Design of Pinned Column Base Plate (AUS)

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STEEL CONSTRUCTIONJOURNAL OF THE AUSTRALIAN STEEL INSTITUTE

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Design of Pinned ColumnBase Plates

AUSTRALIAN STEEL INSTITUTE

VOLUME 36 NUMBER 2 SEPTEMBER 2002

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1 STEEL CONSTRUCTION VOLUME 36 NUMBER 2 SEPT 2002

STEEL CONSTRUCTION -- EDITORIAL

Editor: Peter Kneen

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Design of Pinned Column Base Plates

Contents

This paper deals with the design of pinned base plates. The design actions considered areaxial compression, axial tension, shear force and their combinations. The base plate isassumed to be essentially statically loaded, andadditional considerationsmay be requiredin the case of dynamic loads or in fatigue applications.

1. INTRODUCTION 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1. Design actions in accordance with AS 4100 1. . . . . . . . . . . . . . . . . . . . . . . . . . .

2. NOTATION 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3. BASE PLATE COMPONENTS 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4. AXIAL COMPRESSION 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1. INTRODUCTION 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.2. BASE PLATE DESIGN -- LITERATURE REVIEW 4. . . . . . . . . . . . . . . . . . . .4.3. RECOMMENDED MODEL 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5. AXIAL TENSION 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1. INTRODUCTION 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2. BASE PLATE DESIGN -- LITERATURE REVIEW 12. . . . . . . . . . . . . . . . . . . .5.3. DESIGN OF ANCHOR BOLTS -- LITERATURE REVIEW 17. . . . . . . . . . . . .5.4. RECOMMENDED MODEL 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6. SHEAR 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.1. INTRODUCTION 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2. TRANSFER OF SHEAR BY FRICTION

OR BY RECESSING THE BASE PLATE INTO THE CONCRETE --LITERATURE REVIEW 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3. TRANSFER OF SHEAR BY A SHEARKEY-- LITERATURE REVIEW 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4. TRANSFER OF SHEAR BY THE ANCHOR BOLTS --LITERATURE REVIEW 31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.5. RECOMMENDED MODEL 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7. BASE PLATE AND ANCHOR BOLTS DETAILING 36. . . . . . . . . . . . . . . . . . . . . .8. ACKNOWLEDGEMENTS 38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9. REFERENCES 38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10. APPENDIX A -- Derivation of Design and Check Expressions

for Steel Base Plates Subject to Axial Compression 40. . . . . . . . . . . . . . . . . . . . . . . .11. APPENDIX B-- Derivation of Design and Check Expressions

for Steel Base Plates Subject to Axial Tension 46. . . . . . . . . . . . . . . . . . . . . . . . . . . .12. APPENDIX C -- Determination of Embedment Lengths and Edge Distances 49. . . .13. APPENDIX D -- Design Capacities of Equal Leg Fillet Welds 53. . . . . . . . . . . . . . . .14. APPENDIX E -- Design of Bolts under Tension and Shear 53. . . . . . . . . . . . . . . . . . .


Design of Pinned Column Base Plates

Gianluca RanziSchool of Civil and Environmental Engineering

The University of New South Wales

Peter KneenNational Manager TechnologyAustralian Steel Institute

1. INTRODUCTION

This paper deals with the design of pinned base plates.The design actions considered are axial compression,axial tension, shear force and their combinations asshown in Fig. 1. The base plate is assumed to beessentially statically loaded, and additionalconsiderations may be required in the case of dynamicloads or in fatigue applications.

N*t

N*c

V*x

N*t

N*c

V*y

Figure 1 Column Design Actions:Axial and Shear Loads along minorand major axes (Ref. [26])

Firstly the requirements of AS 4100 Steel Structures[11] in the calculation of the design actions forconnections are outlined. Then for each design actionavailable design guidelines and/or models are brieflypresented in a chronological manner to provide anoverview on how these have improved/changed overtime. Attention has been given to try to ensure that theassumptions and/or limitations of eachmodel presentedare always clearly stated.Among thesemodels, themostrepresentative ones in the opinion of the authors are thenrecommended for design purposes. It is not intended tosuggest that models, other than those recommended,may not give adequate capacities.The design of concrete elements is outside the scope ofthe present paper. Nevertheless some designconsiderations regarding the concrete elements stillneed to be addressed, i.e. bolts edge distances, boltsembedment lengths, concrete strength etc., andtherefore it is necessary to ensure that such designassumptions/considerations are included in the finaldesign of the concrete elements/structure.

1.1. Design actions in accordance with AS 4100

Pinned type column base plates may be subject to thefollowing design actions, as shown in Fig. 1:

an axial force, N*, either tension or compression;

a shear force, V* (usually acting in the directionof either principal axis or both).

Clause 9.1.4 of AS 4100 [11], which considersminimum design actions, does not specifically mentionminimum design actions for column base plates butdoes require that:

connections at the ends of tension or compressionmembers be designed for a minimum force of 0.3times the member design capacity;connections to beams in simple construction bedesigned for a minimum shear force equal to thelesser of 0.15 times the member design shearcapacity and 40 kN.

It is considered inappropriate for these provisions to beapplied to column base plates, since the design ofcolumns is usually governed by a combinations of axialloads and bending moments at other locations.

2. NOTATION

The following notation is used in this work. Othersymbols which are defined within diagrams may not belisted below. Generally speaking, the symbols will bedefined when first used.

ab = distance from centre of bolt hole to inside faceof flange

ae = minimum concrete edge distance (side cover)A1 = bearing area which varies depending upon the

assumed pressure distribution between the baseplate and the grout/concrete

A(i)1 = bearing area at the i--th iteration inMurray--Stockwell Model

A2 = supplementary area which is the largest area ofthe supporting concrete surface that isgeometrically similar to and concentric to A1

AH= assumed bearing area (in the case ofH--shapedsections it is a H--shaped area) in Murray--Stockwell Model

A(i)H = assumed bearing AH at the i--th iteration inMurray--Stockwell Model

Ai = base plate areaApsk = projected area over the concrete edge

ignoring the shear key areaAps = effective projected area of concrete under

uplift


Aps.1 = effective projected area of isolated anchorbolt (no overlapping of failure cones)

Aps.2 = effective projected area of 2 anchor boltswith overlapping of their failure cones

Aps.4 = effective projected area of 4 anchor boltswith overlapping of their failure cones. In thiscase each failure cone overlaps with all other 3failure cones

As = tensile stress area in accordance with AS1275[9]

Ask = area of the shear keybc = width of the column section (RHS and SHS)bfc = width of the column section (H--shaped

sections and channels)bfc1 = width of the column flange ignoring web

thicknessbi = width of base platebs = depth of shear keybt =distance fromfaceofweb to anchorbolt locationdc = column depthdc1 = clear depth between flanges (column depth

ignoring thicknesses of flanges)df = nominal anchor bolt diameterdh = diameter of bolt holedi = length of base plated0 = outside diameter of CHS

fc = characteristic compressive cylinder strength ofconcrete at 28 days

f*p = uniform design pressure at the interface of thebase plate and grout/concrete

fuf = minimum tensile strength of boltfuw = nominal tensile strength of weld metalfyi = yield stress of the base plate used in design

fys = yield stress of shear key used in design

kr = reduction factor to account for length of weldedlap connection

Ld = minimum embedment length of anchor boltLh = hook length of anchor boltLs = length of shear keyLw = total length of fillet weldmp = plastic moment capacity of the base plate per

unit widthms = nominal section moment capacity of the base

plate per unit widthmsk = nominal section moment capacity per unit

width of shear key

m*c = design moment per unit width due to N*cm*sk = design moment to be carried by the shear key

per unit width

m*t = design moment per unit width due to N*t

nb = number of anchor bolts part of the base plateconnection

N*c = column design axial compression load

N*b = N*tnb = design axial tension load carried byone bolt

Ndes.c = design capacity of the base plate connectionsubject to axial compression

Ndes.t = design capacity of the base plate connectionsubject to axial tension

N*p = prying action

N*t = design axial tension load of the columnNtf = nominal tensile capacity of a bolt in tension

N*0 = portion of N*c acting over the column footprintsp = bolt pitch

Si = plastic section modulus per unit width of platetc = thickness of column sectionti = base plate thicknesstg = grout thickness

ts = thickness of shear keytt = design throat thickness of fillet weldtw = thickness of column webvdes = vw = design capacity of theweld connecting

the base plate to the column per unit length

v*h and v*v= components of the loading carried by theweld between column and base plate in onehorizontal direction in the plane of the base plateand in the vertical direction respectively per unitlength

v*w = design action on fillet weld per unit lengthVdes = design shear capacity of the base plate

connection

V*s = design shear force to be transferred by meansof the shear key

Wi and We = internal and external work = capacity factor

f(i)b = maximum bearing strength of the concrete atthe i--th iteration in Murray--Stockwell Model

fb = maximum bearing capacity of the concretebased on a certain bearing area A1

Nc = design axial capacity of the concretefoundation

Nc.lat = lateral bursting capacity of the concreteNcc = design pull--out capacity of the concrete

foundationNs = design axial capacity of the steel base plateNt = axial tension capacity of the base plateNtb = design capacity of the anchor bolt group

under tensionNth = tensile capacity of a hooked barNw= design axial capacity of the weld connecting

the base plate to the column section


vw = design capacity of the fillet weld per unitlength

Vf = design shear capacity of the base platetransferred by means of friction

Vs = design shear capacity of the shear keyVs.c = concrete bearing capacity of the shear keyVs.cc = pull--out capacity of the concreteVs.b = shear capacity of the shear key based on its

section moment capacityVs.w = shear capacity of the weld between the

shear key and the base plateVw= design shear capacity of the weld connecting

the base plate to the column = ratio depth and width of column = coefficient of friction

3. BASE PLATE COMPONENTS

Typical base plates considered in this paper are formedby one unstiffened plate only as shown in Fig. 3. Forhighly loaded columns or larger structures other baseplate solutions or more elaborate anchor bolt systemsmight be required. Guidelines for the design anddetailing of more complex base plates can be found in[4], [13], [14], [16] and [34].Two types of anchor bolts are usually used, which arecast--in--place or drilled--in bolts. The former are placedbefore the placing of the concrete or while the concreteis still fresh while the latter are inserted after theconcrete has fully hardened.Different types of cast--in--place anchors are shown in inFig. 2. These include anchor bolts with a head, threadedrodswith nut, threaded rodswith a platewasher, hookedbars or U--bolts. These are suitable for small to mediumsize structures considering anchor bolts up to 30 mm indiameter.

(a) Hooked Bar (b) Bolt withhead

(c) ThreadedRod with Nut

(d) Threaded rodwith plate washer

(e) U--Bolt

Filletwelds

Square plate

Figure 2 Common Forms of Holding DownBolts (Ref. [26])

There is a large variety of drilled--in anchors available,many of which are proprietary bolts whose installationand design is governed by manufacturersspecifications. References [2], [15], [17], [31] and [33]contain information on these types of anchors.This paper deals only with cast--in--place anchors, andspecifically hooked bars, anchor bolts with a head andthreaded rodswith a nut/washer/plate.Grade 4.6 anchorbolts are recommended to be utilised in base plateapplications.

sp

sg

Figure 3 Typical unstiffened base plate(Ref. [26])

4. AXIAL COMPRESSION

4.1. INTRODUCTION

The literature review presented covers only modelsregarding the design of the actual steel plate as theanchor bolts do not contribute to the strength of theconnection under this loading condition. Unless specialconfinement reinforcement is provided the maximumbearing strength of the concrete fb is calculated inaccordance with Clause 12.3 of AS 3600 [10] asfollows:

fb = min0.85fc A2A1 , 2fc (1)where:

= 0.6fb = maximum bearing capacity of the concrete

based on a certain bearing area A1fc = characteristic compressive cylinder strength of

concrete at 28 daysA1 = bearing area which varies depending upon the

assumed pressure distribution between the baseplate and the grout/concrete

A2 = supplementary area which is the largest area ofthe supporting concrete surface that isgeometrically similar to and concentric to A1


4.2. BASE PLATE DESIGN -- LITERATUREREVIEW

Themain designmodels available in literature differ fortheir assumptions adopted regarding the pressuredistribution at the interface between the base plate andthe grout/concrete and for the relative sizes of the baseplate and the connected column. For example, the firstmodel presented, here referred to as the CantileverModel, is adequate for base plates whose dimensions(di bi ) are much greater than those of the column(dc bfc ), while other models, such as Fling andMurray--Stockwell Models, deal with base plates withsimilar dimensions to the ones of the connected column.

4.2.1. Cantilever Model

Historically the cantilever model was the first availableapproach for the design of base plates. It is well suitedfor the design of large base plates with the dimensionsof the base plate (di bi)muchgreater than those of thecolumn (dc bfc). It has been present in the AISC(US)Manuals over several editions. Its formulation issuitable for the base plate design of only H--shapedcolumns. [5]

dc 0.95dcdi

bibfc

0.8bfca2 a2

a1

a1

(a) Critical sections and assumed loaded area

N*cbidi

Critical sectionin bending am

ti

(b) Deflection of the cantilevered plate

N*cbidi

ti

N*c

(c) Assumed bearing pressure

Figure 4 Cantilever Model (Ref. [26])

This model assumes that, in the case of a H--shapedcolumn, the axial load applied by the column isconcentrated over an area of 0.95dc 0.80bfc whichcorresponds to the shaded area of Fig. 4(a). This causesthe base plate to bend as a cantilevered plate about theedges of such area as shown in Fig. 4(b). The pressureat the underside of the base plate is assumed to beuniformly distributed, as shown in Fig. 4(c), thereforeleading to a conservative design for large base plates.

a1

a2Dashed lines indicateyield lines

a1

a2

Figure 5 Cantilever Model -- Collapsemechanisms

Each of the two collapsemechanisms considered by thismodel assumes two yield lines to form at a distance a1and a2 from the edge of the plate respectively as shownin Fig. 5. Comparing the two collapse mechanisms andaccording to the rules of yield line theory the governingdesign capacity is based on the longest cantilever lengtham, being the maximum of the two cantilevered lengthsa1 and a2 shown in Fig. 4(a).

The design moment m*c and the design capacity of theplate ms are calculated per unit width in accordancewith AS 4100 [11] as:

m*c = N*c

bidia2m2

(2)

ms = fyiSi =0.9fyi t2i

4(3)

where:

N*c = column design axial compression load

m*c = design moment per unit width due to N*cms=plate nominal sectionmoment capacity per unit

widthfyi = yield stress of the base plate used in design

Si = plastic section modulus per unit width of plateam = max(a1, a2)a1 and a2 = cantilevered plate lengthsti, di and bi = thickness, length and width of base

plateand ensuring that the plastic section modulus of thecantilevered plate Si is able to transfer the axialcompression load N*c to the supporting material(verified per unit width of plate):

m*c = N*c

bidia2m2

0.9fyi t2i

4= ms (4)

yields a maximum design axial force of:


N*c 0.9fyi t2i bidi

2 a2m(5)

or equivalently requires a minimum plate thickness of:

ti am2N*c

0.9fyi bidi (6)

Provisions on how to extend this approach for channelsand hollow sections columns have been provided in[21], [26] and [36].The dimensions of the loaded areas and of thecantilevered lengths a1 and a2 for channels and hollowsections are shown in Figs. 6, 7 and 8 and their valuesare summarised in Table 1 based on therecommendations in [21], [26] and [36]. The values inTable 1 assume that the column iswelded concentricallyto the base plate.

Table 1 Cantilever Model -- Cantilevered platelengths a1 and a2 (refer to Figs. 4, 6, 7and 8 for the definition of the notation)

SECTION a1 a2H--shapedsection [21]

di 0.95dc2

bi 0.80bfc2

Channel [26] di 0.95dc2

bi 0.80bfc2

SHS andRHS [36]

di dc + ti2

bi bc + ti2

SHS andRHS [21]

di 0.95dc2

bi 0.95bc2

CHS [21] di 0.80do2

bi 0.80do2

a20.8bfc

a2

a1

a1

0.95dc

bibfc

dcdi

Figure 6 Cantilevered plate lengths -- Channels(Ref. [26])

0.95dc

a1

a1

a2a20.95bfc

dcdi

bi

bc

Figure 7 Cantilevered plate lengths -- RHS andSHS (Ref. [26])

a20.8do

0.8do

a1

a1

a2

dodi

bi

Figure 8 Cantilevered plate lengths -- CHS(Ref. [26])

Parker in [37] notes how other possible yield linepatterns could be investigated for hollow sections suchas the ones shown in Fig. 9. Nevertheless in [36] herecommends to investigate collapse mechanismssimilar to the ones considered by the Cantilever Modelwith values of a1 and a2 as shown in Table 1. In [36] healso recommends to specify plate thicknesses not lessthan 0.2 times the maximum cantilever length in orderto limit the deflection of the plate.Applying this model to base plates with similardimensions to the ones of connected columnwould leadto inadequate design as the capacity of the base platewould be overestimated. Utilizing equations (5) and (6)the capacity of the base plate would increase and theplate thickness ti would decrease while decreasing thecantilevered plate length am. Other design models needto be adopted in these instances.

a2

0.95dc

a1

a1

a2

0.95bc

dcdi

bibc Dashed linesindicate yield

lines


bi

dido

0.8do

0.8do

a1

a1

a2 a2

Figure 9 Possible yield line pattern (Ref. [37])

4.2.2. Fling Model

Fling, in [25], presents adesignmodel applicable tobaseplates with similar dimensions to the ones of theconnected columnand reviews the design philosophyofthe Cantilever Model. Only H--shaped columns areconsidered in this model.He recommends to apply both a strength and aserviceability criteria to the design of base plates.Regarding the Cantilever Method, which is based on astrength criteria, he recommends to apply also aserviceability check by limiting the deflection of thecantilevered plate. He argues that, while increasing thesize of the plate, deflections of the cantilevered platewould increase reducing the ability of the mostdeflected parts of the plate to transfer the assumeduniform loading to the supporting material. Thus theload would re--distribute to the least deflected portionsof the plate which may overstress the underlyingsupport. His proposed deflection limit intends toprevent such overstressing. He also notes that such limitshould vary depending upon the deformability of thesupportingmaterial. Fling suggests 0.01 in. (0.254mm)to be a reasonable deflection limit to be imposed formost bearing plates, even if he clearly states that it isbeyond the scope of his paper to specify deflectionlimits applicable to various supporting materials. [25]Regarding the designmodel for base plates with similardimensions to the ones of the connected column herecommends to apply the following strength andserviceability checks.The strength check is based on the yield line theory andthe assumed yield line pattern is shown in Fig. 10. Theprocedure is derived for a base plate with width andlength equal to the columns width and depth (thereforebi and di equal bfc and dc respectively).The support conditions assumed for the plate are fixedalong the web, simply supported along the flanges andfree on the edge opposite to the web.

Dashed linesindicate yield lines

bes

= tan

d1bes

Figure 10 Fling Model -- Yield Line Pattern(Ref. [25])

The internal and external work produced under loadingare calculated as follows:

Wi = 1bes (2d1 + 4bes)mp+1

bes 4besmp (7)

We = 2f*p(d1 2bes)bes 12+43 f

*pb2es (8)

where:mp = plastic moment capacity of the baseplate per

unit width

f*p = uniform design pressure at the interface of thebase plate and grout/concrete which is assumedto be equal to the maximum bearing strength ofthe concrete fb

Wi and We = internal and external work

d1, and bes = as defined in Fig. 10Fling introduces the following parameter to simplifythe notation:

= d1bes

(9)

Equating the internal and external work yields:

mp(2+ 4+ 4) = f*pb2es( 23 ) (10)

The value of which maximises the required momentcapacity of the base plate is as follows:

= 34+142 12 (11)

which is obtained bydifferentiating for the expressionof the plastic moment derived from equation (10).The requiredbaseplate thickness ti is then calculated as:[25]

ti 0.43bfcf*p

0.9fyi (1 2)= 0.43bfc

fb0.9fyi(1 2) (12)


where:bfc = column flange width

Equation (12) includes a safety factorof 1 and theplasticmoment capacity is increased by 10% to allow for lackof full plastic moment at the corners (as recommendedin [25]).This method assumes simultaneous crushing of theconcrete foundation and yielding of the steel base plateas the pressure at the interface of the base plate andgrout/concrete is assumed to be equal to the maximumbearing strength of the concrete fb.The serviceability check verifies the adequacy of themaximum deflection of the base plate calculated fromelastic theory and assumes the same support conditionsas adopted in the strength check. The maximumdeflection occurs at the middle of the free edge of theplate (opposite to the web).

4.2.3. Murray--Stockwell Model

In 1975 Stockwell presents a design model for lightlyloaded base plates with base plate dimensions similar tothe columns width and depth. His formulation issuitable to onlyH--shaped columns. He defines a lightlyloaded base plate as onewherein the required base platearea is approximately equal to the column flange widthtimes its depth. [40]The novelty of this model is to assume that the pressuredistribution under the base plate is not uniform but isconfined to an area in the immediate vicinity of thecolumn profile and is approximated by aH--shaped areacharacterised by the dimension a3 as shown in Fig. 11.This pressure distribution implies that in relatively thinbase plates uplift might occur at the free edge.A few years later Murray carried out a finite elementstudy to verify the possibility introduced by Stockwellof uplift at the free edge. He established, from bothmodelling and testing, that thin base plates lift off thesubgrade during loading and therefore the assumptionofuniformstressdistribution at the interface is not valid.He also concludes that experimental evidence does notsupport the need for the serviceability check introducedby Fling. [32]Murray further expanded Stockwells model to obtainthe model which is known today as theMurray--Stockwell Model [41] and refines thedefinition of lightly loaded base plates to be relativelyflexible plate approximately the same size as the outsidedimensions of the connected column. [32]According to Stockwell there is only a little differencebetween the procedures specified in Fling andMurray--Stockwell Models as he considers both to bevalid and logically derived. [41]

a3

di

bi

dc

bfc

a3 a3

a3

AH

Figure 11 Murray--Stockwell Model -- Assumedshape of pressure distribution.

The Murray--Stockwell Model assumes that thepressure acting over the H--shaped bearing area isuniform and equal to the maximum bearing capacity ofthe concrete fb. The values of AH and fb are notknown a priori and therefore an iterative procedure canbe implemented to evaluate their values. The value offb is not known a priori as it depends upon the valueof the bearing area A1which in this case is equal to AH.The area contained inside the column profile dc bfc isused as a first approximation for the bearing area AH inthe calculation of fb as shown in equation (13).

f(1)b = min0.85fc A2A(1)1

, 2fc (13)where:

f(1)b = maximum bearing strength of the concrete atthe first iteration

A(1)1 = bearing area at the first iteration equal todc bfc

The H--shaped bearing area AH is then calculated as thearea required to spread the applied load with a uniformpressure equal to f(1)b .

A(1)H =N*cf(1)

b

(14)

where:

A(1)H = assumedH--shapedbearing area AHat the firstiteration

If f(1)b is equal to the maximum possible concretebearing strength 2fc no further iterations are requiredand the value of the H--shaped bearing area hasconverged to A(1)H calculated with equation (14). In thecase f(1)b is less than 2fc, or equivalently if the ratioof A2A1 is smaller than (20.85)2 = 5.53, the value ofthe H--shaped bearing area can be further refined.

Successive values of f(i)b and A(i)H at the i--th iteration

can be calculated as follows:


f(i)b = min0.85fc A2A(i1)1

, 2fc (15)A(i)H =

N*cf(i)

b

(16)

where:

f(i)b = maximum bearing strength of the concrete atthe i--th iteration

A(i)1 = bearing area at the i--th iteration equal to A(i1)H

A(i)H = assumed H--shaped bearing AH at the i--thiteration

The value of AH can be further refined until thedifference between the values obtained from twosubsequent iterations canbeconsidered tobenegligible.The use of the iterative process allows to obtain thesmallest possible value of AH which yields thinner baseplate thicknesses. Ignoring to refine the value of AHwould simply lead to a more conservative plate design.The value of a3 is then obtained from equation (14)observing that AH can be expressed as (refer to Fig. 11):

AH = 2bfca3+ 2a3(dc 2a3)= 2bfca3+ 2dca3 4a23 (17)

where:a3 = cantilevered langthAH = assumed H--shaped bearing areadc and bfc = depth and width of column

and solving for a3 yields:

a3 = 14 (dc+ bfc) (dc + bfc)2 4AH (18)The plate is now designed in accordance with AS4100[11] as a cantilevered plate of length a3 supporting auniform pressure equal to the converged value of themaximum bearing strength of the concrete previouslycalculated:

m*c = fba232

= N*c

AH

a232

0.9 fyi t2i

4= ms

The maximum axial load is then calculated as:

N*c 0.9fyi t2iAH

2a23(19)

or equivalently theminimum required plate thickness tiis determined as:

ti a32N*c

0.9fyi AH (20)

The value of the cantilevered plate length a3 should bemeasured from the centre--line of the columns plateelements as shown in Fig. 11.[21]. Nevertheless in theformulation presented here, as also carried out in [32]and [21], the full flange thickness is included in thecalculation of the cantilevered plate length a3. This onlyleads to a slightly more conservative design.

The Stockwell--Murray Method is recommended byDeWolf in Refs [21] and [22] and introduced in theAISC(US) Manuals in 1986. [7][1] notes that there are cases where the value under thesquare root of equation (18) becomes negative. In suchcases other design models should be adopted.Ref. [21] extends the application of Murray--StockwellModel to channels and hollow section members asshown in Figs. 12, 13 and 14. For these sections thevalue of the bearing area A(1)1 (to be utilised in the firstiteration while calculating f(1)b and A

(1)H ) and the

expressions of the cantilevered length a3 and of theH--shaped area AH are summarised in Table 2. [21][26]The same iterative procedure, as outlined for H--shapedsections, can be adopted to refine the value of AH if thecalculated fb is less than 2fc.

a3

a3

a3

Figure 12 Murray--Stockwell Model:Assumed pressure distribution --Channels (Ref. [26])

a3

a3

a3 a3

Figure 13 Murray--Stockwell Model:Assumed pressure distribution -- RHSand SHS (Ref. [26])

a3d3

do

Figure 14 Murray--Stockwell Model:Assumed pressure distribution -- CHS(Ref. [26])


4.2.4. Thorntons Model

In [42] and [43] Thornton recommends that asatisfactory design of a base plate should be carried outcomplying with the requirements of the Cantilever,Fling (ignoring the serviceability check) andMurray--Stockwell Models.He derived a compact formulation for the designprocedure which includes all three models. Hisformulation is suitable for the design of only H--shapedcolumns.In [42] he also re--derives the collapse load based on thesame yield line pattern assumed by Fling in [25]. It isinteresting to note that while Fling applied the principleof virtual work Thornton based his results on theequilibrium equations [35]. Obviously the results areidentical. Note that Fling increased the required plateplastic moment by 10% to allow for lack of plasticmoment at the corners.The design expression proposed by Thornton in [43]and currently recommended in the AISC(US) Manual[5] is as follows:

ti = am2N*c

0.9fyibidi (21)

where:

am = max(a1, a2, a4)

= min1, 2 X1+ 1 X

a4 = 14 dcbfcN*0 = portion of N*c acting over the column footprint

=N*cbidi

bfcdc

X = 4bfcdc(dc+ bfc)2

N*cfbdibi

= 4a25fb

N*0 = 4a25fbN*c

dcbfcdibi

fb = min0.85fc A2dibi , 2fca5 = bfc+ dc

The concatenation of the three design models(Cantilever, Fling and Murray--Stockwell Models) isachieved in the calculation of am.The Cantilever Model is the governing criteria in thecase am equals either a1 or a2. In the case am is equal toa4 the FlingModel would be governing if equals 1 orMurray--Stockwell Model would be governing if isless than 1. The use of leads to the selection of thethinner plate obtained by using the Fling Model andMurray--Stockwell Model in order not to loose theeconomy in design of the latter model in the case oflightly loaded columns. Recalling the description ofMurray--Stockwell Model no refinement in thecalculation of AH is implemented in equation (21). It isinteresting to note how this approach provides a moremathematical definition of lightly loaded columnwherea column is said to be lightly loaded if its is less than1, or equivalently if its X is less than (45)2 = 0.64.The expression of the plate thickness of Fling Model,re--derived in [42], is simplified by Thornton in [43] inorder to reduce the complexity of the yield line solution.His simplification introduces an approximation in thevalue of a4 with an error of 0% (unconservative) and17.7% (conservative) for values of dcbfc ranging from3/4 to 3. The value of N*0 represents the portion of thetotal axial load N*c acting over the column footprint(dcbfc) under the assumption of uniform bearingpressure under thebaseplate.Murray--StockwellModelis concatenated in equation (21) to carry a design axialload equal to N*0 (not on N*c) over the assumedH--shapedbearing area inside the column footprint.

Table 2 Murray--Stockwell Model(refer to Figs. 4, 6, 7, 8, 11, 12, 13 and 14 for the definition of the notation)

SECTION A(1)1a3 AH

H--shaped section[21]

bfcdc (dc + bfc) (dc + bfc)2 4AH4

2bfca3 + 2a3(dc 2a3)

Channel [26] bfcdc (2bfc + dc) (2bfc + dc)2 8AH4

2bfca3 + (dc 2a3)a3

RHS SHS[21][26] bcdc

(dc + bc) (dc + bc)2 4AH4

dcbc (dc 2a3)(bc 2a3)= 2(dc + bc)a3 4a23

CHS [21][26] d20

4do d2o 4AH

2(d2o d23)4 = (doa3 a23 )where : d3 = do 2a3

4.2.5. Eurocode 3 Model

Clause 6.11 and Annex L of Eurocode 3 deal with thedesign of base plates. [23]

Requirement of the EC3 is to provide a base plateadequate to distribute the compression column loadover an assumed bearing area.The EC3 Model assumes an H--shaped bearing area asshown in Fig. 15(a). It requires that the pressure


assumed to be transferred at the interface baseplate/foundation should not exceed the bearing strengthof the joint fj.EC3 and the width of the bearing areashould not exceed c calculated as follows:

c = tifyi

3fj.EC3MO (22)

where:fj.EC3 = bearing strength of the joint

=jkjfcdj = 2/3 provided that the characteristic strength of

the grout is not less than 0.2 times thecharacteristic strength of the concrete foundationand the thickness of the grout is not greater than0.2 times the smallestwidth of the steel base plate

kj = concentration factor and may be taken as 1 or

otherwise asa1b1ab

a1 and b1 = dimensions of the effective area as

shown in Fig. 16

a1 = mina+ 2ar, 5a, a+ h, 5b1 ab1 = minb+ 2br, 5b, b+ h, 5a1 bfcd = design value of the concrete cylinder

compressive strength = fckcfck = characteristic concrete cylinder compressive

strength (in accordance with Eurocode 2)c = partial safety factor for concrete material

properties (in accordance with Eurocode 2)MO = 1.1 (boxed value from Table 1 of [23])

In the case of large or short projections the bearing areashould be calculated as shown in Figs. 15(b) and (c).[23][23] requires that the resistance moment mRd per unitlength of a yield line in the base plate should be taken as:

mRd =t2ifyi6MO (23)

No specific expression for the sizing of the steel baseplate are provided.

N*c

c

ccc

This area not includedin bearing area

Bearing area

(a) General Case

c c

c

(b) Short Projection (c) Large Projection

c c

c

c

Figure 15 Assumed bearing pressuredistributions specified in EC3 [23]

h Concretefoundation

Baseplate

Elevation

Plan

N*c

b1

a1

b

br

ar a

Figure 16 Column base layout [23]

4.3. RECOMMENDED MODEL

4.3.1. Design considerations

The recommended design model is a modified versionof the one proposed by Thornton in [43] and alsoadjusted to suit Australian Codes AS 3600 [10] and AS4100 [11]. The Thornton Model is currentlyrecommended by the AISC(US) Manual [5].Unfortunately the Thornton Model presented in [5],[42] and [43] is suitable for the design of H--shapedcolumns only. His formulation has been here modifiedfor H--shaped sections and extended for channels andhollows sections adopting a similar approach as in [43]which is outlined in Section 10.The modification to the Thornton Model introducedhere regards the manner in which Murray--StockwellModel is implemented. It is in the authors opinion thatthe calculation of AH and consequently of (refer to theliterature review for further details regarding thenotation) should be calculated based on N*c (total axialcompression load) and not N*0 (portion of the total loadN*c acting over the column footprint under theassumption of uniform bearing pressure). This intendsto ensure that Murray--Stockwell Model would governthe design only for base plates of similar dimensions tothe ones of the connected columns and for lightly loadedcolumns, which represents the actual base plate layoutfor which the model has been developed. The designwould then be based on only one assumed pressure


distribution. Calculating AH based on N*0 could lead tothe design situation for lightly loaded columns wherethe plate thickness is governed by Murray--StockwellModel even for plate dimensions larger than those of theconnected columns as the model would select thethinner plate between the ones calculated with FlingModel and with Murray--Stockwell Model.It is interesting to note how the assumed bearing area(H--shaped in the case of H--shaped column sections)could extend also beyond the footprint of the columnsection as shown in Fig. 17 in the case of H--shapedsections and hollow sections. [34] No specific designguidelines are provided in [34]. A similar pressureditribution is considered in the Eurocode 3 Model. [23]Nevertheless in the recommended model theapplication of Murray--Stockwell Model is alwayscarried out based on assumed bearing areas inside thecolumn footprint even for base plates with dimensionsgreater than the columns depth and width as otherbearing distributions need to be validated by testings.

aaa aaa

bb

bb

b bb b

Ineffective areas

Figure 17 Possible assumed bearing areas (Ref.[34])

4.3.2. Design criteria

There are two different design scenarios which areconsidered here:

the column is prepared for full contact inaccordance with Clause 14.4.4.2 of AS 4100 [11]and the axial compression may be assumed to betransferred by bearing. Design requirements are asfollows:

Ndes.c = [Nc ; Ns]min N*c (24)the end of the column is not prepared for fullcontact and the welds shall have sufficientstrength to carry the axial load. The designrequirements are as follows:

Ndes.c = [Nc ; Ns ; Nw]min N*c (25)where:

Ndes.c = design capacity of the base plate connectionsubject to axial compression

Nc = design axial capacity of the concretefoundation

Ns = design axial capacity of the steel base plateNw= design axial capacity of the weld connecting

the base plate to the column section

N*c = design axial compression load

4.3.3. Design Concrete Bearing Strength

The maximum bearing strength of the concrete fb isdetermined in accordance with Clause 12.3 of AS 3600[10].

fb = min0.85fc A2A1 , 2fc (26)where:

= 0.6A1 = bidi

The axial capacity of the concrete foundation Nc isthen obtained multiplying the maximum concretebearing strength fbby thebaseplate area Ai as follows:

Nc = fbAiIt is interesting to note from equation (26) thatincreasing the supplementary area A2 increases theconcrete confinement which yields larger designcapacities Nc. The loss of bearing area due to thepresence of the anchor bolt holes is normally ignored.[21]

4.3.4. Steel Base Plate Design

The base plate thickness required to resist a certaindesign axial compression N*c is calculated as follow:

ti = am2N*c

0.9fyi di bi (27)

where:

am = max(a1, a2, a4)

= min1, k X1+ 1 X

X = YN*ca1, a2, a4, k and Y are tabulated in Table 3.

When X is greater than 1, should be taken as 1.


Table 3 Values for the design and check specified by the recommended model for axial compression.

Section a1 a2 a4 k Y a5

H--shapedsections

di 0.95dc2

bi 0.80bfc2

dcbfc4 2

dibidcbfc

4N*cfba25 bfc + dcChannels di 0.95dc

2bi 0.80bfc

22dcbfc3

32

dibidcbfc

8N*cfba25 2bfc + dcRHS di 0.95dc

2bi 0.95bc

22dibi23

1.7 dibidcbfc

4N*cfba25 bc + dcSHS di 0.95bc

2bi 0.95bc

2bc3

32dibibc

4N*cfba25

2bc

CHS di 0.80d02

bi 0.80do2

d02 3

2 dibid0

4N*cfbd20

Thicknesses of base plates with dimensions similar tothose of the connected column section calculated withequation (27) might be quite thin, especially in the caseof lighlty loaded columns (where Murray--StockwellModel applies). It is therefore recommended to specifyplate thicknesses not less than 6mm thick for generalpurposes and not less than 10mm for industrialpurposes.Similarly a procedure to evaluate/check the capacity ofan existing plate is carried out as follows:

Ns =0.9fyi dibi t2i

2am2(28)

where:

= max1,1k22 k a4ti Y

20.9fyidibi

1am = maxa1, a2, a4 a1, a2, a4, k and Y are tabulated in Table 3.

This model is applicable to column sections as outlinedin Table 3 with the exception of H--shaped sections forwhich bfc2 is greater than dc as a different yield linepattern from those considered would occur.

4.3.5. Weld design at the column base

The design of the weld at the base of the column iscarried out in accordance with Clause 9.7.3.10 of AS4100. [11] The weld is designed as a fillet weld and itsdesign capacity Nw is calculated as follows:

Nw = vwLw = 0.6fuwttkrLw (29)where:

vw = design capacity of the fillet weld per unitlength

= 0.8 for all SP welds except longitudinal filletwelds on RHS/SHS with t < 3 mm (Table 3.4 ofAS 4100)0.7 for all longitudinal SP fillet on RHS/SHSwith t < 3 mm (Table 3.4 of AS 4100)

0.6 for all GP welds (Table 3.4 of AS 4100)fuw = nominal tensile strength of weld metal (Table

9.7.3.10(1) of AS 4100)tt = design throat thicknesskr = 1 (reduction factor to account for length of

welded lap connection)Lw = total length of fillet weld

Refer to Section 13. for tabulated values of the designcapacity of fillet welds vw.

5. AXIAL TENSION

5.1. INTRODUCTION

There is notmuchguidance available in literature for thedesign of unstiffened base plates subject to uplift.The literature presented here outlines the availableguidelines for the design of base plates and of anchorbolts. Twomodels presented here for the design of baseplates for hollowsections,which are the IWIMMModel(named here after its authors) and Packer--BirkemoeModel, were firstly derived for bolted connectionsbetween hollow sections. [37] and [36] suggest theirsuitability also for the design of base plates. Thesemodels include also guidelines for determining therequired number of anchor bolts. Such guidelines areincorporated in the literature review for the design of thesteel base plates as their application is only suitable forthe particular base plate model they refer to and as theydo not account for the interaction between the anchorbolts and the concrete foundation, which is dealt with inthe literature review on anchor bolts.

5.2. BASE PLATE DESIGN -- LITERATUREREVIEW

The models presented here differ for their assumptionsregarding the failure modes investigated. It isinteresting to note that the design guidelines currentlyavailable deal with a limited number of base platelayouts.For each model outlined here, the column sections andthe number of bolts considered by the model arespecified after the model name.


5.2.1. Murray Model(H--shaped sections with 2 bolts)

In [32] Murray presents a design procedure for baseplates of lightly loaded H--shaped columns with onlytwo anchor bolts subject to uplift. He also notes that tohis knowledge no studies have been published on thedesign of lightly loaded column base plate subjected touplift loading prior to his [32]. His design model isbased on yield line analysis and the yield line patternassumed is shown in Fig. 18.The expressions of the internal and externalwork can bewritten as follows:

Wi = mp 2bfc 2b + 1b 4 2bfc= mp

4b2 + 2b2fcbbfc

(30)

We = N*t

2sg22bfc

= N*t sg

2bfc(31)

where:

N*t = design tension axial load

sg and b = as defined in Fig. 18Equating the external and internal work the expressionof mp can be written as follows:

mp = N*t

2sgbfc

bbfc4b2 + 2b2fc

(32)

The value of b which maximises the required plateplastic capacity is obtaineddifferentiating equation (32)for b and is equal to:

b = bfc2

(33)

Thepresence of the flanges requires b to remain alwaysless or equal to dc2 and therefore the value of bwhichmaximises the plate plastic capacity varies dependingupon the column cross--sectional geometry as follows:

b = bfc2

forbfc2 dc

2(34)

b = dc2

forbfc2 dc

2(35)

Theminimumplate thicknesses required under a certainaxial load N*t are obtained substituting equations (34)and (35) into equation (32) as shown below:

ti N*tsg 20.9fyibfc4

for bfc2 dc

2(36)

ti N*tsgdc

0.9fyi(d2c + 2b2fc)

for bfc2 dc

2(37)

Murray carried out a finite element study to investigatethe adequacy of the proposed model. He also validatedthe reliability of equations (36) and (37) using limited

experimental results, which consisted of 4 base platespecimenswith dimensions ranging from8 x 6 (203.2x 152.4 mm) to 12 x 8 (304.8 x 203.2 mm) andthicknesses varying from 0.364 in. (9.246mm) to 0.377in. (9.576 mm).This method is included in the design modelrecommended by the current AISC(US) Manual [5].

bfc2

bfc2

dc2 dc2bb

b = 2 (bfc2) dc2

bfc2b b

sg2sg2

1 unit

Figure 18 Murray Model Assumed Yield LinePatterns (Ref. [32])

5.2.2. Tensile Cantilever Model(Generic Model)

Tensile Cantilever Method, as it is referred here,assumes that the tension in the anchor bolts spreads outto act over an effective width of plate (be) which isassumed to act as a cantilever in bending ignoring anystiffening action of the column flanges.

dh

11

bt bt

bt

be

Figure 19 Tensile Cantilever Model (Ref. [26])

It can be applied to generic base plate layouts.Nevertheless it provides conservative designs as itignores the two way action of the base plates.Reference [47] suggests a 45 degree angle of dispersionas shown in Fig. 19. This is based on considerations ofelastic plate theory as described in reference [13].The designmoment and the designmoment capacity arethen calculated as:

m*t = N*t

nbbt (38)

ms =0.9be t2i fyi

4(39)

where:

m*t = design moment per unit width due to N*t


nb = number of anchor boltsbt =distance fromfaceofweb to anchorbolt locationdh = diameter of the bolt holebe = 2bt+ dh

The axial capacity of the base plate can then bedetermined equating the designmoment and the sectionmoment capacity as follows:

N*t 0.9fyibet2i

4nbbt

(40)

or equivalently the minimum base plate thickness tiunder a certain loading condition is calculated as:

ti =4N*t bt

0.9fyi be nb (41)

5.2.3. IWIMMModel(CHS with varying number of bolts)

The IWIMM Model has been named here after theinitials of the authors of the model. [27] The model wasfirstly derived for the design of CHS boltedconnections. [37] and [36] suggest its use also for thedesign of base plates of CHS columns.The base plate layout considered by thismodel is shownin Fig. 20.The plate thickness is calculated based on the designaxial tension load N*t as follows:

ti 2N*t

fyi f3 (42)where:

= 0.9d0 = outside diameter of a CHStc = thickness of column section

f3 = 12k1k3+ k23 4k1

k1 = lnr2r3k3 = k1+ 2r2 =

d02

+ a1r3 =

d0 tc2

a1 and a2 as defined in Fig. 20[27] recommends to keep the value of a1 as small aspossible, i.e. between 1.5df and 2df (where df is thenominal diameter of the bolts), while ensuring aminimum of 5 mm clearance between the nut face andthe weld around the CHS.

N*t

a1do

ti ti

a2

N*t

Figure 20 Bolted CHS Flange--plate Connection(Ref. [36])

[27] also recommends to determine the number ofrequired anchor bolts as follows:

nb N*tNtf

11f3

+ 1f3 lnr1r2

(43)where:

= 0.9Ntf = nominal tensile capacity of the bolt

r1 = d02 + 2a1

r2 = d02 + a1a1 = a2

This procedure does not verify the capacity of theconcrete foundation and its interaction with the anchorbolts needs to be checked.Assumptions adopted by this model are an allowancefor prying action equal to 1/3 of the ultimate capacity ofthe anchor bolt (at ultimate state), a continuous baseplate, a symmetric arrangement of the bolts around thecolumn profile and a weld capacity able to develop thefull yield strength of the CHS.[28] notes that adopting the above prying coefficient forthe bolted CHS connection in the base plate design isconservativedue to thegreater flexibility of the concretefoundation when compared to the steel to steelconnection. [36]

5.2.4. Packer--Birkemoe Model(RHS with varying number of bolts)

The Packer--Birkemoe Model is here named after theauthors of the model. [36] This model deals with baseplate for RHS as shown in Fig. 21 and it has beenvalidated only for base plates with thickness varyingbetween 12mm and 26mm.The model includes prying effects in the designprocedure. The prying action decreases whileincreasing a2as shown inFig. 21.Thevalueof a2shouldbe kept less or equal to 1.25 a1, as no benefit in the baseplate performance would be provided beyond suchvalue. a1 is defined as the distance between the bolt lineand the face of the hollow section.Generally 4--5 bolt diameters are used as spacing of thebolts sp but shorter spacing are also possible.

Based on the design loads the required number ofanchor bolts should be calculated assuming that the


prying action absorbs about 20--40% of the anchor boltcapacity. The coefficient is then calculated as follows:

= 1 dhsp (44)

where:sp = bolt pitch as defined in Fig. 21

The designer should then select a preliminary platethickness in the following range:

KN*b1+ ti KN*b (45)

where:

K = 4a3103

fyisp(where fyi is in MPa)

a3 = a1 df2+ tcN*b = design axial tension load carried by one bolt

=N*tnb

df = nominal anchor bolt diameterThe value of represents the ratio of the bendingmoment per unit width of plate at the bolt line to thebending moment per unit width at the inner hoggingplastic hinge. In the case of a rigid base plate is equalto 0 while for a flexible base plate with plastic hingesforming at both the bolt line and at the inner face of thecolumn (see Fig. 21) is equal to 1. From equilibrium,the value for preliminary base plate layout iscalculated as follows:

= KNtft2i

1 a2+ df2(a2+ a1+ tc) (46) should be taken as 0 if its value calculated withequation (46) is negative.The capacity of the steel base plate is then calculated asfollows:

Nt =t2i(1+ )nb

K (47)

where:Nt = axial tension capacity of the base plate

Nt calculated with equation (47) must be greater thanN*t. The actual tension in one bolt, including pryingeffects, is determined as follows:

N*b N*t

nb1+ a3a4 1+ (48)

where:

= KN*tt2i nb

1 1a4 = min1.25a1, a2+ df2

The value of previously calculated in equation (46)does not have to equal the value of calculated fromequation (48) as the former assumes the bolts to beloaded to their full tensile capacity.It interesting to note how equation (48) provides anestimate of the prying action present in the base plate.

a1

a3

= = = =

tc

N*t

= =

N*t

sp

a2

a4

sp

Figure 21 Packer--Birkemoe Model (Ref. [36])

5.2.5. Eurocode 3 Model(H--shaped sections with varyingnumber of bolts)

The Eurocode 3 does not provide a specific designprocedure for the design of base plates subject totension. Nevertheless it provides very useful guidelinesfor the design of bolted beam--to--column connections(Appendix J.3 of [23]) which can be adapted for thedesign of base plates considering all anchor bolts asbolts on the tension side of the beam--to--columnconnection.The design of the end plate or of the column flange ofthe beam--to--column connection is carried out in termsof equivalent T--stubs as shown in Fig. 22.

eme

m 0.8a 2a

emin

tf

tf

0.8re m

emin

r

l

Figure 22 T--stub connection in EC3 (Ref. [23])

EC3 considers that the capacity of a T--stub may begoverned by the resistence of either the flange, or thebolts, or the web or the weld between flange and web ofT--stub. The failure modes considered are three asshown in Fig. 23. The axial capacity is calculated asfollows:


Ft.Rd = minFt.Rd1, Ft.Rd2, Ft.Rd3 (49)where:

Ft.Rd1 =4Mpl.Rdm

Ft.Rd2 =2Mpl.Rd+ nBt.Rd

m+ nFt.Rd3 = Bt.RdMpl.Rd =

0.25lt2ffyMOn = emin 1.25ml = equivalent effective length calculated in

equations (50), (51), (52) and (53)

Bt.Rd = tensile capacity of bolt groupMO = partial safety factor

= 1.10 (boxed value from Table 1 of [23])Ft.Rd1, Ft.Rd2 and Ft.Rd3 = tensile capacities of the

T--stub based on failure modes 1, 2 and 3respectively

Mode 1: Completeflange yielding

Mode 2: Bolt failurewith flange yielding

Mode 3: Bolt failure

Ft

Ft

Ft

Q Q

QQ

Ft2 + Q

Ft2 + Q

Bt2Bt2

Bt2Bt2Figure 23 Failure modes of a T--stub flange

(Ref. [23])

It is interesting to note that the amount of prying actionfor a certain baseplate layout canbeobtained as the ratioFt.RdBt.Rd as shown in Fig. 24.

21+ 2

21+ 2

1 2

Mode 3

Mode 2

Mode 1

1

FBt.Rd

= nm =4MplRd

mBt.Rd =l t2f fyMOmBt.Rd

Figure 24 Prying action in T--stub for the threefailure modes considered in (Ref.[23])

The tension zone of the end plate should be consideredto act as a series of equivalentT--stubswith a total lengthequal to the total effective length of the bolt pattern inthe tension zone, as shown in Fig. 26.[23] The length tobe utilised in the design of the equivalent T--stub iscalculated as follows:

for bolts outside the tension flange of the beam

leff.a = min0.5bp, 0.5w+2mx+0.625ex,4mx+1.25ex, 2mx) (50)

for first row of bolts below the tension flange ofthe beam

leff.b = min(m, 2m) (51)for other inner bolts

leff.c = minp, 4m+ 1.25e, 2m (52)for other end bolts

leff.d=min(0.5p+2m+0.625e, 4m+1.25e, 2m) (53)where:

= as defined in Fig. 27It is interesting to note that the failuremodes consideredfor example by equations (52) and (53) are the same asthose considered to evaluate the capacity of anunstiffened flange. The yield line patterns of suchfailure modes are shown in Fig. 25.


em

p p

Centreline of web

Centreline of web

Centreline of web

(a) Combined bolt group action

(b) Separate bolt patterns

(c) Circles around each bolt

Figure 25 Yield line patterns for unstiffenedflange (Ref. [23])

Transformation of extension to equivalent T--stub

Equivalent T--stubfor extension

Portion between flanges

bpw

exmx

p

p

e mme

ex mx

leff.a

leff.b

leff.c

leff.d

bp bp2 leff.a

leff.a

Figure 26 Effective lengths of equivalent T--stubflanges representing an end plate(Ref. [23])

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

2 65.5 5 4.754.54.45

2

1 = m1m1 + e

2 = m2m1 + e

e m1

m2

1

Figure 27 Value of Effective lengths of tocalculate equivalent T--stub flanges(Ref. [23])

5.3. DESIGN OF ANCHOR BOLTS --LITERATURE REVIEW

Available design guidelines regarding the behaviour ofanchor bolts in tension distinguish between thebehaviour of anchor bolts with an anchor head and ofhooked anchor bolts and therefore these will bediscussed here separately. For the purpose of this paperan anchor head is defined as a nut, flat washer, plate, orbolt head or other steel component used to transmitanchor loads from the tensile stress component to theconcrete by bearing. [2]

5.3.1. Anchor bolts with anchor head

The first detailed guidance on the design of anchor boltsis provided by the American Concrete InstituteCommittee 349 in 1976 in [3]. These recommendationsare produced for the design of nuclear safety relatedstructures. Some of the ACI Committee 349 members,very active in the preparation of [3], publish an article[17] where the guidelines provided in [3] are modifiedto suit concrete structures in general.


The design criteria at the base of [2] and of [17] is thatanchor bolts should be designed to fail in a ductilemanner, therefore the anchor bolt should reach yieldingprior to the concrete brittle failure. This is achieved byensuring that the calculated concrete strength exceedsthe minimum specified tensile strength of the steel.[2][17]Typical brittle failure of an isolated anchor bolt is bypulling out of a concrete cone radiating out at 45 degreesfrom the bottom of the anchor as shown in Fig. 28. [2]and [17] recommend to calculate its nominal concretepull--out capacity based on the tensile strength 4 fc(where fc is in psi) or 0.33 fc (where fc is in MPa)acting over an effective area which is the projected areaof the concrete failure cone.In both [3] and [17] it is recommended to use a capacityreduction factorof0.65 in the calculationof the concretecone capacity,which can be increased to 0.85 in the casethe anchor head is beyond the far face reinforcement.The value of 0.65 applies to the case of an anchor boltin plain concrete. This intends to be a simplification ofa very complex problem. [3][17]In the current version of ACI349 [2] the capacityreduction factor is equal to 0.65 unless the embedmentis anchored either beyond the far face reinforcement, orin a compression zone or in a tension zone where theconcrete tension stress (based on an uncracked section)at the concrete surface is less than the tensile strength ofthe concrete 0.4 fc subjected to strength loadcombinations calculated in accordance with currentloading codes (i.e. AS1170.0 [8]) in which cases acapacity reduction factor of 0.85 can be used. [2] Anembedment is defined in [2] as that steel componentembedded in the concrete used to transmit applied loadsto the concrete structure. The ACI Committee 349recognises that there is not sufficient data to definemoreaccurate values for the strength reduction factor. [2]Experimental results have generally verified the resultsof this approach. [31]

The value of 0.33 fc represents an average value ofthe concrete stress on the projected area accounting forthe stress distribution which occurs along the failurecone surface varying from zero at the concrete surfaceto a maximum at the bolt end. [31] In calculating theprojected area of the failure cone the area of the anchorhead should be disregarded as the failure cone initiatesat the outside periphery of the anchor head. [2]Experimental results have shown that the head of astandard bolt, without a plate or washer, is able todevelop the full tensile strength of the bolt provided, asspecified in [2], that there is a minimum gross bearingarea of at least 2.5 times the tensile stress area of theanchor bolt and provided there is sufficient side cover,

that the thickness of the anchor head is at least 1.0 timesthe greatest dimension from the outermost bearing edgeof the anchor head to the face of the tensile stresscomponent and that the bearing area of the anchor headis approximately evenly distributed around theperimeter of the tensile stress component. [2]The placing of washers or plates above the bolt head toincrease the concrete pull--out capacity should beavoided as it only spreads the failure cone away from thebolt--line which may cause overlapping of cones withadjacent anchors or edge distance problems. [31]

Ld

Ld

45o

Failureplane

Projected surface

Figure 28 Concrete failure cone (Ref. [26])

If reinforcement in the foundation is extended into thearea of the failure cone additional strength would bepresent in practice since the nominal capacity of thefailure cone is based on the strength of unreinforcedconcrete.The concrete pull--out capacity of a bolt group iscalculated as the average concrete tensile strength0.33 fc times the effective tensile area of the boltgroup. This effective area is calculated as the sum of theprojected areas of each anchor part of the bolt group ifthese projected areas do not overlap; when overlappingoccurs overlapped areas should be considered only oncein the calculation of the effective tensile area, thusleading to a smaller concrete pull--out capacity ifcompared to the sum of the concrete pull--out capacitiesof each anchor in the bolt group considered in isolation.[2][17]


= L2d 2cos1 s2LdL2d

3600+ s2 L

2d s

2

4Shaded

Area(a) Two Intersecting Failure Cones

LdLd

ss

= L2d 2cos1 s2LdL2d

3600+ s2 L

2d s

2

4Area

Circle -- Sector + Triangle(b) Failure Cone Near an Edge

s2

LdLd

Ld

+ Ld=

(Note: the inverse cosine term listed in theequations is in degrees)

Figure 29 Calculation of the projected area oftwo intersecting failure cones or onefailure cone near an edge (Ref. [30])

Simple procedures to calculate the effective tensileareas of bolt groups are provided in [30], i.e. theprocedure to calculate two intersecting cones is shownin Fig. 29. [30]Depending upon the bolt group layout other possiblefailure modes could take place such as the one shown inFig. 30 where an entire part of the concrete foundationwould pull--out. In such cases the effective tensile areashould be calculated selecting the smallest projectedarea due to the possible concrete failure surfaces asshown in Fig. 30. A similar average tensile strength asin the case of the pull--out cones can be adopted. [2][17]

Tension Force

Figure 30 Potential Failure Modewith limited depth (Ref. [2])

Transverse splitting is another failure mode which canoccur between anchor heads of an anchor bolt groupwhen their centre--to--centre spacing is less than theanchor bolt depth and is shown in Fig. 31. This failuremodeoccurs at a load similar to theone required to causea pull--out cone failure in uncracked concrete andtherefore no additional design checks need to beconsidered. [2][17]

Tension Force

Transversesplitting

Figure 31 Transverse splitting failure mode(Ref. [2])

It is interesting to note that in the case of shallow anchorbolts the angle at the bolt head formed by the failurecone tends to increase from 90 degrees to 120 degrees.An anchor bolt is classified as shallow when its lengthis less than 5in. (127 mm). Nevertheless for designpurposes caution should be applied is using anglesgreater than 90 degrees as cracksmight be present at theconcrete surface. It is recommendednot use anglesotherthan 90 degrees. [2][17]The previous considerations assume the concreteelement to be stress--free and only subjected to theanchor bolts loading. [2] and [17] consider the casewhen there is a state of biaxial compression and tensionin the plane of the concrete. The former loadingcondition would be beneficial to the anchor boltsstrength while the latter loading state would lead to asignificantly decrease in strength. Nevertheless, it is inthe opinion of the ACI 349 Committee that a failurecone angle of 90 degrees can still be utilised as it isassumed that any cracking would be controlled by themain reinforcement designed in accordance withcurrent concrete codes, i.e. AS 3600 [10].The design procedure proposed by ACI 349 and [17] isalso recommended by DeWolf in [21].[21] notes that the use of cored holes, such as shown inFig. 32, should not reduce the anchorage capacity basedon the failure cone, provided that the coredhole doesnotextend near the bottom of the bolt. This situation shouldbe avoided if the dimensions shown in Fig. 32 arefollowed. [26]

but 75mm

df

3df

Ld

Projection

Figure 32 Suggested layout for Cored Holesto Permit Minor Adjustments inPosition on Site (Ref. [26])


45o Blow outcone

Failuresurface

45o

Figure 33 Failure Surface of Blow--out Conedue to Lateral Bursting of theConcrete (Ref. [31])

Lateral bursting of the concrete can occur when ananchor bolt is located close to the concrete edge asshown in Fig. 33, which is caused by a lateral forcepresent at the bolt head location.This lateral force may be conservatively assumed to beone--fourth of the nominal tensile capacity of the anchorbolt for conventional anchor heads which can becalculated in accordancewithClause9.3.2.2ofAS4100[11] as follows:

Ntf = Asfuf = 0.75A0fuf = 0.75d2f 4

fuf (54)

where:As = tensile stress area in accordance with AS1275

[9] and conservatively approximated with 0.75A0

A0 =d2f 4

= shank area

fuf = minimum tensile strength of a boltThe failure surface has the shape of a cone whichradiates at 45 degrees from the anchor head towards theconcrete edge.The concrete capacity is calculated as theaverage concrete tensile strength 0.33 fc appliedover the projected cone area as follows: [2][3][17]

Nc.lat = 0.33 fc a2e (55)where:

= 0.65 in Ref. [3], 0.85 in Refs. [2] and [17]Nc.lat = lateral bursting capacity of the concreteae = side cover

Equating the assumed lateral force (equal to 0.25 Ntf) tothe concrete lateral bursting capacity allows to expressthe minimum required side cover as a function of boththe concrete and anchor bolt strengths as shown below:

0.25Ntf = Nc.lat = 0.33 fc a2e (56)and solving equation (56) for ae yields:

ae = dffuf

7 fc (57)where:

= 0.65 in Ref. [3],= 0.85 in Refs. [2] and [17]

Adopting the capacity reduction factor equal to 0.85the minimum side cover to avoid lateral bursting of theconcrete can be calculated as follows:

ae = dffuf

6 fc (58)Equation (58) has also been recommended in [26] and[47].

Tension Force

Spiralreinforcement

PotentialFailureZone

Figure 34 Reinforcement Against LateralBursting of Concrete Foundation(Ref. [2])

Based on the guidelines provided in reference [3],simplified design guidelines regarding minimumembedment lengths and minimum edge distances arepresented in reference [39]. These minimumembedment lengths are calculated with an additionalsafety factor of 1.33 when compared to the guidelinespresented in reference [3]. These simplified guidelinesare as follows:

for Grade 250 bars and Grade 4.6 bolts:Ld 12dfae = min(100, 5df)for Grade 8.8 bolts:Ld 17dfae = min(100, 7df)

where:Ld = minimum embedment length

Theseminimumembedment lengths and edge distanceshave also been recommended in references [18], [21]and [26].Reinforcement needs to be specified in the case anchorbolts are located too close to a concrete edge (the edgedistance ae is less than the one required by equation(58)) or their embedment length is less than the onerequired to develop the bolts full tensile strength. Suchreinforcement should be designed and located tointersect potential cracks ensuring full developmentlength of the reinforcement onboth sides of such cracks.The placement of the reinforcement should beconcentric with the tensile stress field. [2]


In the specific case of insufficient embedment length apossible reinforcement layout to enhance the concretepull--out capacity is detailed in Fig. 35 using hairpinreinforcement. The hairpins need to be placed asspecified in Fig. 35 in order to effectively interceptpotential failure planes. Other reinforcementconfigurations can be specified in accordance with AS3600 while still complying with the specificationspreviously outlined for hairpin reinforcement toconsider the reinforcement to be effective. Thesespecifications are the maximum distance from theanchor head and theminimum embedment length equalto 8 reinforcement diameters.

Tension Force

Ld

Ld3

Ld3

8x diameter of thehairpin reinforcement

Development lengthfrom AS3600

Maximum distance fromanchor head for reinforcementto be considered effective

Locate legs of hairpinreinforcement in this region

Figure 35 Possible Placement of Reinforcementfor Direct Tension (Ref. [2])

In the case of insufficient side cover ae there are noexperimental results to validate a design procedure toinclude reinforcement to avoid lateral bursting of theconcrete. The ACI 349 Committee recommends the useof spiral reinforcement as shown in Fig. 34 while alsosuggesting to refer to accepted practices for prestressinganchorages to resist the lateral bursting force. [2][2] and [17] recommend that if proper anchorage of thereinforcement cannot be accomplished in the availabledimensions, the anchorage configuration should bechanged.

5.3.2. Hooked bars

There are different opinions regarding the ability ofhooked anchor bolts to carry tensile loading. Someauthors do not recommend to use them to resist upliftloads, while others have provided some designguidelines.The major concern regarding the use of hooked bars intension is that they tend to fail by straightening andpulling out of the concrete as shown by research carriedout by the PCI.[24][24] and [31] discuss the behaviour of smooth anchorbolts and recommend to use hooked anchor bolts witha bearing head as smooth bars are less able to developtheir strength along their length than deformed bars.[24] recommends to use the following formula todetermine thepull--out capacityof ahookedanchorbolt:

Nth = 0.7fcdf Lh (59)where:

= 0.80 (as recommended in [26])Nth = tensile capacity of a hooked bardf = nominal diameter of the hooked barLh = length of the hook

DeWolf in [22] recommends to use hooked anchor boltsonly under compressive axial loading, and where nofixity is needed at the base except during erection. Evenfor this case he recommends to design the hook to resisthalf thedesign tensile capacityof thebolt usingequation(59). He also recommends to use anchor bolts with amore positive anchorage which is formed when bolts orrods with threads and nut are used. [22] Similar designconsiderations are presented in reference [47].The recommendations of the AISC(US) Manuals havechangedover time. In reference [6] thedesign ofhookedanchor rods under tension is recommended to be carriedout based on the design procedure presented in [24] asoutlined in equation (59) while in reference [5] the useof hooked anchor rods is recommended only for axiallyloaded members subject to compression only.

5.4. RECOMMENDED MODEL

5.4.1. Introduction

Available design guidelines have been included in therecommended design models where possible.Additional design models/provisions are here providedfor those instances, to the knowledge of the authors, notcovered by available design guidelines. Their use hasbeen clearly stated and their derivations are illustratedin Section 11.It is interesting to note that depending upon themagnitude of the plate flexural deformation and the boltelongation which occur in the loaded base plateconnection, a prying action might be present.The possible collapse mechanisms which can occur aresimilar to those which can occur in bolted connections.These are shown in Fig. 36.

N*tN*bN*t N*tN*b N

*b

N*p N*p

Schematic failure modes

Bending moment diagramsshowing plastic hinges

Figure 36 Possible plate deformationsand anchor bolt elongations(modified from Ref.[13])

In the case the plate flexural deformation is smaller thanthe bolt elongation no prying actionwould take place asshown in Fig. 36(a). In the case the plate flexural


deformation is of similar or of greater magnitude as thebolt elongation, as shown in Fig. 36(b) and (c), pryingactions N*p should be accounted for in the design.Possible bending moment diagram occurring in theplate in all three collapsemechanisms are also shown inFig. 36. [13]For design purposes the use of a prying factor of 1.4 isconservatively recommended as suggested in [37] and[36].

5.4.2. Design Criteria

The recommended model for axial tension is based onthe following design criteria:

Ndes.t = [Nt ; Nw ; pNtb]min N*t (60)with the following constraint to ensure a ductile failureof the anchorage system (connection of anchor bolt toconcrete):

Ncc > Ntb (61)and complying with the anchor bolts embedmentlengths and concrete edge distances specified inSections 5.4.5. and 5.4.6. andwhere:

Ndes.t = design capacity of the base plate connectionsubject to axial tension

Nt = design tensile axial capacity of the steel baseplate

Nw= design axial capacity of the weld connectingthe base plate to the column

Ntb = design capacity of the anchor bolt groupunder tension

p = 1/1.4 = 0.72 prying reduction factor asrecommended in references [36] and [37] unlessnoted otherwise in 5.4.3.

Ncc = design pull--out capacity of the concretefoundation

N*t = design axial tension load

5.4.3. Anchor bolt design

The tensile design capacity of the anchor bolt groupNtb is calculated in accordance with Clause 9.3.2.2 ofAS4100 [11] as the sum of the design capacities of eachsingle bolt Ntf.

Ntb = nbNtf = nbAsfuf (62)where:

= 0.8Refer to Section 14. for tabulated values of the tensilecapacities of anchor bolts.In the case the base plate is designed based onPacker--Birkemoe Model the preliminary number ofbolts required is obtained from equation (62) which isthen refined in the section describing the steel plate

design. Once the steel plate design is complete thecapacity of the anchor bolt groups needs to bere--checked. The value of p to be adopted in the Packer-- Birkemoe model is specified in equation (95).In the case the design of the base plate is carried out baseon IWIMM Model (refer to Section 5.4.7.) the tensiledesign capacity of the anchor group should becalculated as follows:

Ntb =nbNtf

1 1f3+1

f3 lnr1r2(63)

where: = 0.9p = 1 to be used in equation (60) as prying effects

are already included in equation (63)

r1 = d02 + 2a1

r2 = d02 + a1a1 = a2 (condition to apply equation (63))f3 = 12k1

k3+ k23 4k1 k1 = lnr2r3k3 = k1+ 2r2 =

d02

+ a1r3 =

d0 tc2

a1, a2 and d0 are defined in Fig. 20

5.4.4. Design of concrete pull--out capacity

The pull--out capacity of the concrete Ncc variesdepending upon the anchor bolts layout and it can becalculated in accordance with AS 3600 as follows:

Ncc = 0.33 fc Aps (64)where:

= 0.7 (based on required for Clause 9.2.3 of AS3600)

Aps = effective projected area

Equation (64) is similar to the expression provided inClause 9.2.3 of AS 3600 to calculate the concretecapacity of a slab against punching shear, whichinvolves a similar failure mechanism as the one of thepull--out cone.Thevalueof h tobecalculated inClause9.2.3 of AS 3600 would be equal to 1 as the shape of theeffective loaded area is a circle. AS 3600 recommendsa strength reduction factor under shear of 0.7 (Table 2.3of AS 3600).The capacities of a few common bolt layouts as shownin Fig. 37 are here outlined. [47]


L1

L145o

Projectedarea

L2

L2

s

Single Cone Two Intersecting Cones(a) (b)

L4

s

L4

Four IntersectingCones

(c)

Figure 37 Common bolt layouts (Ref. [47])

The effective projected areas of each anchor bolt layoutshown in Fig. 37 is calculated as follows:Aps.1 = effective projected area of isolated anchor bolt

(nooverlappingof failure cones) as shown inFig.37(a)

= L21Aps.2 = effective projected area of 2 anchor bolts with

overlapping of their failure cones as shown inFig. 37(b);

= d22 1 2 cos1(s2L2)360 + s2 L22 s24Aps.4 = effective projected area of 4 anchor bolts with

overlapping of their failure cones. In this caseeach failure cone overlaps with all other 3 failurecones as shown in Fig. 37(c).

= d240.75 2 cos1(s2L4)360 + s

2L24 s24 + s24

where the inverse cosine term is in degrees.

5.4.5. Concrete cover requirements

The cover requirements for an anchor bolt aredetermined in accordance with [2] and [17] in order toprevent lateral bursting of the concrete which can occurwhen a bolt is located close to a concrete edge as shownin Fig. 33.The minimum cover to be provided is calculated asfollows: [17][2]

ae = max100, dffuf

6 fc (65)Tabulated values of equation (65) are presented inSection 12.The following simplified expressions, which have beenderived in Section 12., can be used in place of equation(65) leading to slightly more conservative side coversthan those calculated with equation (65).

for Grade 4.6 bolts and Grade 250 rodsae = 4 df when fc = 20, 25 and 32 MPa

100 when fc = 20, 25 and 32 MPafor Grade 8.8 boltsae = 6 df when fc = 20 and 25 MPa

= 5 df when fc = 32 MPa 100 when fc = 20, 25 and 32 MPa

The requirement of a minimum side cover of 100mm isbased on recommendations of [21], [26] and [39].

5.4.6. Minimum embedment lengths

The recommended minimum embedment length Ld ofan anchor bolt is determined in accordance with thedesign guidelines specified in [2] adjusted to suit AS3600.

Edge of ConcreteFoundation

ae

Ld

Lh

Figure 38 Hook, embedment lengths and edgedistances for anchor bolts (Ref. [26])

The minimum embedment length Ld for an isolatedanchor bolt should be calculated as follows: (refer toFig. 38)

Ld = d2f + d2f + 4

2 100 (66)where:

= 0.7 (based on in Clause 9.2.3 of AS 3600)

= fufAs0.33 fc

Even if it has been observed that for shallow anchors theangle at the bolt head formed by the concrete failurecone tends to increase from 90 degrees to 120 degrees(therefore increasing the concrete pull--out capacity) aminimum limit of 100mm is here introduced in equation(66) as cracks might be present at the concrete surface.Refer to Section 12. for the derivation of equation (66)and of the simplified expressions shown below whichcan be used in place of equation (66).

for Grade 4.6 bolts and Grade 250 rods


Ld = 9 df when fc = 20, 25 and 32MPafor Grade 8.8 boltsLd = 13 df when fc = 20 MPa

= 12 df when fc = 25 MPa= 11 df when fc = 32 MPa

Hooked anchor bolts, as shown in Fig. 38, need to bedetailed with a minimum embedment length asspecified for bolts with an anchor head of same nominaldiameter (specified by equation (66) or by its alternativesimplified expressions) and with a minimum hooklength calculated as follows:[24][26]

Lh Asfuf0.7fcdf

(67)

where:Lh = hook length of anchor bolt

The anchorage length (embedment length and hooklength) should be such as to prevent bond failurebetween the anchor bolt and concrete prior to yieldingof the bolt. When possible, a more positive anchorageshould be adopted at the end of the hook, for example bymeans of a nut.

5.4.7. Design of the Steel Base Plate

The recommended procedure to design or check thesteel base plate varies depending upon the columnsection and number of bolts considered.Recom

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