 2, arecalculated by Eqs. (5)–9. Flange strength normalized by

local buckling strength S�Mp, shown in column (18) ofTable 2, is the strength sustainable by the beam flangeonly. It is natural that no haunch is needed if the strengthexceeds 1.0, because the beam flange can sustain thebending moment even if the beam web does not workat all. Deformation capacity, h, is listed in column (23)of Table 2. This value corresponds closely to the ratioof plastic deformation capacity to yield deformation of amonotonic curve converted from a load-deflection curve.Fig. 5 shows the relation between deformation capacitiesand haunch length ratio (ld). It shows that rupture,marked by the painted circle, is distinguished by ld of35–40% from the local-buckling-marked empty circle,although hs are scattered. This leads to the fact that bet-ter haunch-length selection can realize local bucklingdesired for beam design that requires enough defor-mation capacity because it determines the fracture. Thisis why strength only is discussed in this paper.

236 N. Tanaka / Engineering Structures 25 (2003) 229–239

Fig. 4. Continued

3.3. Relation of M.S.D. and test results

Fig. 6 shows the M.S.D. for BC-series with weldedwebs, where marks indicate the same as in Fig. 5, exceptfor the painted triangle indicating the optimum haunchlength ratio (lopt). The figure shows that the crossingpoint of the Fd-Line and La-Line can usually distinguish

rupture from local buckling, although the rupture modeof the specimens having a haunch length nearly equal tothe length indicated by the intersection is not correctlyselected. The La-Line approximately corresponds to thelocal buckling strength. Specimen BW3 has a shorthaunch, ld of 12%, ruptured as shown in Photo 1. Thissuggested to the author a condition requiring an adequate

237N. Tanaka / Engineering Structures 25 (2003) 229–239

Fig. 5. Relation of deformation capacity (h) and ld .

Fig. 6. M.S.D. for BC series with welded web.

but excessive haunch length for a haunched beam. TheFd-Line is smaller than the rupture strength because thestrength of the beam web is neglected in the Fd-Line.However, this is favorable for a beam design under somesafety margin.

Fig. 7 shows the M.S.D. for BC-series with boltedweb, where the crossing point of the Fd-Line and La-Line is a good indicator of rupture.

Fig. 7. M.S.D. for BC series with bolted web.

Fig. 8. M.S.D. for S series with short beam span.

Fig. 9. M.S.D. for S series with long beam span.

The M.S.D. for S-series with short beam spans or longbeam spans are shown in Figs. 8 and 9, respectively. Allfracture modes are clearly estimated by the M.S.D.

Fig. 10 shows the M.S.D. for RB-series with shortbeam spans. The RB20 specimen ruptured after localbuckling, although it has a haunch length to only bucklelocally at the beam end based on the M.S.D. This is why

Fig. 10. M.S.D. for RB series with short beam span.

238 N. Tanaka / Engineering Structures 25 (2003) 229–239

Fig. 11. M.S.D. for T series.

vertical stiffeners, set in the vicinity of the start point ofthe haunch as shown in Fig. 4(c), constrained full localbuckling. Therefore, the haunch should not be stiffenedif local buckling is expected for design. The rupturestrength is much higher than the Fd-Line compared withthe other specimens. This is because the beam webworks more effectively owing to constraint of out-of-plane bending of the column flange by filleted concretein the column, while the Fd-Line does not consider thebeam-web strength and the constraint effect.

For T-series, specimens T1 and T2 originally need nohaunch, as indicated in chapter 3.1 (see the column (18)of Table 2). This could be realized when a beam flange’sbending strength is greater than that of a beam web witha thicker flange, a wider flange, a thinner web, or ashorter depth. This case may be a thicker flange. How-ever, the additive haunch exerted no bad effect on thedeformation capacity, as shown in column (23) of Table2. However, specimen T3, which needs a haunch forwhich the M.S.D. is as shown in Fig. 11, ruptured. Thisis due to the stiffener, as shown in Fig. 4(d), in spite ofhaving adequate haunch length to buckle at the startpoint of the haunch.

The WB-series also needs no haunch due to its widerbeam width. Fig. 12 shows the M.S.D. Both specimens

Fig. 12. M.S.D. for WB series.

Fig. 13. M.S.D. for SN series with middle beam span.

buckle in the vicinity of the start point of the haunchregardless of the local buckling of the beam end indi-cated by the M.S.D. This is mainly because the Lb-Lineneglects the strength of the beam web. However, the ver-tical stiffener exerted no bad effect on specimen WB-2R as shown in Fig. 4(e). This may be because thehaunch length is long enough relative to that of specimenT3 or RB20 to prevent rupture, and thus weaken a badeffect of the vertical stiffener.

All specimens of the SN-series with haunched beamsbuckle and show not a little deformation capacity. Figs13 and 14 show the M.S.D. for the SN-series with amiddle beam span or a short beam span, respectively.The haunch length is generally too long, leaving roomfor further improvement of the design method.

3.4. Optimum haunch length ratio

An optimum haunch length ratio (lopt) is defined hereas a haunch length ratio at the crossing point of the Fd-Line and La-Line in the M.S.D. Fig. 15 shows therelation between lopt and the beam span-to-depth ratio(� /D). lopt tends to increase, accompanied by anincrease in � /D. This tendency is approximately

Fig. 14. M.S.D. for SN series with short beam span.

239N. Tanaka / Engineering Structures 25 (2003) 229–239

Fig. 15. Optimum haunch length.

reflected by Eq. (14). The author recommends 25–35%of lopt to beam haunch as a convenient value forhaunched beam design.

lopt(%) � 0.77�

D� 21.2 (14)

4. Concluding remarks

The test results and calculations showed the following.

1. Twenty-nine specimens including the author’s andother researchers’ show that rupture is avoided byattaching a haunch to a beam end, which generateslocal buckling at the beam end or the start point ofthe haunch. The maximum strength diagram (M.S.D.)proposed by the author identifies most fracture modes.This enables us to select a mode such as local buck-ling that is desirable in a beam design to provideadequate deformation capacity for beam-to-columnconnections.

2. However, there is little improvement in beam per-formance using too short a haunch. This leads to anoptimum haunch length as indicated in Eq. (14). Asa guide, an optimum haunch length ratio (lopt) of 25–35% is recommended.

3. A vertical stiffener in the vicinity of the start pointof the haunch leads to beam rupture due to local buck-ling constraint. Therefore, stiffeners should not beused at the haunch if local buckling is expected indesign.

In order to further improve the M.S.D., which hasbeen applied to an actual design, the following shouldbe considered.

1. The effect of gradient stress in the beam flange ondiagonal rupture strength for only uniform stress wasconsidered here.

2. The effect of a stiffener on local buckling and rup-ture strength.

Acknowledgements

I would like to express my appreciation to Dr. Yosh-iaki Kurobane, professor of Sojo University, for hisadvice, and to Mr. Sawamoto, senior research engineerof Kajima Technical Research Institute, who carried outmany tests with the author.

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