Journal of Stmctuml Engineering No. 31-18 Vol. 31, No.3, October-December 2004 pp. 181-188

Desigll1l of bolted! enrl-piate beam-to-column Ci[lHll!l1ectioll1ls

Sriram Kalaga*

Application of several design methods for bolted, end-plate beam-to-column connections is discussed. Over 700 connections were designed employing seven different design procedures and using light, medium and heavy wide­flange beam-sections. Relative efficiency of the methods was ascertained on the basis of the obtained end-plate thickness. ApplicabiUty of these methods in routine designs is discussed with emphasis on practical signific­ance.

Structural steel frame works usually involve beam-to­column joints of one or several types depending on struc­tural and end rigidity requirements. The general design intent in most connections is to ensure full transfer of beam moments and shears to the column, without appreciable rotation. of the connected members. In most steel frame connections, the beams transmit moment via their tension flanges while shear is primarily carried by the web. The per­formance of most joints depends on the amount of moment transferred which in turn defines the required rotational rigidity.

Based on the rotational restraint offered, the AISC Man­ual of Steel Construction 1•

2 and most steel codes world­wide, classify structural joints into three basic categories:

Type 1 Rigid Frame Connections Type 2 Simple Framing Joints Type 3 Semi-Rigid Joints

Rigid connections (ex: fully welded) provide full rota­tional restraint whereas little restriction on rotations is imposed on Type 2 joints. Connections, which are neither too rigid nor too flexible, fall in the 3rd category. Most steel frame join'ts are of Type 3 where the moment - rota­tion characteristics are difficult to ascertain theoretically. One of the most popular semi-rigid beam-to-column joints used by engineers for ease of fabrication and erection is the bolted end plate connection shown in Fig. 1. The connec­tion utilizes high-strength bolts and essentially consists of a plate welded to the beam end and bolted to the column

·flange. Moment from the beam is transferred to the col­umn through the complex interaction of the bolts and the plate.

The relatively simple geometric configuration of the end plate connection belies the associated analytical complex­ities. The joint essentially behaves in a non-linear man­ner with additional difficulties arising out of the following factors 3:

Column flange

f End plate

.,--aeam nang .. I> _ft

)M • • Column I Seam web

r~,~ .. • • II

Side elevation Front view

FIG, I. BOLTED END PLATE CONNECTION

(a) Number of small components (b'1 Bending spans between the fasten ; and connected

parts is often smaller than the thick ~ss of the parts (c) Contact regions between the plate an, its support vary

with changing load conditions (d) Bolt heads and fillet welds have'great stiffening influ­

ence on the joint deformations (e) The forces applied and the reactions developed are

often in more than one plane (f) Prying action in bolts which develops as a result of

transmitted forces and end plate deformations

Extensive research was directed to the modeling, anal­ysis and design of the end plate connection over the years employing elastic and plastic theories, finite element pro­cedures and full-scale testing3- 11 · 13•14 . One noteworthy simplification adopted for analytical purposes is the Split Tee Analogy4·8• 11 • 14 , which basically considers the joint as made up of T-stl!bs. The plastic theory was employed by a majority of researchers in developing rational design methodologies 1·8 ·

13•14

: The moment-rotation or M-e char-

'Consulting Structural Engineer, 48 Roxbury Circle, Jackson, Michigan 49203, USA

JOURNAL OF STRUCfURAL ENGINEERING Vat .. 31, N0.3, OCTOBER-DECEMBER 2004 181

acteristics of the joint - determined both experimentally as well as by finite element modeling. c are also employed in formulating a design technique3·9•10 . These individual treatments by researchers led to a number of distinctly dif­ferent design formats, all of which more or less aim at achieving an optimum end plate thickness .. A comparative study of these methods would be of practical significance to designers; but no detailed review of the applicability and relative merits of these procedures is conducted so far. This study aims to address that gap.

This study presents a review of the cun·ently available design methods for bolted end plate beam-to-column con­nections. Seven design procedures were selected for exten­sive application review. The designed connections involve a wide range of standard beain sections (W·), categorized on the basis of weight as light (14-53lb./ft), medium (55-94lb./ft) and heavy (99lb./ft and above). Hundreds of end plate connections were designed using the selected meth­ods with the help of computer programs specially devel­oped for the purpos·e. The plate thickness was chosen as the basis of comparison and for ensuring a uniform review.

DJESIGN MJETHODS

The seven design methods evaluated here are classified into four sections as follows:

1. Elastic Method 2. Plastic Methods 3. Limit State Design 4. Design based on M-e Response

Elastic Method

In this method 12, the end pbi.te thickness is evaluated by considering the bending moment in the plate. •It is assumed that there is no prying force in the connection arid that the flange force is uniformly distributed among all the bolts in the connection. Specified allowable stresses for bending in the plate and for tension in the bolts are used. The method also assumes equal yield stresses for both the beam and the plate material and considers the joint essentially as aT-stub joint (Fig. 2).

T T

Beam flange

Q B a Q Q B' B Q

Prying forces Deformations

FIG. 2. THE SPLIT TEE ANALOGY .AND PRYING FORCES

The design equations for end plate t~ickness Tep are:

TC/) = 6M/W,pF1J

We,= W1+l.O

FR = 0.75Fy

M = B*b

where:

(la)

(l b)

(!c)

(ld)

M 8 = Moment in the end plate due to bolt force B

b = T-stub Parameter (Fig. 2)

F8 =Allowable Bending Stress in Plate

Fy =Material Yield Stress (beam and plate steel)

W f = width of beam flange

w., = End Plate Width (taken as 1" more than W 1 )

In the absence of prying forces Q, the bolt force B = ~T.

Plastic Method - 1

This method 13 assumes equal stressing in bolts above and below the tension flange of the beam. The end plate is allowed to deform to bring about this equalization. Yield stresses of both beam and plate material are the same. The design procedure basica!Iy consists of deterinining the bolt area required to sustain the flange force at yield with a given yield stress of the bolt material. The formulation leads to a polynomial expression involving connection geometry and plate thickness. In addition, the ,method also gives a few equations to assess the strength of the column flange and the. need for stiffeners.

The design equations are:

Aan = WtTtFY!FrB

N = ABn/Ab

[WtTt/WepTep]2

{ (BLf2T,p) 2 + ~} = LO

A B R = Required bolt area

Wf, T1 =Width and thickness of the beam flange

Fr 8 = Yield Stress of tne bolt

Ab = Area of a single bolt

N = Number of bolts required

Re-arranging terms, Eqn (2c) becomes

(2a)

(2b)

(2c)

(4Wep 2)(Tep 2 )2

- (3Wj 2

TJ 2)(Tep 2)- (Wj 2 T1 2 BL 2)

= 0 (2d)

Solution of the above quadratic equation gives the required end plate thickness. In Eqns 2c & d, BL is the distance between the bolts above and below the tension flange which is often conservatively taken as 1.15* W f (Fig. 3).

Plastic Method - 2

Tl.Je 'Split Tee' Analogy concept is used here to propose a comprehensive design process for the connection8. Three

182 JOURNAL OF STRUCfURAL ENGINEERING VOL. 31, N0.3, OCTOBER-DECEMBER 2004

:

types of end plate behavior are identified, namely, thick, intermediate and thin. The first is characterized· by zero bending in the plate and the absence of plastic hinges and prying force . Upper limit for this case is when yielding begins at the beam flange weld. Once this load is exceeded, a plastic hinge forms at the flange, the plate is deemed to be of an intermediate thickness with prying force. between zero and Qmax· The third stage is identified by the formation of a second plastic hinge at the bolt line when the end plate is deemed to be thin and the prying force reaches a maximum. In other words , this categorization implies that for an ideal design, the end plate should be thick under service loads, intermediate under factored loads and function as a thin plate under ultimate load.

T;2F -Tr f

sT ~ ,.

Bl I

,_,L_

< II

sf l'--= D~ . I Tep

8 8 '---

FJG. 3. END PLATE GEOMETRY: PLASTIC DESIGN I

The above treatment provides for expressions for the three thicknesses of which only the limiting values, thick and thin plate thicknesses, are of academic interest (Fig. 4).

T

Plastic hinges

"' No plastic hinges

8

0 = 0 8 8 Q;O Q=Omax

Thick plate Thin plate

FIG. 4. END PLAT E GEOMETRY: PLASTIC DESIGN 2

Tep(thick) = (2.11bTJ WJ Fy pj WcpFr p )112 (3a)

T.,(thin) = {2(Wr TJ Fr pb-1jl6Jr Ds 3 Fr s)/ Fr (0.85W,P

where:

F y F = Yield Stress of beam material

F y p = Yield Stress of plate material

FrB =Bolt Yield Stress

D s = Bolt Diameter

Wep' = End Plate width per bolt

(3b)

Plastic Method - 3

This method is based on collapse mechanisms of the joint as a function of the prying force 14 . Three mechanisms are considered: A-with zero prying; B-with prying force Q between 0 and Qmax; and C - with Q = Qmax· It is clear that mechanisms A and C are extremes of mechanism B. The joint is once again idealized as a T-stub and one half of the connection is considered.

For collapse mechanism B, bolt fracture is the determin­ing factor with the formation of a plastic hinge at the weld. The associated equilibrium equations are:

Force: T = Bu - Q (4a)

Moment: T * b- Q *a= My (4b)

Combining, T * b- (Bu - T) *a = Mr (4c)'

For Mechanism A: Q = 0, Bu = T and Bolt Fracture Governs

(4d)

My is the moment required to cause a plastic hinge at weld = lj2W.pTep 2 Fr

For half the joint, equation 4d becomes:

T * b = lf4W.pTep 2 Fy

Which gives the associated end plate thickness as

Tep = (4bTjW,pFr) 112

(4e)

(4f)

For Mechanism C: Q = Qmax, and Flange Failure Governs. Qmux is reached when a plastic hinge forms at the bolt line.

(4g)

For half the joint, equation 4d becomes:

T *b= Mr+Mr·

= Mr[l +(net area of plate I gross area of plate)]

= 1/4 W,pTep 2 [1 + A net/ Agi'Oss J.Fy (4h)

which gives the associated end plate thickness as

Tep = (4bTfaWepFr) 112 (4i)

where ex = I + (A net/ Across)

Mechanism C is obviously a desired choice for design as it avoids sudden bolt fracture. It must be added here that Mechanism A results in a higher plate thickness and a smaller bolt whereas Mechanism C gives a smaller end plate thickness but the largest bolt.

Plastic Method - 4 (AISC)

The AISC (American Institute of Steel Construction) Manual 1 recommends this plastic design method and is based on extensive finite element analyses of the joint9· 10. The method stipulates that the connection be

JOURNAL OF STRUCTURAL ENGINEERING VOL. :ll , N0.3, OCTOBER-DECEMBER 2004 183

designed for th.e full ·plastic moment capaCity MP of the beam section and that the beam flange force due to applied moment is equally distributed to all bolts in the region. The procedure differs from other plastic designs in that the lever arm for computing the plate moment is more precisely defined. A factor of safety of 1.33 is applied to the bending stress in the plate and involves empirical constants based on the yield stresses of beam and bolt materials. Prying forces are not considered.

The design equations are:

FBF = Mp/(Dbeam- Tp)

AsN = FBI' /2N Fr

Pp = 1.5 + 1/2Do + 1.4Tw/2

PE = PF- l/4DB- Sw

X= WpTp/(Dbeam- 2Tp)Tw

= Area of Flange I Area of Web

Y=PE/De

W,, = 1.15Wp

Cs = (Wr/W,")l/2

CA =Constant= 1.13 for A325 bolts;

1.14 for A490 bolts (36 ksi steel)

= 1.09 for A325 bolts;

1.11 for A490 bolts (50 ksi steel)

aM= CACo(X)l/3(Y)0.35

Mv = 1/4aMFnFPE

T,, = 6MD/0.75Fy w., where

FBF =Tensile force in the beam flange

Dbcam = Depth of the beam section

(5a)

(5b)

(5c)

(5d)

(5e)

(5f)

(5g)

(5h)

(5i)

(5j)

(5k)

(51)

(5m)

AnN =Nominal Area per bolt (assuming 2 bolts

per row)

Sw =Size of Fillet Weld

Tw = Web thickness

PE = Moment Lever Arm

W F = Width of the beam flange

M = Design parameter

M v = Design Moment

The above procedure is generally known to be on the conservative side.

Limit State Design Method

Packer and Morris 11 proposed a design procedure based on the limit states of the end plate connection behavior and backed by an yield line analysis of the joint. The method assumes 4 bolts in the tension region and considers the joint as a set ofT-stubs. Limits are prescribed for the bolt

forces but the joint is designed for the full plastic moment capacity MP of the beam. An expression for end plate thick­ness is given on the basis of effective moment on the end plate.

The design equations are:

F u B = ultimate bolt force = M p /3 ( Dbeam - Tp) ( 6a)

Fpy =flange force at yield = M p/(Dbeam - TF) (6b)

N =number of bolts= Fpy/TuB

T,, = [FpybfFr(Wep- D 8 )]112

where

b = T-stub parameter

(6c)

(6d)

T u 8 = Minimum specified tensile Strength of the bolt

= 120 ksi (827 MPa) for A325 bolts and 150 ksi

(1034MPa) for A490 bolts

Design based on M-e Response

The moment - rotation response characteristics of the con­nection were utilized by Krishnamurty et al3·

9• 10 in develop­

ing a rational design procedure. The procedure uses a con­nection rigidity ratio 'p' which is defined asp= Me/ M ;, where Me and Mp are the transmitted moment and the full fixing moment of the beam, respectively. Expressions pro­posed for the end plate thickness are based on regression analyses of data from extensive 3-dimensional finite ele­ment analysis. of the joint and contain all significant vari­ables associated with the connection. A value of= p 0,80 to 0,90 is suggested for the end plate joint although the connection is basically deemed to be semi-rigid 1•2•

The associated design equations are:

fJ = 0.0056W~-6ly)-03/ Dbeam 1.30Tw 0.26sl.58 (7a)

iJ.. = 1.0/ Ff.38 Fit0 (7b)

C = 1.40fJ!J..b2-03/AsR 0.36 (7c)

Tep = [C/t'Ml- p)]0·72 [pMp]u4 (7d)

where

S = Section Modulus of Beam

Fy 8 = Yield Stress of Bolt

b =Actual bolt distance from flange (usually

taken as 1.5")

AsR =Bolt Area per row

p = Connection Rigidity

M p = Plastic Moment Capacity of the Beam

e.. = End Rotation of a simply-supported beam

The average value of (Is is taken as 0.0015 radians cor­responding to the experimental M -responses of typical end plate connections.

184 JOURNAL OF STRUCTURAL ENGINEERING VOL. 31, N0.3, OCTOBER-DECEMBER 2004

TABLE I

WIDE FLANGE BEAM SHAPES SELECTED FOR STUDY

Light Medium

Engli sh Metric M p t M o2 Engli sh Metric

1 W 12 X 14 W310 x 21 52.2 72.5 W 12 X 65 W 310 X 97

2 W 10 X 15 W 250 X 22 48.0 66.7 W 21 X 50 W 530 X 74

3 W 12 X 19 W310 x 28 74.1 103 .6 W 14 X 68 W 360 X 101

~ W 14 X 22 W 360 X 33 99.3 137.9 W 12 X 79 W310x 118

5 W 10 X 33 W 250 X 49 116.4 161.7 W 21 X 57 W 530 X 85

6 W 12 X 30 W 310 X 45 129.0 179 .2 W 24 X 55 W 610 X 84

7 W 14 X 30 W 360 X 45 141.9 197.0 W21 X 62 W 530 X 92

8 W 16 X 31 W410 X 46 162.0 225.0 W 24 X 62 W 610 X 92

9 W 10 X 45 W 250 X 67 165.0 229.2 W 21 X 68 W 530 X 101

10 W 18 X 35 W 460 X 52 200.0 278.0 W24 X 68 W610 X 101

I I W 16 X 40 W 410 X 60 218.0 303.0 W 24 X 76 W610 X 1"13

12 W 18 X 40 W 460 X 60 235.0 327 .0 W 24 X 84 W610 x 125

13 W 12 X 53 W 310 X 79 233.7 324.6 W 27 X 84 W690 X 125

14 W 16 X 50 W410 X 74 275.0 383.0 W 24 X 94 W610 X 140

15 W 21 X 44 W 530 X 66 286.0 397.2 W 27 X 94 W 690 X 140

1 -· for 36 ksi steel 2 - for 50 ksi steel M p is in kip-feet units

(1 ksi = 6.89 MPa and I kip-foot= 1.34 kN-m)

END PLATE DESIGNS

Heavy

M p t M p2 English Metric M"t Mp 2

290.4 403.3 W 30 X 99 W760 x 147 936.0 1300.0

330.0 458.0 W 30 X 108 W 760 X 161 1040.0 1440.0

345.0 479.0 W30 x 116 W760 x 173 1130.0 1580.0

357.0 493.3 W 33 X 118 W 840s x 176 1250.0 1736 .1

387.0 538.0 W 33 X 130 W 840 X 193 1400.0 1950.0

402.0 558 .0 W 36 X 135 W920 x 201 1530.0 2125.0

432.0 600.0 W 33 X 141 W840x210 1540.0 2140.0

459.0 638.0 W 36 X 150 W 920 X 223 1740.0 2420.0

480.0 667.0 W 36 X 160 W 920 X 238 1870.0 2600.0

528.0 733.3 W 36 X 170 W 920 X 253 2000.0 2780.0

600.0 833.3 W 36 X J94- W 920 X 289 2300.0 3200.0

672.0 933.0 W 33 X 201 W 840 X 299 2320.0 3220.0

732.0 1016.2 W 36 X 230 W 920 X 342 2830.0 3930.0

762.0 1058.0 W 36 X 280 W 920 X 417 3510.0 4880.0

834.0 1160.0 W 36 X 300 W 920 X 446 3780.0 5250.0

6. Wherever a T-stub idealization is adopted, the values of the parameters 'a' and 'b' were taken as a = 1" (25mm) and b = 1.25" (32mrn).

7. The end plate width Wep was taken as equal to W F + 1.0" wherever required.

8. For Plastic Design 2, both thick and thin plate thick­nesses were computed but only the smaller value was used for comparison purposes.

9. For designs based on M-11 response, two sets of values of 'p ' and ·e; were used; namely, p = 0.8 and 0.9 and 11s = 0.0015 and 0.0020 radians.

The seven design procedures outlined in the previous sec­tions were used to design a total of 720 bolted end plate connections. Forty five different beam sections (!-shapes) in three categories - light, medium and heavy - were employed in the designs. Fifteen beams comprised each category. The shapes were selected from the AISC Manual 1

on the basis of least weight per linear foot, low area of cross section, high plastic modulus and thereby high plas­tic moment capacity. Table I shows the selected sections and the associated data, which includes the plastic moment capacity M p of the shape for both 36 ksi and 50 ksi steels. Metric equivalents of the shapes were also shown in the table (depth in millimeters and weight in kg/m). The end plate thickness was selected as the sole basis of com­parison of the various methods. Also, to maintain unifor­mity in design and comparison, the following criteria were adopted.

All designs were accomplished by special computer pro­grams written in Fottran6•

7 along with specific data files needed for each design method.

1. All joints (except in elastic cases) were designed to the full plastic momentcapacity.ofthe beam section. Elas­tic designs were based on the elastic resisting moment of the beam section MR = 0.66FrSx, where Sx is the section modulus.

2. Only A-325 bolts off (19 mm) diameter were used in all designs.

3 . Both 36 ksi (248 MPa) and 50ksi (345 MPa) steel beams were considered.

4 . All connections were designed with 4 bolts in the ten­sion region,

5. Yield Stresses of beam and end plate were assumed identical in all cases.

RESULTS AND OBSERVATIONS

Figures 5 to 12 show the variation in the end plate thick­ness with beam moment for the different design methods examined. Figures 7-9 relate to plastic designs with 36 ksi (248 MPa) steel while Figs. 10-12 relate to those with 50 ksi (345 MPa) steel. Percentage variation in end plate thickness between 36 and 50 ksi steels for each category is shown in Table 2.

The following observations are made on the basis of the results obtained:

I . As expected, the elastic designs proved to be the most conservative of all. Plate thicknesses ranged from 1 .5" (38 mm) to more than 10" (254 mm). Use of steel with higher yield strength only resulted in a larger plate

JOURNAL OF STRUCTURAL ENGINEERING VOL. 31, N0.3, OCTOBER-DECEMBER 2004 185

.E ui U) Q) c:

""' " £ "' 1ii

0:: c.

I-.

10

8

6

4

2

0

1 a Light 1b Medium 1c Heavy

1" = 25.4 mm, 1 kip-fl = 1.34 kN-m

BOO 1000 1200 14001600 1800 2000 MR Resisting moment-kip.!\

FIG. 5. MOMENT vs PLATE THICKNESS CURVES - ELASTIC DESIGNS 36 ksi STEEL

10

8 -~ ui

1 d Light VJ 6 Q)

c: 1e Medium "" " 11 Heavy £ Q) 4 1ii 0::

c. 2 I-.

0 ~~~~~-----1_"_=~2_5_.4 __ m_m~·~1~k~ip_~ __ =_1~.3-4~k_N_-~m~ 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

MR Resisting moment-kip.ft

FIG. 6. MOMENT vs PLATE THICKNESS CURVES -ELASTIC DESIGNS 50 ksi STEEL

24 !1 ughl 2.2

2 Plastic design - 1 2 J Plastic diisign - 2

1.9 ~ ~~:~ ~::::~ =! -~

1_6

6 Limit slate design

~ ~ ~=: ::::~:: ~:) ~ 1.4

~ 1.2

"* 1 0: ,_~ 0.8

0.6

0.4

0.2

(a) O,= 0.0.0015 p = 0,6 (b) o, = 0 ,0 ,0020 p = 0.9

1"=25.4mm, 1 kip-ft =1.34kN-m

20 40 60 60 100 120 140 160 160 200 220 240 260 280 Mp Beam plastic moment capacily-kip.ft

FJG. 7. MOMENT vs PLATE THICKNESS CURVES- PLASTIC DESIGNS 36 ksi STEEL

thickness since the designs use M R, the elastic resist­ing moment, which is a function of Fr.

2. Plastic and Limit State designs gave reasonable esti­mates of the plate thickness in all design categories.

3. Of the four plastic design methods -considered, orily method 2 showed noticeable sensitivity to the use of higher strength 'steel. Plastic method 4 and the limit State· designs showed some sensitivity only in the "Heavy" category.

4. The AISC procedure and the Limit State method both gave almost identical values of plate thickness.

5. A major drawback of the Limit State procedure is noted in the limitation imposed on the bolt forces. Except for a few connections in the "Light" category, all others indicated possible joint failure by excessive bolt forces while transmitting the full plastic moment of the beam. The method also suffers from the restric­tion of only 4 bolts in the tension region where heavier beams require more than 4 bolts.

6. Designs based on the moment-rotation response showed remarkable inconsistency in all categories of design. The pattern of results can be attributed to the semi-empirical exponential terms along with the influence of assumed values of the variables ()5

Medium 1.2

.£ ui ~ -6 0.8 £ 2 £ 0.6

:;:-,_ 0.4

0.2

200 400

2 Plastic design - 1 3 Plastic design- 2 4 Plaslic design - 3 5 Plastic design - 4 6 Limit state design 7 M-9 Response (a)

_8 M-e Response (b)

(a) 05 = 0.0.0015 p = 0.8 (bl a,= o.o.oo2o p = o g

1" = 25,4 mm,1 kip·ft % 1.34 kN-m

600 800

Mp Beam plastic moment capacity-kip.ft

FIG. 8. MOMENT vs PLATE THICKNESS CURVES- PLASTIC DESIGNS 36 ksi STEEL

2.2 Heavy

:5 1.8 .

~- 1.6 Q)

-IS 1.4

;s 1.2 2 £ 1

,_i:- 0.8

0.6

0,4

2 Plastic design- 1 3 Piastre design - 2 4 Plastic design- 3 5 Plastic design - 4 6 Umilsta\e design 7 M-e Response {a) 8 M-0 Response (b)

(a) a, = 0.0.0015 p = 0.8 (b) a,= o.o.oo2o p = o.9

1" = 25.4 mm, 1 kip-ft = 1.34 kN-m

0~~-~ 1~ 1- =~ = = ~ MP Beam plastic moment capacity-kip. ft

FIG. 9. MOMENT vs PLATE THICKNESS CURVES - PLASTIC DESIGNS 36 ksi STEEL

186 JOURNAL OF STRUCTURAL ENGINEERING VOL. 31, N0.3, OCTOBER-DECEMBER 2004

Mp Beam plastic moment capacity-kip. It

FIG. 10. MOMENT vs PLATE THICKNESS CURVES- PLASTIC DESIGNS 50 ksi STEEL

1.6 Medium

1.4

.s 1.2

ui <f) QJ c: "" (,) 0.8 £ Plastic design - 1

J!! Plastic design- 2

"' 0.6 Plaslic design- 3 0: Plastic design -4

Q.

0.4 Limit slate design

f--w M-9 Response (a) M-9 Response (b}

0.2 (a) e, = 0.0.0015 p = O.B (b) e.= o.o.oozo p = 0,9

1" t <5.4"""' 1 kl ·h= 1.34 kN-m

0 200 400 600 600 1000

Mp Beam plastic moment capacity-kip. It

FTG. 11. MOMENT vs PLATE THICKNESS CURVES -PLASTIC DESIGNS 50 ksi STEEL

2.2

2

.s 1.8 ui 1.6 <I) QJ c: 1.4 "" (,)

;s 1.2 J!! "'

0:0. 0.8 f--w 0.6

0.4

0.2

0 0

Heavy

1000

Plastic design- 1 Plastic design - 2 Plastic design - 3 P/aslic design - 4 limit state design M-e Response (a)

B M-1! Response (b) (a) a,= o.o.oo15 p = O.B (bJ e, = o o.oo2o p = o.s

1" = 25.~ """· 1 II• 1.3HN-m

Mp Beam plastic moment capacity-kip.ft

FIG. 12. MOMENT vs PLATE THICKNESS CURVES- PLASTIC DESIGNS 50 ksi STEEL

TABLE2

PERCENTAGE VARIATION OF PLATE THICKNESS BETWEEN 36 AND 50 ksi STEELS

PlastJc Des1gns L1m11 M tJ

Method Elastic State Response Category Design (1) (2) (3) (4) Design Design,_

Light +15.5 0 +0.9 0 -0.1 0 +33.1 Medium +16.2 0 +0.3 0 0 0 +32.9 Heavy +16.8 0 +0.1 0 -0.6 -0.6 +3!.3

*(for l)s = 0.0020 and p = 0.9)

and p. The only advantage of this method is the facil­ity to design a joint with greater control on the joint rotation, which is important in some frames. The designs based on M - () respon'se also showed an increase in the end plate thickness for each grade of steel as Bs and p were changed from 0.0015 and 0.8 to 0.0020 and 0.9, respectively. While the effect of other parameters remains to be verified, connection rigidity 'p' seems to have some influence on the plate thickness. Some of the design procedures gave a lower value of the end plate thickness for a heavier beam with larger plastic moment capacity. This pattern is observed in Plastic Designs 1 and 2 and designs based on M - () response. This is ascribed to the presence of geomet­rical properties of the section in the design process whose variation between various shapes is not a func­tion. of M p but a physical property of the shape itself.

CONCILUSIONS

The application of seven different design methods to bolted end plate steel beam-to-column connections is described. Over 700 connections employing 45 different beam shapes and two types of steel were designed with the help of spe­cial computer programs and compared on the basis of the obtained end plate thickness. Results attest to the distinct characteristics of each method and the complexity of the connection.

The study is rather extensive if not exhaustive; but some useful conclusions can be drawn from practical design per­spectives. The T-stub idealization of the joint involving plastification and/or collapse mechanisms appears to be an effective means of addressing joint behavior. From con­sistency standpoints, plastic designs 2 and 3, which gave reasonable estimates of the plate thickness, seem to be the most economical and acceptable for the purpose of rou­tine designs. A more comprehensive design study will help generalize the inferences made here.

Acknowledgements

The author wishes to express his appreciation to Prof. Keith Faherty, Chairman, Civil Engineering, MU and to Prof. N. Yoganandan, Chairman, Biomedical Engineering and Neurosurgery, MCW and staff for their encouragement and advice during the course of this study. Computer facilities provided by the Dept. of Civil Engineering at Marquette University are also gratefully acknowledged.

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