Design rules for connections in Japan

J. Constract. Steel Research 10 (1988) 357-374

Design Rules for Connections in Japan

Ben Kato Department of Architecture, Universityof Tokyo, 7-3-1. Hongo, Bunkyo-ku,Tokyo, 113Japan

ABSTRACT Design rules for structural joints and connections in Japan are outlined. They are specified for both serviceability limit states and ultimate limit states. A commentary on their application is given.

NOTATION Ab hA, fA e

gA~ ,A~ B0 fs f~ bF fF gF M0 Mx

M~0

Body area of bolt Effective area of bolt Effective area of fillet weld Effective area of groove weld Effective area of tension members Design bolt tension Allowable shear stress of bolt Allowable tensile stress of bolt Maximum tensile strength per bolt Maximum tensile or compressive strength of fillet weld Maximum tensile or compressive strength of groove weld Maximum bending moment of T-flange Maximum bending moment of joint of H-section about strong axis Maximum bending moment of joint of H-section about strong axis without axial force 357

J. Construct. Steel Research 0143-974X/88/$03.50O 1988Elsevier Science Publishers Ltd,

England. Printed in Great Britain

358

Ben Kato

M~,

Maximum bending moment of joint of H-section about weak axis Maximum bending moment of joint of H-section Myo about weak axis without axial force Maximum shear strength per bolt bQ fQ Maximum shear strength of fillet weld gQ Maximum shear strength of groove weld ~Q Maximum shear strength of splice of H-section sf Allowable shear resistance by friction per bolt fT Maximum tensile strength of one flange splice hT Maximum tensile strength of T-stub flange-to-column connection Maximum tensile strength of splices of H-section sT , T(, T~,, ~ , , 7"3)Maximum strength of tension members with bolt holes Maximum tensile strength of one web splice wT V Total volume of joint panel Effective volume of joint panel Z Plastic section modulus Reduced plastic section modulus due to the effect of bolt eZ holes Specified minimum tensile strength of bolt O" b O" u Specified minimum tensile strength of steel material O-y Specified minimum yield stress of steel material

INTRODUCTION Current design rules for steel structures including their connections in Japan 1 are based on the allowable stress design concept. However, new national codes for seismic design 2 were enforced in 1981 in which two categories of safety criteria were prescribed, namely against a moderate earthquake which is expected with a reasonably high probability during the life of a structure, the structure should be proportioned to remain elastic and to remain within a specified deflection limit, i.e. it should be designed according to the allowable stress design basis for unusual loading; while against a major earthquake, which is unlikely to occur within the life of a structure but is used in the design to examine the ultimate structural safety, the structure may be permitted to undergo considerable structural damage but the collapse of the structure and resulting loss of human life must be avoided. The latter check of structural safety must be carried out on the basis of ultimate limit state design with due evaluation of ultimate strength

Design rulesfor connections in Japan

359

of connections in a structure. Furthermore, a committee for drafting the ultimate limit state design specifications for steel structures was organized in the Architectural Institute of Japan (AIJ) in 1981. The work is not completed as yet, but in these new specifications, the design rules for other types of loading such as wind turbulence and snow loading would be included in addition to that for seismic loading, and the unified design rule would be developed within one or two years, possibly taking a form of LRFD. In this paper, allowable stress design criteria for connections are outlined first, and ultimate strength design criteria for connections against a major earthquake loading follow.

A L L O W A B L E STRESS DESIGN C R I T E R I A

General connection design requirements The basic design principle for steel structures is that for instantaneous loading (loading of structures for daily use), allowable load-carrying capacities of members and connections are specified in terms of allowable stresses, while for unusual loading, such as moderate earthquake, strong wind turbulence (typhoon) and heavy snow loading (the expectation of the occurrence of which is estimated to be once or twice during structure's service life), allowable stresses are increased by 50%. These increased stresses are almost equal to the elastic limit or stability limit of members. Considering that the quality and performance of connections are less reliable than those for structural members, and also considering the importance of the role of connections in a whole structure, allowable stresses for connections are assigned to be more conservative. As for mechanical fasteners, rivet, high-strength bolt and other bolts are applicable for structural design, however these days, high-strength bolts are exclusively used for practical design in Japan. Therefore, provisions for high-strength bolts and welding and connections using them are described in the following.

Details with regard to bolting (high-strength bolts) (1) Allowable stresses (a) Allowable stresses are specified for instantaneous loading for three grades of high-strength bolts as shown in Table 1. However, the use of F11 T bolts is not recommended if the possibility of the occurrence of delayed fracture is taken into consideration.

36[)

Ben Kato TABLE 1 Allowable Stresses for High-strength Bolts (MPa) Grade

Tension, ,t;

Shear, j~

F8 T FI0 T FI 1 T

245 304 324

118 147 157

Allowable stresses shall be computed for the body area of fasteners. For unusual loading, above stresses may be increased bv 50%. TABLE 2 Design and Standard Bolt Tensions (kN) Design bolt tension

Sulndard bolt wnsion

Grade

FST F10 T F11 T

MI6

M20

M22

M24

MI6

M20

M22

M24

83.6 104.0 109.8

130.4 161.8 170.6

161.8 201.0 211.8

188.3 233-4 246-2

91.9 114.7 120-6

143.2 178.5 187-3

178.5 221.6 233"4

2(16.9 256.9 27(I-7

1.6

2.0

2.2

2.4

2-01

3.14

3.80

4.52

1.57

2.45

3.03

3.53

diameter (cm) body area (cm 2) effective area (cm 2)

Allowable shear stresses f, given in Table 1 are determined on the basis of design bolt tensions B0 specified in Table 2 as follows. L

Sf-

Sf -

-

-

Ab

/'£ BI) P

0"45Bo -

-

-

1"5

1 Ab

(l)

(2)

in which Sf is the allowable shear resistance by friction per bolt (kN); A~ is the body area of bolt (cm2); B0 is the design bolt tension (kN); tz = 0.45 is the slip coefficient; and u = 1.5 is the factor of safety against slip. In execution, high-strength bolts should be tightened so as to introduce initial tensions specified as 'standard bolt tension' in Table 2.

Design rulesfor connections in Japan

361

c

T Ts=Separation7

/ ~"

T

0

L./

:/ Bo

Bolt Slress, B

Fig. 1. Stress in high-strength bolt.

Considering some scattering of initial tension in practice, 'design bolt tension' is increased by 10% to specify the 'standard bolt tension'. When a bolted joint is subject to tension, the increase of tensile stress in a bolt is not substantial until the separation takes place, but after the separation has taken place, the bolt will be pulled directly by the applied force, as shown in Fig. 1. Allowable stresses f~ in Table 1 apply to apparent stresses due to external tensile forces acting on high-strength bolts. They are equivalent to 60% of the design bolt tensions. For unusual loading, the allowable tensile stress becomes 90% (1.5 x 60%) of the design bolt tension which is still lower than the separation point. In the calculation of applied tensile force on bolts, the prying action of the joint must be taken into account if necessary. (b) High-strength bolted connections need not be restricted by bearing stress, but in ultimate strength design the ultimate bearing capacity must be assessed. (c) Effect of repeated stress variation need not be considered for highstrength bolted connections.

(2) Alignment of bolts (a) Minimum connections. Connections joining principal members, except for lacing and tie plates in built-up members, should be effected by the use of at least two bolts. (b) Placement of bolts. Groups of high-strength bolts at the ends of any axially stressed member should have their centers of gravity on the gravity axis of the member wherever practicable, except in a design where effect of eccentricity is taken into consideration. (c) Bolts in combination with welds. Bolts used in a connection should not be considered as sharing the working load with the weld used in the

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362

TABLE 3

Minimum Edge Distance (ram)

Types of edges

(d)

(e)

(f)

(g) (h)

Diameter of fasteners (mm )

Sheared or manual flame-cut edges

Rolled, automatic flame-cut, sawn or milled edges

M I6 M20 M22 M24

28 34 38 44

22 26 28 32

same connection, except that bolts installed prior to welding may be considered as sharing the load with the weld. In making welded alteration to structures, existing rivets and high-strength bolts may be utilized for carrying stresses resulting from existing dead loads; however, all additional loads should be carried by welds. Number of bolts in line of stress. In a connection (up to eight bolts in line of stress) the effect of shear lag need not be considered and each bolt may be assumed to carry equal stress. Diameter of holes. The diameter of a bolt hole should be 1-0 mm plus the nominal body diameter of bolt for an M16 bolt, and should be 1.5 mm plus the nominal body diameter of bolts for M20, M22 and M24 bolts. Minimum pitch. The minimum distance between centers of holes of bolts should not be less than 2.5 times the nominal diameter of respective fasteners. Minimum edge distance. The minimum edge distance from the center of holes of bolts should be as given in Table 3. Minimum edge distance in line of stress. In connections of tension members, where there are not more than three bolts in a line parallel to the direction of stress, the distance from the center of the end bolt to the end of the connected part toward which the stress is directed should not be less than 2.5 times the nominal diameter of the bolts used.

Details with regard to welding

(1) Scope of application This sub-section prescribes the requirements for the design and computation of structural steel elements connected mainly by manual arc welding or by automatic submerged arc welding. Welds produced by welding methods other than those described above may, when proved satisfactory by testing,

Design rules for connections in Japan

363

be regarded as equal to those produced by the welding methods specified herein.

(2) Types of welds In general, the type of welds carrying loads will be selected from the following three types: complete-penetration welds fillet welds partial penetration welds. Fillet welds will not be allowed to carry load where they are used to join two steel elements making an angle of less than 60° , or more than 120° . In the case of tubular steel elements, the foregoing lower and upper limits of the angle may be taken as 30° and 150°, respectively. Partial-penetration welds will not be used for joints subject to tension normal to the weld line, to bending about the longitudinal axis of the weld, or to repetitive loading.

(3) Size of fillet welds The size of fillet welds will not exceed the thickness of the thiner steel base metal joined. However, the size of fillet welds may be increased to 1.5 times the plate thickness or to 6 mm maximum for tee-joint connecting plates not more than 6 mm thick. For plates more than 6 mm thick the size of fillet welds will be not less than 4 mm and not less than 1-3X/t (mm), where t(mm) is the thickness of the thicker base metal joined. This requirement, however, will not apply to fillet welds 10 mm or larger in size. For fillet welds connecting a branch pipe to a main, the size may be increased to two times the wall thickness of the thinner (branch) pipe joined.

(4) Length of fillet welds The effective length of a load-carrying fillet weld will basically be not less than ten times the nominal fillet size and not less than 40 mm. Where the effective length of a side fillet weld exceeds thirty times the nominal fillet size, the allowable stress for such welds will be reduced to allow for non-uniform stress distribution along the length of the weld. If side fillet welds are used alone in end connections of flat bar tension members, the length of each fillet weld will not be less than the width of the flat bar connected.

(5) Lap joint Lap joints carrying computed stresses will, as a rule, be accomplished by use of not less than two lines of fillet welds. The minimum lap length in such

364

Ben Kato

joints will not be less than five times the thickness of the thinner part joined and not less than 30 mm.

(6) End returns of fillet welds Side or end fillet welds terminating at ends or sides, respectively, of parts or m e m b e r s will, as a rule, be returned continuously around the corners for a distance not less than twice the nominal size of the weld.

(7) Effective areas of weld metal (a) Effective area of groove weld. The effective area of a groove weld should be taken as the effective length of the weld times the effective throat thickness. (i) The effective length of a groove weld will be the width of the connection measured normal to the longitudinal axis of a member. (ii) Effective throat thickness of partial penetration weld made by manual welding. Effective throat thickness of single-Vee, -bevel, -U and -J groove welds in materials with a thickness of 12 m m or over and X, K, H and double-J groove welds in materials with a thickness of 38 m m or over should be taken as the value specified in (1) or (2) below, but not less than 2x/t (mm), where t (mm) is the thickness of the thinner plate joined. (1) For single-bevel and K-groove welds, effective thickness will be the depth of groove, less 3 mm. (2) For single-Vee, -U, -J, X, H and double-J groove welds, effective thickness will be equal to the depth of the groove. (iii) Effective throat thickness of partial penetration welds made by automatic submerged arc welding. Effective thickness of single-Vee, -bevel, -U and -J groove welds in materials of 19 m m or over in thickness, and X, K, H and double-J groove welds in materials of 32 m m or over in thickness will be equal to the depth of groove, but not less than 2x/t (mm), where t (mm) is the thickness of the thinner plate joined. (b) Effective area of fillet weld. The effective area of fillet weld should be taken as the effective length of welds times the effective throat thickness. Stress in fillet welds should be computed on the basis of the effective area irrespective of the direction of loads. The effective length of fillet weld should be considered as the overall length of fillet weld including end returns less twice the size of fillet.

(8) Allowable stresses Allowable stresses under instantaneous loading on effective throat of arc weld may be taken as the values prescribed below provided that the welding

Design rules for connections in Japan

365

electrode used is appropriate for the type of steel to be welded and that welding is performed under satisfactory control. Welds in SS50 and SS55 steels, however, should not be allowed to carry any stress. (a) Allowable stresses for fillet weld and partial-penetration weld on effective area of welds described in item (7) should be the same as allowable shear stress for base metal. (b) Allowable stress for complete penetration groove welds should be the same as that for base metal to be welded. (c) Where steels of different qualities are welded, allowable stress for welds should be taken as the smaller value of the allowable stresses for base metals.

(9) Minimum connections Connections joining principal members, except for lacing and tie plates in built-up members, should be designed to support not less than 29 kN, if welded.

(10) Combination of welds If two or more types of weld are combined in a joint, the effective capacity of each type of weld should be computed on the basis of the allowable stress for each type of weld. Beam-to-column connections (moment connections) Where beam-to-column connections are required to carry bending moment, shear and axial force, the ends of members should be so connected that they will be sufficiently capable of transmitting all the foregoing forces. The load-carrying capacity of a joint-panel formed by surrounding-beams and columns against unusual horizontal loadings such as moderate earthquake and wind turbulence should be examined according to the following formulae. In general, the beam-to-column connections should satisfy the following conditions: (i) The connection is of the through-column type. (ii) Appropriate diaphragms are arranged at the levels of the upper and lower flanges of a beam inside the panel zone. (iii) Columns and beams should be rigidly connected (connecting of beam flanges must be performed by groove welding as a general rule, but cases of T-stub flange joining, using high-strength bolts, are also acceptable). 4 bMl + bM2 --<3 - ~ V~o'y

(3)

366

Ben Kato

~cQ

bM2 tw

!M1

ib

¢Q2~ Fig. 2. Joint-panel.

~ --hc I

v . m m m .

t~

tA~

Fig. 3. Shear area of cross-shape column. in which O-y is the specified minimum yield stress of joint panel material (MPa); V. is any of the following values depending on the shape of the connection of the column (unit cm3). (V represents the total volume of the joint panel zone.) (a) W h e n the section is H-shaped, V~ = V = hbhct, (see Fig. 2). (b) W h e n the section is box-shaped, the sum of the volumes of the two webs is parallel to the plane of action of bending m o m e n t . W h e n the section is box-shaped, square and with uniform thickness, Vo = ½V. (c) W h e n the section is tubular, Vo = ½V. (d) W h e n the section is cross-shaped (see Fig. 3), Ve=f~)V

(~) = Ot --

w.

a 2 + 2.6(1 + 2/3) o£2 +2.6 hb b

B --

Af Aw

Af

= btt

Aw = h~t.

Vw = A , h b = hbhctw: volume of the panel of H-columns directly

connected to the beam where hb is the web height of the beam (cm); hc is the web height of the column (cm); tf is the flange thickness of the

Design rulesfor connections in Japan

367

column (cm); tw is the web thickness of the column (cm); B is the flange width of the column (cm); and bMt, bM2 is the bending moment to act on the end (contact face with the column) of the left and right beams, respectively, at times of typhoons or earthquakes (kN cm). Connections for truss members Connections joining truss members will be capable of transmitting computed working stresses in the members satisfactorily, and will have a strength not less than one-half of the strength allowable for the members connected. Column splices High-strength bolts and welds in column splices will be capable of transmitting computed working stresses in the joints satisfactorily and they should be so proportioned that their strength will not be less than one-half of the strength allowable for the members with respect to each type of stress. If, however, the cross-section through the joint is not subject to tensile force and the abutting ends of two column sections are milled or otherwise finished for direct bearing, one quarter of compression and bending moment acting on the splice may be assumed to be transmitted by direct bearing. Furthermore, column splices should be designed to safely carry such tensile stress as would result from stress combinations under wind turbulence or earthquake if the live load were neglected.

ULTIMATE STRENGTH DESIGN C R I T E R I A General connection design requirements As mentioned in the 'Introduction', structures are permitted to undergo considerable plastic deformation against the major earthquakes. In order to enable a structure to form collapse mechanism and develop sufficient plastic deformation, connections should be stronger than members joined. Considering the characteristic behavior of each type of connection and possible scattering of material strengths, the following design criteria are specified: (1) The ultimate strength of an end connection of diagonal bracing should be 20% stronger than the axial yield strength of the bracing member joined.

368

Ben Kato bending moment diagrram

beam configuration

[

picastic region T = 1- Mp/Mu

Fig. 4. Rotation capacityof beam. (2) The ultimate moment capacity of a beam-to-column connection of a m o m e n t frame should be 30% stronger than the full plastic m o m e n t of the beam joined. Also the ultimate shear capacity of it should be 30% stronger than the yield shear strength of the beam joined. The rotation capacity of beam ends depends upon the spread of plastic region along the beam length, as illustrated in Fig. 4. Therefore a larger increase of moment capacity, than that for the end connection of diagonal bracings, is required at the beam ends. (3) When the beam or column splices are located at the vicinity of m e m b e r ends of a moment frame and are expected to be plastified against the major design earthquake, the ultimate bending and shear capacity of them should be 10% stronger than the full plastic m o m e n t and yield shear strength of members joined, respectively. When the connections are made by high-strength bolts, the number of bolts in line of stress should not be less than three for flange connection, and the section modulus of splice plates should be larger than that of members joined.

Maximum strength of high-strength bolt and weld

(1) High-strength bolt Maximum strengths per bolt may be taken as the values prescribed below: (i) Axial tension .F = bAeO'b

(4)

(ii) Shear bQ

= 0'75bAeO'b

(5)

369

Design rules for connections in Japan

TABLE 4

Specified Minimum Tensile Strength of High-strength Bolts (MPa)

O-b

F8 T

FIO T

F11 T

785

981

1 079

in which bF is the maximum tensile strength per bolt (kN); hA. is the effective area of bolt (cm 2, see Table 2); ~Q is the maximum shear strength per bolt (kN); and o-~ is the specified minimum tensile strength of bolt (given in Table 4). (2) Welds (a) Groove weld (i) Tension and compression (6)

gF = gAeff u

(ii) Shear 1 gQ = gAe~7~O'u

(7)

(b) Fillet weld (i) Tension and compression 1

(8)

fF = fA~:~7-~o-u (ii) Shear 1

fQ = fA~7~O-u

(9)

in which gF is the maximum tensile or compressive strength of groove weld (kN); gQ is the maximum shear strength of groove weld (kN); ~A~ is the TABLE 5 Specified Minimum Tensile Strength of Steel Material (MPa)

Ou

SM41, SS41

SM50

402

490

370

Ben Kato

effective area of groove weld (cm2); fF is the maximum tensile or compressive strength of fillet weld (kN); fQ is the maximum shear strength of fillet weld (kN); fAe is the effective area of fillet weld (cm2); and o-o is the specified minimum tensile strength of base material joined, and is given in Table 5.

Maximum strength of connections

(1) Tension members with bolt holes Maximum strength of tension members with bolt holes can be taken as the smaller value computed by eqns (10) or (11) tTl = tAro'.

(10)

t T 2 = neto'u

(ll)

in which cro is the specified minimum tensile strength of steel members joined (MPa, see Table 5); n is the total number of bolts; e is the edge distance in line of stress (cm); t is the smaller value of plates thickness of joined members; and ,A0 is the effective area of tension members (cm 2) which will be computed as follows.

Flat plates tAt = ( b - m d ) t

(12)

in which b is the width of plate (cm); m is the number of bolts counted across the width of plate; and d is the diameter of bolt hole (cm).

Angles and channels t A c = A g - • Vtl - m d t 2

(13)

in which Ag is the gross area of angle or channel section (cm2); and Evtl is the reducing area, as shown in Fig. 5, and v is given in Table 6. Maximum shear strength of high-strength bolts in a joint is given as t T3 = n bQ

(14)

Therefore, the maximum strength of a bolted connection of tension element is given by the smallest value of ,T1, ~T2 and tT3.

(2) T-stub flange-to-column connections (see Fig. 6) Maximum tensile strength of one side of a T-stub flange-to-column con-

Design rules for connections in Japan

371

TABLE 6 v-Value (cm)

Crosssection

1

Number o f bolts joining the tension member 2 3 4

angle channel

h - te h - te

0-7h 0.7h

jl~_l

0.5h 0-4h

4'*-

d

d

0"33h 0.25h

5 0.25h 0.2h

' 't2

Fig. 5. Effective area.

nection (hT, or h T2) can be computed from formulae shown in Table 7. According to the condition applicable, and unless the number and alignment of bolts at each side of T-flange do not differ substantially, the maximum strength of a T-stub flange-to-column connection can be taken as the sum of the strength at each side (eT = hT, + hT2). TABLE7 M a x i m u m T e n s i l e S t r e n g t h o f O n e S i d e o f T - s t u b F l a n g e - t o - c o l u m n C o n n e c t i o n s ( h T i , 2 , kN) 2a>/3+3'

(t~ -- 3 " ) n b F l

Mo <(/3 -- 3")n b E /

4 fl(a - 7)nbFl

l+c~-y

h/I,2

2a~/3+7

4

.~ Mo <

o~(,/~ -- 3 ' ) n b F /

2Mo

1 + ~ +3'

(/3-3,)1

Mo
3"nbFl + 2Mo (/3+3")1

l+a-3'


a ( ~ - 3")nbFl

1 +c~+-y

~nbFl < Mo


Mo

--+ombF l

nhF

in which l = b - ½ r = effective flange width (cm), r = size of fillet (cm), t = thickness of T - s t u b flange (cm), n = n u m b e r of bolts in one side of T-flange, 0F = m a x i m u m tensile s t r e n g t h p e r bolt (kN, see eqn (4)), M0 = ~ wflo-u = maximum bending m o m e n t o f T - f l a n g e (kN cm), w = length o f T - s t u b flange (cm), a , / 3 = non-dimensional edge distances for bolt a l i g n m e n t , a n d 3' = n o n - d i m e n s i o n a l width of across flats of bolt head.

Ben Kato

372

6L~l

- I

c~

f hT=hT~.hT,

t

Ic

Fig. 6. D i m e n s i o n s o f T - s t u b flange.

(3) Splices of H-section members (a) Maximum tensile strength. Maximum tensile strength of splices of Hsection members, sT, can be computed by eqn (15). sT = 2fT+wT

(15)

in which fT is the maximum tensile strength of one flange splice (kN), and wT is the maximum tensile strength of one web splice (kN). For high-strength bolted joints, fT and wT can be obtained as the smallest value of ,T,, ,T2 and tT3 given by eqns (10), (11) and (14), respectively. The maximum strength of splice plate should not be less than that of plate element joined. For welded joints, fTand wTcan be obtained by making use of eqn (6) for groove welded joints, and eqn (8) for fillet welded joints. (b) Maximum shear strength. Maximum shear strength of splices of Hsection members can be computed by eqn (16) for strong axis shearing, and by eqn (17) for weak axis shearing Strong axis shearing:

sQ = wQ

(16)

Weak axis shearing:

~Q = 2fQ

(17)

in which wQ is the maximum shear strength of web splice (kN), and fQ is the maximum shear strength of flange splice (kN, one flange). For high-strength bolted joints, wQ and fQ can be computed by eqn (5). For welded joints, wQ and fQ can be computed by eqn (7) for groove welded joints, and by eqn (9) for fillet welded joints.

Design rules for connections in Japan

373

(c) M a x i m u m b e n d i n g m o m e n t . (i) Strong axis bending Mx = Mz~

for p ~ y

(IH)

Mx - 1 - p M~ 1-y

for p > y

(19)

in which Mx is the maximum bending moment of joint about strong axis (kN cm), and Mx0 is the maximum bending moment of joint about strong axis without axial force, and can be computed by the following equations (kN cm). For groove welded joint:

Mz~ = Zcru

(20)

in which Z is the plastic section modulus of member joined (cm3). For high-strength bolted joint, Mx0 should be the smaller value of eqns (21) and (22) Mxo

(21)

= eZo'u

Mxo = f T ( H -

t) + 0"5wTj

(22)

in which e Z = Z - m d t ( H - t) is the reduced plastic section modulus, taking the effect of bolt holes into account (cm3); H is the height of H-section (cm); t is the flange thickness (cm); j is the distance between stress centers of web fasteners (cm); m is the number of bolts counted across the width Of flange; d is the diameter of bolt hole (cm); p = N / N v = N / s T i s the axial force ratio (~Tis given by eqn (15)); N is the working axial force (kN); and y = wT/(2 sT). (ii) Weak axis bending My = My0

for p -< 2y

(23)

My-

for p > 2y

(24)

11-- p2y M~

in which My is the maximum bending moment of joint about weak axis (kN cm); Myo = ½ f T B is the maximum bending m o m e n t about weak axis without axial force (kN cm); and B is the overall width of flange plate. Maximum strengths of splices of H-section members were dealt with in

374

Ben Kato

this sub-section. However, formulae given in this sub-section may also be used in the evaluation of maximum strengths of beam-to-column connections for their pertinent elements.

REFERENCES 1. Design StandardforSteelStructures. The ArchitecturallnstituteofJapan(A1J), June 1970. 2. Building Code ofJapan, and Enforcement Order. TheMinistryofConstruction, Japan, June 1981.