1

Bolted Joints between Steel Beams and Reinforced Concrete Columns

F. Kope, M.Sc., M. ASCE, AICPS Antiseismic Structural Engineering, Bucuresti, Romania

kope@antiseismic.com

C. Onofrei, M.Sc., M. AISC, AICPS Antiseismic Structural Engineering, Bucuresti, Romania

onofrei@antiseismic.com

P. Olteanu, M.Sc., M. AICPS Antiseismic Structural Engineering, Bucuresti, Romania

paul@antiseismic.com

Abstract

The steel beams to RC columns joint are usually done by welding the beam to a steel core within the column. This solution is well covered in one of the Journal of Structural Engineering papers “Guidelines for Design of Joints between Steel Beams and Reinforced Concrete Columns”. The same methodology is assumed in the Romanian code “Cod de proiectare pentru structuri de beton armat cu armatura rigida” NP033-99. However, in case that a contractor avoids using on-site welding due to various difficulties, and a continuous steel beam through the reinforced concrete column is still required, a bolted connection between the beam and the inner steel core should be considered. This paper presents an extension of these guidelines to a bolted connection type. A nonlinear finite element analysis with proper definition of contact relationships between components is performed in order to assess the role of each principal contributor (i.e. steel panel, inner concrete and outer concrete regions).

Introduction

Shear strength in RCS (reinforced concrete steel) connections is provided by three mechanisms: steel web panel, inner diagonal concrete strut and outer diagonal concrete strut.

1. Steel web panel. In RCS connections the behaviour of the steel web panel is similar to that in steel frames.

2. Inner concrete. The inner diagonal concrete strut is activated through bearing of the concrete on the steel beam flanges and face bearing plates welded between the beam flanges at the column faces.

3. Outer concrete region. The horizontal concrete struts are mobilized through extended face bearing plates (FBP) or steel column, above and below the steel beam – these struts may be separated into two components: one parallel to the beam and one perpendicular. Those perpendiculars are self equilibrating and those parallel to the beam are sent further to the outer compression field. (see Figure 8 of ref [1])

In addition to possessing adequate shear strength, RCS joints must be able to sustain large bearing stresses in the concrete regions just above and below the steel beam flanges. Because bearing failures in RCS connections are less ductile and could lead to poor dissipation capacity compared to joint shear failures, it is desirable to design RCS connections to possess a bearing strength larger than their shear strength in order to avoid a potential bearing failure, according to ref. [12]. The basically means in order to achieve this goal is necessary a proper detailing of the joint using steel band plates (SBP) and vertical joint reinforcement directly linked to the beam flanges.

The ASCE Task Committee guidelines [1] and Romanian design guidelines for RCS (reinforced concrete-steel) structures, ref. [2], do not take into account the effect of RC slab, nor the transverse beams, for the calculation of the joint strength. The presence of these elements (slab and transverse beams) usually increases the effective joint width such that a larger concrete strut mechanism is developed to resist joint shear forces.

The joint calculation is based on ASCE guidelines [1] and a finite element analysis of bolted connection.

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Discussion related to load and resistance factors approach used in ASCE Guidelines [1] vs. Romanian

code for composite steel and concrete structures [2]

The code for composite structures [2] sets a number of provisions concerning the joint between the steel beam and reinforced concrete column, which basically follows the design criteria presented in ASCE guidelines [1]. This section presents a comparison between the two procedures.

Both guidelines recommend checking the same failure modes: vertical bearing and panel shear failure.

The joint adequacy is checked using same equations provided in exactly the same format, with the main difference concerning the load and resistance factors. The Romanian design criteria are provided in section 4.2.4.3 of ref. [2]. The vertical bearing and panel shear failure is checked through eq. 4.90 and 4.93, respectively, of ref. [2].

Usually, the panel shear failure governs (vertical bearing is not the critical check – once the steel band plates are provided above and below the steel beam to confine the reinforced concrete column). Therefore, the panel shear failure is discussed below.

The loading factor of 1.25 in case of shear panel failure mode is almost cancelled by the ratio (H/Ho) applied to the sum of bending moments. The term on the right side of both equations of ref. [1] do not use any

resistance factor (φ=0.7)– however the design strength Rc is used instead of specified compressive strength f’c.

The equations provide almost the same results if:

c cf ' Rφ⋅ = (1)

A short consideration related to the US specified concrete strength is deemed as necessary. The US required average compressive strength of concrete (which is used as a basis for selection of concrete proportions) has the same meaning as the EC2 mean value of concrete compressive strength. Moreover, they are measured almost in the same conditions using short-time compression tests on cylinders 6in diameter by 12 in high in case of ACI and 150 by 300mm for EC2. The following chart presents a comparison between concrete grade related parameters used in ACI, EC and Romanian regulations.

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Where

- fck is the characteristic compressive cylinder strength of concrete at 28 days (note that 95% confidence on normal distribution corresponds to 1.645 SD)

- fcm is the mean value of concrete cylinder compressive strength

- fck,cube is the characteristic compressive cube strength of concrete

- fcm,cube is the mean value of concrete cube compressive strength

- V represents the coefficient of variation = (SD/µ); where SD stands for standard deviation and µ denotes the mean value

- f'c is the specified compressive strength of concrete

- f’cr is the required average compressive strength of concrete

The standard deviation (SD) may be easily calculated in case of EC2 knowing that:

ck cm ck cmf f 1.645 SD and f f 8MPa= − ⋅ = − (2)

The SD is 4.86MPa which further corresponds to a coefficient of variation of

V SD/ 4.86/ 33 0.15= µ = = (3)

which is related to a concrete class C25/30 (fcm = 33MPa). Note that the standard deviation is considered independent of mean strength in EC2, which is entirely true only for grades above C20/25. The ACI approach is somehow different from this regard – it allows using actual SD values, which is convenient in case of modern ready-mix plants as the coefficient of variation for a god control over the concrete strength is V=0.10. This basically yields a standard deviation in case of C25/30 of only SD=0.1*33= 3.3MPa.

The confidence level in case of ACI appears to be more relaxed by comparison with EC2, assuming 1.34SD instead of 1.64SD. This is true only for concretes with SD lower than 3.45 MPa (or in case of C25/30 with a V=0.10). Considering the usual case (V=0.15) ACI yields almost the same result as EC2 for a C25/30 or 4000psi concrete grade:

2.33SD 3.45MPa 2.33 (0.15 33) 3.45MPa 8MPa− = ⋅ ⋅ − ≅ (4)

The following Figure presents a comparison between the two cases. Note that the coefficient of variation V=0.15 is also assumed by ACI Committee 214 for an “average control” standard over moderate-strength concretes; (V=0.10 corresponds to what is termed excellent control, and V=0.20 to poor control). Recent studies in the US recommend a single value V=0.10 (in case of average control) as it would appear to be more appropriate for modern ready-mix concretes.

Bc30 C25/30 B400

fck,cube

fck(150-by-300mm cylinders)

(150mm cubes)

fck,141-cube(141mm cubes)

fck =(0.87-0.002 fck,141-cube )fck,141-cube

fcm,140-cube(140mm cubes)

STAS 10107/0-90 Eurocode 2 STAS 10107/0-76

fck,140-cube=(1 - 1.645 V) fcm,140-cube

4000psiACI 318

f 'c(152-by-305mm cylinders)

f 'c = f ' - 1.34 SD (if SD < 3.45MPa)cr

f 'c = f ' - (2.33 SD - 3.45MPa) (if SD > 3.45MPa)cr

fck = f - 1.645 SDcm

[27.5MPa]

~ 1*SD

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Figure 1. Comparison between various compressive strengths considering two coefficients of variation V=0.1 and 0.15

One more important comment: the reader is advised that this comparison is not entirely valid as the Load Level of ACI is different with respect to Eurocode (the load factors are different).

Now, using f’c=26MPa and Rc=15.5MPa (considered as a conservative value for the compressive strength of a C25/30 (Bc30) concrete grade):

0.7 26 3.6MPa 15.5 3.9MPa⋅ = ≅ = (5)

All the three contributors to the shear resistance of the joint are evaluated in the same manner in both guidelines. The shear resistance of the steel panel contributor is given using the same equations with the main

difference that the design strength of Rr / 3 is used instead of 0.6fy, which basically yields the same results. The concrete strut and compression field are also evaluated using the same equations as provided in ref. [1] (except for the typing error noticed in ref. [2]) – the previous note regarding design strength vs. specified compressive strength applies.

There are some other minor differences between the two guidelines; therefore it is considered that the ASCE design criteria [1] can be followed throughout this report using a calibrated specified compressive strength of 31MPa.

Joint Forces

The joint should be design for the interaction of forces transferred to the joint by adjacent members, including bending shear and axial load.

The design forces as per ref. [1] do not include the effects of axial forces in the concrete column, and since axial forces in the beams are usually small, these are also excluded from calculations. It is considered conservative to neglect the effects of axial compressive loads normally encountered in design. Moreover, it is predictable that the strength of the concrete joint mechanisms will be greater in joints where beam frame into four, rather than two sides of the column, due to additional confinement.

The following Figure illustrates the joint forces considered in the connection analysis:

13 17 21 25 29 33 37 41 45 49 530

0.05

0.1

0.15fcmfck

V=0.10 Excellent Control

V=0.15 AVERAGE CONTROL (same as EC2 specification)

f 'c=28.6MPa (1.34SD)

fck=27.5MPa (1.64SD)

f 'c=25.5MPa (2.33SD-3.45MPa)

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Figure 2. Notation of Joint design forces

The following assumptions were considered:

1. The column and beam axial forces were neglected (as specified by ref. [1])

2. The joint bending moments as resulted from the frame analysis were transmitted to the face of elements (columns and beams) so that the joint equilibrium is maintained.

The following Table lists the joint forces reduced to the face of elements (these values are associated to average design strengths for the capacities of adjacent beams – 1.35Ra and 1.75Rc).

Table 1. Joint design forces

BEAM COLUMN

Type Vb1 [Mp]

Mb1 [Mp-m]

Vb2 [Mp]

Mb2 [Mp-m]

∆Vb [Mp]

Vc1 [Mp]

Mc1 [Mp-m]

Vc2 [Mp]

Mc2 [Mp-m]

∆Vc [Mp]

Value -5.5 509.0 120.8 341.3 126.3 84.5 45.8 171.8 722.5 87.3

Note: The positive values of these quantities are established in the previous Figure

The hogging bending moment (Mb1) reflects the flexural capacity of the composite beam (including slab) – which is overly conservative for the steel beam connection calculation.

General Limitations

Joint aspect ratio (as per. ref . [1, par. 1.2]):

0.75 h /d 1.04 2.0≤ = ≤ (6)

Where h=1200mm is the depth of concrete column measured parallel to the beam; and d=1150mm is the depth of steel beam measured parallel to the column.

Material specification (as per. ref . [1, par. 1.2]):

1. normal weight concrete (2.4Mp/m3 specific weight) (1Mp = 1 megapond ≈ 1tf)

2. Reinforcing bars (PC52) with yielding strength of 345MPa (according to ref. [4]) which is less than recommended value of 410MPa

Vb2Vb1

Mb2

Mb1

Vc

Vc2

Mc2

Vb

Mc1

Vc1

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3. Structural steel used for beams: OL37 with yielding strength of 240MPa and for the connection elements is OL52 with yielding strength of 340MPa (see ref. [5]). These values are lower than recommended value of 345MPa.

Joint Failure Modes for Continuous Beam through Column

The identified failure modes for continuous beam through column are listed below according to ref. [1], [2], [8] and [14]

1. Panel shear failure – (this failure mode is characterized roughly by the same behavior to that typically associated with structural steel or reinforced concrete joints; however in composite joints, both structural steel and reinforced concrete panel elements participate);

2. Vertical bearing failure – (bearing failure occurs at locations of high compressive stresses and may be associated with rigid body rotation of the steel beam within the concrete column. The vertical reinforcement linked to the beam flanges, as shown in Figures 6b of ref. [1] or Figure 24b of ref. [2], is one means of strengthening against bearing failure).

The identification of failure modes were extended, see reference [8], by investigating the behaviour of similar composite beam-column joints during reversed inelastic cyclic loading, considering various factors such as sub-assemblage failure modes, joint failure modes, joint detailing, column axial load, concrete compression strength, and concrete bearing strength of the column and joint.

These studies demonstrated that composite beam-column joints can be detailed such that their performances during seismic loading are comparable to those of seismically designed steel and RC beam-column joints, according to ref. [8].

Current design practice of the composite connection and restrictions related to

selection of connection type

The common design practice of the composite connections between steel beams and reinforced concrete columns, implies two types of connections (as illustrated in ref. [11]):

- Through-beam (where the beam runs continuously through the joint); and

- Through-column (where the beam flanges are interrupted at the joint, so as to minimize the impact on the column reinforcing bar arrangement and to facilitate concrete placement in the joint).

Apart from major distinction of “through-beam” and “through-column” type connections, the main differences lie in attachments of the various stiffener plates, cover plates and bearing plates which act together with reinforcing bars to mobilize force transfer between the steel and concrete.

The principal elements of connection are:

- Horizontal column ties. Horizontal reinforcing bar ties should be provided in the column within the beam depth and above and below the beam to carry tension forces developed in the joint.

- Steel Band Plates (SBP). These plates are provided to confine the concrete above and below the beam. The recommended value for the height of band plates correspond to 0.25x dbeam according to ref. [12]

- Face bearing plates (FBP) and Extended face bearing plates (EFBP). The face bearing plates within the beam depth are provided to resist the horizontal shear force in the concrete strut.

- Vertical joint reinforcement (VJR). The joint detailing considerations include requirements for the attachment to the flange of structural steel beam of vertical joint reinforcement. In case of bolted connection within column width the VJR provides additional anchorage of the beam for pullout

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forces developed from bending, these forces occur due to discontinuity of connection within column depth.

Tests of alternative configurations show that the differences in behaviour between interior and exterior joints are not as significant as for the reinforced concrete joints, but there are modest differences in joint shear strength that need to be considered in design, see ref. [9] and [13]

The most of the composite connection configurations between steel beams and reinforced concrete columns are based on welded joint detailing. Only few tests were done using bolted connections within column width (as illustrated in reference [8]).

The bolted connection within column width performed unsatisfactorily in case of beam flanges not connected continuously through the joint. In this case, the beam remained essentially elastic and all damage occurred in the joint region. Because the steel beams are not continuous through the RC column, elongation of the joint may occur, as described in ref. [8].

The prevention of this behaviour is of primary concern in order to counteract the loss of connection stiffness.

Due to restrictions concerning the on-site welding, it may be necessary to design a bolted connection within reinforced column width, although current practice for high seismic zones basically requires a continuous beam through the joint.

Effective Joint Width

The joint shear strength is calculated based on an effective width of the concrete joint, which is the sum of the inner and outer panel widths. The concrete in the inner panel is mobilized through bearing against the FBP between the beam flanges. The participation of concrete outside of the beam flanges is dependent on mobilization of the horizontal compression struts that form through direct bearing of the extended FBP on the concrete above and below the joint.

The following equations used to calculate the effective joint width (bj) are semiempirical and based on tests [ref. 1].

The effective width (bj) of the joint within the column is equal to the sum of the inner and outer panels widths (bi and bo), given as:

j i ob b b 438 218.2 657mm= + = + = (7)

Where

- bi is taken equal to the greater of the FBP width, bp=438mm or the beam flange width, bf=350mm, meaning bi=438mm

- bo is calculated using the overall cross-section geometry according to the following equation:

m i

oo

C(b b ) 1.25 (612.5 438) 218.2mmb min 218.2mm

2d 2 (0.25 d) 2 (0.25 1150) 575mm

− < ⋅ − = = = = ⋅ ⋅ = ⋅ ⋅ =

(8)

do=0.25d (d=beam depth) in case a steel column is present or the lesser of 0.25d or the height of the extended FBP when these plates are present.

Where bm is given by:

8

f

m f

f

(b b)/ 2 (350 1200)/ 2 775

b min b h 350 1200 1550 612.5mm

1.75b 1.75 350 612.5

+ = + =

= + = + = = = ⋅ =

(9)

and

f

x y 1200 438C 1.25

h b 1200 350

= ⋅ = ⋅ =

(10)

y is the greater of the steel column width (bc=320mm) or extended FBP width (bp=438mm), meaning y=438mm; and x=h=1200mm in case that extended face bearing plates (FBP) are present.

Vertical Bearing Check

The vertical bearing of the joint is considered to be adequate when the following equation is satisfied:

c b cn vr vrn vrnM 0.35 h V [0.7hC h (T C )]+ ⋅ ⋅ ∆ ≤ φ + +∑ (11)

The equation elements are

c bM 0.35 h V (458 7225) 0.35 1.2 1263 8213kNm+ ⋅ ⋅ ∆ = + + ⋅ ⋅ =∑ (12)

3cn c jC 0.6 f ' b h 0.6 31 657 1200 14664 10 N= ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ = ⋅ (13)

Where f’c is the specified compressive strength of concrete in MPa.

Tvrn and Cvrn are the nominal strengths in tension and compression respectively, of the vertical joint reinforcement, which is attached directly to the steel beam, and hvr is the distance between the bars. The reinforcement is considering acting only in tension:

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vrn vrn

3c j

25T C 2 300 0 295 10 N

4

0.3 f ' b h 0.3 31 657 1200 7332 10 N OK

π⋅+ = ⋅ ⋅ + = ⋅ ≤

⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ = ⋅

(14)

The right term of vertical bearing check equation is:

cn vr vrn vrn[0.7hC h (T C )] 0.7[0.7 1.2 14664 1.1 295] 8849kNmφ + + = ⋅ ⋅ + ⋅ = (15)

The vertical bearing check is:

8849

8213 kN 8849 kN safety factor FS 1.08 OK8213

< ⇒ = = (16)

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Joint Shear Check

The horizontal shear strength, of the joint is the sum of the nominal resistance of:

1. The steel panel, Vsn

2. The inner concrete compression strut, Vcsn

3. The outer concrete compression field, Vcfn

The horizontal shear strength is considered adequate if the following equation is satisfied:

b1 b2c sn f csn w cfn 0

V VM jh [V d 0.75V d V (d d )]

2

+− ≤ φ + + +∑ (17)

Where jh is given by the following:

c

vrn vrn c b

Mjh

(T C C ) V /2

458 7225

0.7(295 0 12627) 1263/ 2

0.92 0.7h 0.7 1.2 0.84m OK

jh 0.92m

= =φ + + − ∆

+= =

+ + −

= ≥ = ⋅ =

⇒ =

∑

(18)

( )3c c j cC 2 f ' b a 2 31 10 0.657 0.31 12627 kN= ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ = (19)

2 2

c

c

h h 1.2 1.2a K 0.28

2 4 2 4

a 0.31m 0.3 h 0.3 1.2 0.36m OK

= − − = − −

⇒ = ≤ ⋅ = ⋅ =

(20)

( )

c b vrn vrn vrc j

3

2

1 hK M V (T C ) h

2 f ' b 2

1 1.2(458 7225) 1263 0.7 (295 0) 1.1

20.7 2 31.5 10 0.657

0.28m

= + ∆ − ϕ⋅ + ⋅ = ϕ⋅ ⋅ ⋅

= + + − ⋅ + ⋅ = ⋅ ⋅ ⋅ ⋅

=

∑

(21)

The left side of the join shear check equation became:

b1 b2c

V V 55 1208M jh (458 7225) 0.92 7152 kNm

2 2

+ − +− = + − =∑ (22)

The right side of joint shear check equation is given by evaluating each of the shear resistance contributors as described above. The values of Vsn, Vcsn and Vcfn are given in the following sections.

sn f csn w cfn 0[V d 0.75V d V (d d )]

0.7 [3710 1.13 0.75 5015 1.11 2569 (1.15 0.25 1.15)]

8442 kN

φ⋅ + + + =

= ⋅ ⋅ + ⋅ ⋅ + ⋅ + ⋅ =

=

(23)

The joint shear check:

10

8442

7152 kN 8442 kN safety factor FS 1.18 OK7152

< ⇒ = = (24)

Steel panel

The nominal strength of the steel panel is calculated as follows:

( )3 3sn ysp spV 0.6 F t jh 0.6 240 10 (18 10) 10 0.92 3710 kN−= ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ + ⋅ ⋅ = (25)

Fysp and tsp are the yield strength and thickness of the steel panel (considered as the web thickness of the steel beam plus the 10mm doubler plate), respectively, and jh was calculated before.

Concrete strut

The nominal strength of the concrete compression strut mechanism, Vcsn is calculated as follows:

csn c p

c p w

csn

V 1.7 f ' b h 1.7 31 438 1200

5015kN 0.5 f ' b d 0.5 31 438 1110 7536kN OK

V 5015 kN

= ⋅ ⋅ = ⋅ ⋅ =

= ≤ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ =

⇒ =

(26)

Where bp=438mm is the width of face bearing plate limited by bf + 5tp = 350+5·25=475mm, and dw=1110mm is the distance between beam flanges (height of the web).

Compression field

The nominal strength of the concrete compression filed mechanism, Vcfn, is calculate as follows:

cfn c s

c o

cfn

V V ' V ' 590 1979

2569 kN 1.7 f ' b h 1.7 31 575 1200 6531 kN OK

V 2569 kN

= + = + =

= ≤ ⋅ = ⋅ ⋅ ⋅ =

⇒ =

(27)

The force resisted by the concrete is:

c c oV ' 0.4 f ' b h 0.4 31 219 1200 590 kN= ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ = (28)

The strength provided by the horizontal ties is calculated as (considering ties of φ20mm @ 120mm):

2

s sh yshh

h 20 1200V ' A F 0.9 2 350 0.9 1979 kN

s 4 120

π ⋅= = ⋅ ⋅ ⋅ = (29)

The cross sectional area of reinforcing bars in each layer of ties spaced at sh through the beam depth, should not be less than:

2sh hA 0.004 b s 0.004 1200 120 576 mm≥ ⋅ ⋅ = ⋅ ⋅ = (30)

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The area measured through a vertical plane perpendicular to the beam (Ash) for the assumed configuration of

ties (φ20mm @ 120mm) represents 628mm2 which is greater than 576mm2.

The ties adjacent to joint are of no concern since steel band plates are provided above and below the beam.

Finite Element Analysis of Bolted Connection

The bolted connection was calculated using a finite element model of the entire connection. Due to complex mechanism that develops within in the joint, it was necessary to model each principal contributor (i.e. steel panel, inner concrete and outer concrete regions) along with a proper definition of their contact relationships.

Analytical model

The model was developed with SOLVIA Finite Element System [15]. The analysis was carried out using a simplified plane stress model. Each of the three principal contributors to shear resistance of the joint was modeled using 4-node plane stress elements (2-D solids). The out-of-plane degrees of freedom were deleted since plane-stress elements allow only for translation degree-of-freedom. The reinforcement was modeled using 2-node truss elements.

The concrete regions were introduced in the model using a nonlinear concrete model (the main attributes of the concrete model are that it is a hypoelastic model based on a nonlinear uniaxial stress-strain relation that is generalized to take biaxial and triaxial stress conditions into account and that it models tensile failure (i.e. cracking) and compression failure (i.e. crushing) by failure envelopes). The smeared crack approach was adopted for tensile failure modeling, i.e. the cracked concrete is treated as a continuum.

The compressive and tensile concrete stresses were considered as average values. The average compressive and tensile strengths are based on STAS 10107 [4] provisions as follows:

- The compressive stress for C25/30 is given by the relation: 1.75⋅Rc = 1.75⋅18=31.5MPa.

- The tensile compressive stress for C25/30 is also given by the relation: 1.75⋅Rc = 1.75⋅1.25 = 2.2 MPa

- Initial elasticity modulus was considered 32500MPa

The structural steel of beams was modeled using elastic material to allow for determining the maximum bolt forces (otherwise the maximum bolt forces would have been limited by the associated yielding capacity of the steel beam).

The forces provided in the input data section were transferred to the end of members so that the overall equilibrium is preserved.

The following figures illustrate the principal characteristics of the finite element model developed for the connection analysis.

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Figure 3. The outer concrete region along with longitudinal and tie reinforcement

Figure 4. The inner concrete region along with vertical joint reinforcement connected to the steel

beam flanges

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Figure 5. The core steel column (left) and steel beam ends with vertical joint reinforcement (right)

Bolt stiffness

The forces developed in bolts are directly related to the stiffness ratio between the three contributors to the joint shear resistance and bolt stiffness. Therefore, an accurate calculation of bolt stiffness is required to identify properly the tributary forces to the bolts.

The following two section presents the tension and shear stiffness for a single bolt.

Tension stiffness

The tension stiffness of bolts is calculated using the following equation:

7 2

tensionb

EA 2.1 10 ( 0.024 / 4)k 211115 (Mp/m)

l (0.02 0.025)

⋅ ⋅ π ⋅= = =

+ (31)

Shear Stiffness

The shear stiffness is calculated conservatively as the maximum between Eurocode 3 Appendix J [19] and Rex ref. [18]. (Note that this stiffness includes only the bearing stiffness for a bolt against a single plate).

Eurocode 3:

shear,bearingb b t b uk 24 k k d F 24 1.25 2.3 24 345 57132 Mp/m= ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ = (32)

Where (1Mp=1megapond ≈1tf)

• kb is conservatively considered as 1.25 (kb=Le/4db<1.25, Le is the end distance, db is bolt diamter),

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• kt = 1.5tp/dm16=1.5⋅25/16=2.3<2.5 (tp is the plate thickness ~25mm, dm16 is nominal diameter of M16 bolt -16mm),

• Fu is the ultimate stress ~345Mpa

According to equations 12, 13 and 14 from Rex [18] (assuming standard hole size and an initial bearing deformation of 0.102mm):

shear,bearing 0.8b p y b

0.8

k 120 t F (d / 25.4)

120 25 240 (24 / 25.4) 68807 Mp/m

= ⋅ ⋅ ⋅ =

= ⋅ ⋅ ⋅ = (33)

shear,bending 3b p e b

3 6

k 32Et (L /d 1/ 2)

32 210000 25 (50/ 24 1/ 2) 66.68 10 Mp/m

= − =

= ⋅ ⋅ ⋅ − = ⋅ (34)

shear,shearingb p e b

6

k 6.67 G t (L /d 1.2)

6.67 80769 25 (50/ 24 1.2) 1.19 10 Mp/m

= ⋅ ⋅ ⋅ − =

= ⋅ ⋅ ⋅ − = ⋅ (35)

The proposed prediction model of Rex [18] shown that the initial stiffness depends on three primary stiffness values in the plate. The stiffness associated with bending, shearing and bearing combine to determine the final initial stiffness. The model that accounts for these three stiffness values is simply three springs in series. The final stiffness is given by Blevins [20]:

shearb

shear,bearing shear,bending shear,shearingb b b

6 6

1k

1 1 1

k k k

164983 Mp/m

1 1 1

68807 66.68 10 1.19 10

= =

+ +

= =

+ +⋅ ⋅

(36)

Analysis Results

This section presents the analysis results from the finite element analysis of the connection. The stress diagrams presented in the following Figures provides information in Mp/m2

• Figure 6 presents the crack distribution along with the compressive stress field in the inner joint region. The thickness of the inner joint region (an implicitly the thickness of its finite plane-stress elements) was considered equal to the beam flange width – 350mm. The maximum principal compressive stress in the strut is roughly 20MPa. Two compressive diagonal struts were developed – due to presence of the flange steel-column. The maximum bearing stress is already attained – but is very localized and since the model disregarded the steel band plates this not represents a concern

(maximum strain is 4⋅10-3 which is acceptable in case of strong confinement provided by the steel band plates above and below the steel beam).

• Figure 7 presents the crack distribution along with the compressive stress field in the outer joint region. The effective thickness (bo) of this contributor to the shear resistance of the joint was considered as the remaining thickness of the effective joint width bj (657-350=307mm). The overall maximum compressive stress in the diagonal strut is approximately 25MPa. Same considerations as stated at previous point apply.

• Figure 8 shows the normal stress developed in the beam and also the von Mises effective stress developed in the steel panel of the core column.

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• The structural steel of adjacent beams was modeled using elastic material (to allow for application of capacity bending moment of composite section – including slab – otherwise the bending moment would have been limited by the yielding capacity of the beam). This assumption lead to occurrence of excessive stress in the beam – moreover this means that the beam yields at a considerable lower loading level (506MPa/(240MPa ·1.35)=1.56).

• The steel panel of the core column remains below the yielding limit (max. stress in the steel panel ≅ 315MPa) – the von Mises stress diagram is presented at right of Figure 8.

• Figure 9 presents the distribution of the contact forces. The principal contact relationships was set between:

- Concrete – steel beam flanges and face bearing plates

- Concrete – steel column flanges

- Concrete – connection flange plates

- Connection flange plates – beam flanges

Figure 10 illustrates the position of the bolts. The maximum encountered tension force was 477kN/2rows=238kN – this force was identified only at one exterior bolt from the bottom flange associated with the capacity bending moment of the composite section. This force is unlikely to occur due to limitation of the steel beam capacity which yields at a significant lower loading level. Even though, the remaining bolts exhibit forces of 257/2rows=129kN which allows for redistribution of the loading in case of failure of the exterior bolt. (The tension capacity of a M24 bolt Gr.10.9 is 202kN).

In case of shear loading of the same group of bolts located on the beam flange, the maximum shear force for a single bolt disregarding the exterior one, is 520kN/2rows = 260kN. The capacity of a single bolt M24 Gr.10.9 in shear is the minimum between (shear=196kN; bearing=81.6x2.5=204kN) = 196kN. Therefore the capacity is exceeded by 260/196 = 32%. Considering that the beam yields at 1/1.56=0.64 loading level – the actual safety factor is (196/260)·1.56=1.18, which means that the beam attains its capacity before failure of bolts.

The flange connection is not critical even in case that its capacity might be exceeded, since the shear resistance of the joint is provided by the steel panel – which in our case is given by the beam web + column web + shear tabs. Therefore, the critical connection is along the path of this mechanism.

The web connection (which is important in order to assure a proper shear capacity of the joint) was done using 4 group of bolts located at the end of the compressive-tensile-diagonals present in the steel panel as shown at the right of Figure 8. The maximum bolt shear force is 180kN < 195kN (OK).

Note that these forces are conservative estimates since the slab was not considered in analysis. Moreover, the design strength of the bolts was conservatively taken into account instead of the average yield strength of bolts.

For instance, a simple calculation shows that the ratio between the bending moment of the composite section calculated using average strengths (5150kNm) to the bending moment of the same section but using this time the design strengths (3900kNm) is 5150/3900=1.32. The maximum bolt shear load should be divided by this value (260kN/1.32=196kN) to be consistent with the bolt design shear strength of 196kN – which further leads to a safety factor of 1. However, this safety factor reflects the fact that the entire bending moment associated to the composite section (including the concrete slab) is to be resisted only by the bolts – which is still conservative.

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Figure 6. Crack distribution and Concrete state in the inner joint region

Figure 7. Crack distribution and Concrete state in the outer joint region

Zone confined by

steel band plates

Principal

compressive stress

vs. loading function

Principal

compressive strain

vs. loading function

Co

mp

ress

ive

dia

go

na

l st

rut

Principal

compressive stress

vs. loading function

Principal

compressive strain

vs. loading function

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Figure 8. Stress state in the structural steel

Figure 9. Contact forces distribution

This region

indicates a large

exceedance of yield

stress � beam

yields

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Figure 10. Bolted Connection Configuration

Conclusions

The success of a connection design in terms of deformation and strength is directly related to the overall behavior of the building. Apparently, for a regular concrete building this goal may be attain more easily, but for a composite structure this may be challenging. The success of connection design (in terms of stiffness and strength) directly affects the response of the building and implicitly the possibility to meet the target drift ratio, therefore special care have to be provided to particular connection types, especially if they have not been tested enough.

The connection was evaluated using ASCE guidelines [1] (the load and resistance factors were considered in a consistent manner – see discussion). Also, a finite element model was developed to determine the bolt forces by appropriately accounting for contact relationships between main contributors to the shear resistance of the joint.

References:

1. ASCE Task Committee on Design Criteria for Composite Structures in Steel and Concrete –

“Guidelines for Design of Joints between Steel Beams and Reinforced Concrete Columns”. ASCE Journal of Structural Engineering, Vol. 120, No. 8, August, 1994.

2. Universitatea Tehnica de Constructii Bucuresti – “Cod de Proiectare pentru Structuri din Beton Armat cu Armatura Rigida”. NP033-99. MLPAT ord. nr.61/N. august 1999.

3. Dalban C., Chesaru E., Dima S., Serbescu C. – “Constructii cu structura metalica”. Editura didactica si pedagogica Bucuresti. 1997.

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4. Institutul Roman de Standardizare – “Calculul si alcatuirea elementelor structurale din beton, beton armat si beton precomprimat”. STAS 10107/0-90.

5. Institutul Roman de Standardizare – “Calculul Elementelor de Otel”. STAS 10108/0-78.

6. Arhitectural Institute of Japan – “AIJ Standards for Structural Calculation of Steel Reinforced Concrete Structures”. 1987

7. EUROCODE Editorial Group – “Design of Composite Steel and Concrete Structures”. Eurocode No.4. Prepared for the Commission of the European Communities. 1992

8. Bugeja M, Bracci J. M., Moore W. P. – “Seismic Behavior of composite RCS Frame Systems”. ASCE Journal of structural engineering Vol. 126, No. 4. April 2000.

9. Parra-Montesinos G., Wight J. K. – “Seismic Response of Exterior RC Column-to-Steel Beam Connections”. ASCE Journal of structural engineering. Vol. 126, No. 10, October 2000.

10. Bracci J. M., Moore W. P., Bugeja M. N. – “Seismic Design and Constructability of RCS Special Moment Frames”. ASCE Journal of Structural Engineering. Vol. 125, No. 4, April, 1999.

11. Deierlein G., Noguchi H. – “Overview of US-Japan Research on the Seismic Design of Composite Reinforced Concrete and Steel Moment Frame Structures”. ASCE Journal of Structural Engineering. Vol. 130 No. 2, February 2004.

12. Liang X., Parra-Montesinos G. – “Seismic Behavior of Reinforced Concrete Column-Steel Beam Subassemblies and Frame Systems”. ASCE Journal of Structural Engineering. Vol. 130. No. 2, February 2004.

13. Nishiyama I., Kuramoto H., Noguchi H. – “Guidelines: Seismic Design of Composite Reinforced Concrete and Steel Buildings”. ASCE Journal of Structural Engineering. Vol. 130. No. 2. February 2004.

14. Kuramoto H., Hishiyama I. – “Seismic Performance and Stress Transferring Mechanism of Through-Column-Type Joints for Composite Reinforced Concrete and Steel Frames”. ASCE Journal of Structural Engineering. Vol. 130. No. 2 February 2004.

15. SOLVIA Engineering AB – “SOLVIA Finite Element System”. Version 03. 1987-2006. Sweden.

16. INCERC Bucuresti – “Cod de practica pentru executarea lucrarilor din beton, beton armat si beton precomprimat”. Indicativ NE 012-99

17. American Concrete Institute – “Building CODE requirements for structural concrete”. ACI318M-02. ACI Committee 318. 2002

18. Rex C. O., Easterling W. S. – “Behavior and Modeling of a Bolt Bearing on a Single Plate”. ASCE Journal of Structural Engineering. Vol.126. No.6. June 2003.

19. EUROCODE 3 – “Design of Steel Structures”. Commission of the European Communities, Brussels. 1993

20. Blevins R. D. – “Formulas for natural frequency and mode shape”. Krieger Publishing Company. Malabar, Florida. Reprinted edition 2001.