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Contents

1. End Plate Beam Splice Connection

1.1 General1.2 Equivalent -stub1.3 Welds1.4 Moment resistance1.5 Shear resistance1.6 Rotational stiffness

2. Input data of the connection

2.1 Data of Column2.2 Data of Beam

2.3 Connection Details2.4 Bolts

3. Strength Results - Node : -99 LC : -99

3.1 Applied Moments and Forces3.2 Stiffness Results3.3 Column's Web in shear - Full Results3.4 Column's Web In Compression - Full Results3.5 Beams Flange And Web In Compression - Full Results3.6 Column's Flange in Bending - Full Results3.7 Column's Web In Tension - Full Results3.8 End Plate in Bending - Full Results3.9 Beams Web In Tension - Full Results3.10 End Plate in Bending - Full Results (Mz)3.11 Column's Flange in Bending - Full Results (Mz)3.12 Strength Results (My)3.13 Strength Results (Mz)3.14 Connection's Final Strength3.15 Strength Results (Vz)3.16 Strength Results (Vy)3.17 Connection's Final Strength (V)3.18 Strength of the Welds

4. Summary4.1 Summary Table4.2 Legend

1. End Plate Beam Splice Connection

1.1 General


2/23

The is based on the "basic component method". This method calculatesthe connection final strength from the resistances of it's "basiccomponents".

The "basic components" are:

a) End plate in bending

The resistance and the failure mode of an end plate in bending togetherwith the associated bolts in tension is considered similar to those of anequivalent T-stub for both: each individual bolt-row required to resist tension each group of bolt-rows required to resist tension

b) Beam flange and web in compression

The resistance of the beam flange and the adjacent compression zone of the beam web is obtained by the formula:

Fc,fb,Rd = M b,Rd / ( h - t Fb ) ( J 3.5.7)

c) Beams web in tension

In the case of bolted connection the resistance of the beam's web intension is obtained by the formula:

Ft,wb,Rd = b eff,t,wb * t wb * f y,wb / mo ( J 3.5.8)Where the effective width b eff,t,wb of the web is taken as equal to theeffective length of the equivalent T-stub representing the end plate inbending.

1.2 Equivalent -stub

As said before the modeling of the equivalent T-stub is used in order tocalculate the resistance of some of the connection's "basic components".

The components of the connection are modeled as T-stubs and examinedindividually or as bolt groups.


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Three possible modes of failure are taken into account which are thefollowing:

a) Complete yielding of the flange

mRd,1plM4

Rd,TF =

b) Bolt failure with yielding of the flange

nm

Rd,tBnRd,2plM2

Rd,TF

+

+=

c) Bolt failure

Rd,tBRd,TF =

1.3 Welds

In addition to the checks of the "basic components", the check of theresistance of the welds between the beam and the end plate is beingperformed, using the following formulas (EC3 Annex M):


4/23

)Mww/(uf )2

//2(32 ++

Mwu /f where : - = N sd /Aw + y,sd / w y + M z,sd / w z

wsd,z A/V=

wsd,y// A/V=

1.4 Moment resistance

The final moment resistance of the connection is obtained from theformula:

=r

Rd,tr Fr hRd, jM

where :Ftr,Rd id the effective tension resistance of bolt row rh r is the distance of the bolt row r from the center of the

compression

1.5 Shear resistance

Concerning the resistance of the connection in shear the followingchecks are performed:

a) resistance of the bolts in shearb) resistance of the blades in bearingc) resistance in slipping (prestressed bolts)

The strength of a bolt in shear is being calculated by using the followingEC3 formulas :

mb

sf nbf 6,0

Rd,vf

=

, for 4.6 / 5.6 / 8.8 bolt qualities

mb

sf nbf 5,0Rd,vf

=, for 4.8 / 5.8 / 10.9 bolt qualities

mb

f nbf 6,0Rd,vf

=, for all the bolt qualities when the shear plane passes

through the unthreaded portion of the bolt The strength of the end plate in bearing is being calculated by using theformula :

mb

tnbf 5,2Rd,bf

=

The contribution of one bolt to the strength of the connection in slippingis being calculated by using the following EC3 formula :

ms

Cd,pf nsk

Rd,sf

=

The strength in shear of the bolts that are simultaneously tensioned andsheared is being reduced as follows:


5/23

boltsdprestressenotfor ,0.1Rd,tF4.1

Sd,tF

Rd,vFSd,vF +

B)(categoryboltsdprestressefor ,ser ,M

)F*8.0F(nskser ,Rd,sf

ser ,Sd,tCd,P

=

C)(categoryboltsdprestressefor ,ult,M

)F*8.0F(nskRd,sf

Sd,tCd,P

=

The resistance in shear for each bolt row is the minimum result of theabove checks and the final resistance of the connection in shear is foundby adding the resistances of all the bolt rows of the connection.

1.6 Rotational stiffness

The procedure of the solution is described in the Annex J of EC3 in theparagraph J.4. The rotational stiffness of the joint is determined by theflexibility of the "basic components" through the elastic stiffnesscoefficient k

ias shows the next EC3 formula :

=

i i

2

j

k1

zES

(J.34)where:

k j is the stiffness coefficient of the "basic component" iz is the lever arm

is the fraction of the stiffness S j,ini /S jS j,ini is the initial rotation stiffness given by the same expression

(J.34) with =1.0When elastic global analysis is used the joints should be classifiedaccording to their stiffness.

In the case of a semi-rigid joint its rotational stiffness should be taken asequal to the value of Sj.As a simplification the rotational stiffness may be taken equal to: S J,ini when M J,Sd does not exceed 2/3 M J,Rd S J,ini /n when M J,Sd exceeds 2/3 M J,Rd

Simplified bi-linear design moment-rotation characteristic

Steel connections program calculates both values of S J and S J,ini .


6/23

These joints are classified as rigid, nominally pined or semi-rigidaccording to its stiffness through the comparison of their rotationalstiffness S J,ini and the boundaries given by EC3 Annex J, which are:

Braced frames Unbraced framesZone 1: rigid, if S J,ini 8EI/L b Zone 1: rigid, if S J,ini 25EI/L b

Zone 2: semi-rigid Zone 2: semi-rigidZone 3: nom.pinned , if S J,ini 0.5EI/L b Zone 3: nom.pinned, if S J,ini 0.5EI/L b

Boundaries for stiffness clasification

2. Input data of the connection


7/23

BTMP3

2.1. Data of Column

Type.................................................................. Welded

Steelgrade............................................................Fe510

Height.................................................................. 2000 mm

Width................................................................... 2000 mm

Webthickness............................................................. 50 mm

Flangethickness..........................................................50 mm

2.2. Data of Beam

Type.................................................................. Welded

Steelgrade............................................................Fe510

Height................................................................... 300 mm

Width.................................................................... 150 mm

Webthickness............................................................. 10 mm

Flangethickness..........................................................20 mm


8/23

2.3. Connection Details

Connection type..............................................Apex Connection

Number ofBeams............................................................ 2

Steelgrade............................................................Fe510

End plate'sHeight....................................................... 320mm

End plate'sWidth........................................................ 150mm

End plate'sThickness..................................................... 25mm

Weld thicknessAf.......................................................... 5 mmWeld thickness

Aw.......................................................... 5 mm

2.4. Bolts

Boltstype...............................................................M24

Bolt's steelgrade...................................................... 10.9

Number of boltrows........................................................ 2Number of bolt

columns..................................................... 2Distance

W................................................................90 mm

Edgedistance............................................................. 30 mm

DistanceH(1)............................................................100 mm

Top edgedistance........................................................100 mm

Bottom edgedistance..................................................... 120mm


9/23

3. Strength Results - Node : -99 LC : -99

BTMP4

3.1. Applied Moments and Forces

Moment left(KNm) = 85.00Shear left = 21.11Axial left = 200.89

Moment right(KNm) = 85.00Shear right = 21.11Axial right = 200.89

3.2. Stiffness Results

K5(1)=................................................................57.34

K10(1)=................................................................5.65

K5(2)


10/23

=................................................................57.91

K10(2)=................................................................5.65

Keq=...................................................................8.38

Zone=..................................................................... 2

3.3. Column's Web in shear - Full Results

Not checked because Beta = 0 (no shear in web panel)

3.4. Column's Web In Compression - Full Results

TwcEff.................................................................. 0.00 mm

BeffComp................................................................ 0.00 mm

LamdaP.................................................................. 0.00

Omega................................................................... 0.00

Sigma,comp.............................................................. 0.00 MPa

Kwc..............................................................

....... 0.00FcwcRd...........................................................

....... 0.00

3.5. Beams Flange And Web In Compression - Full Results

Av,b.................................................................... 0.00 mm

VplbRd.................................................................. 0.00 kN

McRd.................................................................... 0.00 kNmm

FcfbRd.................................................................. 0.00 kN

FcfbRd(1)............................................................. 654.65 kN

FcfbRd(2)............................................................ 1162.97 kN


11/23

3.6. Column's Flange in Bending - Full Results

Bolt Row 1 (Unstiffened Column Flange - End Bolt Row (Last Floor))Geometrical Parameters

Ec.................................................................... 955.00 mm

E1c................................................................... 100.00 mm

Ep..................................................................... 30.00 mm

Emin................................................................... 30.00 mm

Mc..................................................................... 20.00 mm

Nc..................................................................... 25.00 mm

P................................................................

..... 100.00 mmEffective Lengths Calculation as Individual Bolt RowCircular Pattern for Row 1

2*PI*mc............................................................... 125.66 mm

PI*mc +2*E1c.........................................................262.83 mm

EffectiveLength...................................................... 125.66mmOther Pattern for Row 1

4*mc +1.25*Ec.......................................................1273.75 mm

2*mc + 0.625*Ec +E1c................................................. 736.88 mm

EffectiveLength...................................................... 736.88mm

Mpl1,Rd............................................................. 25346.94 kNmm

Mpl2,Rd............................................................ 148631.00 kNmm

Fmode1...........................................................

.... 5069.39 kNFmode2...........................................................

.... 6888.22 kNFmode3...........................................................

..... 508.32 kN

Fmin.................................................................. 508.32 kNEffective Lengths Calculation as Member of Bolts GroupCircular Pattern for Row 1


12/23

PI*mc +P.............................................................162.83 mm

2*E1c +P.............................................................300.00 mm

EffectiveLength...................................................... 162.83mmOther Pattern for Row 1

2*mc + 0.625*Ec +0.5*P............................................... 686.88 mm

E1c +0.5*P...........................................................150.00 mm


Group of bolts from row 2 to row 1

Effective Length CircularPattern..................................... 325.66 mm

Effective Length OtherPattern........................................ 836.88 mm

Mpl1,Rd............................................................. 65687.85 kNmm

Mpl2,Rd............................................................ 168801.50 kNmm

Fmode1.............................................................. 13137.57 kN

Fmode2............................................................... 8067.09 kN

Fmode3............................................................... 1016.64 kN

Fmin................................................................. 1016.64 kN

Fmin-FtRd(2)..........................................................508.32 kN

Final Strength FtcfbRd (1)............................................ 508.32 kN

Bolt Row 2 (Unstiffened Column Flange - End Bolt Row)Geometrical Parameters

Ec.................................................................... 955.00 mm

E1c................................................................... 100.00 mm

Ep..................................................................... 30.00 mm

Emin................................................................... 30.00 mm

Mc..................................................................... 20.00 mm


13/23

Nc..................................................................... 25.00 mm

P..................................................................... 100.00 mm

Effective Lengths Calculation as Individual Bolt RowCircular Pattern for Row 2

2*PI*mc............................................................... 125.66 mmOther Pattern for Row 2

4*mc +1.25*Ec.......................................................1273.75 mm

Mpl1,Rd............................................................. 25346.94 kNmm

Mpl2,Rd............................................................ 256921.20 kNmm

Fmode1............................................................... 5069.39 kN

Fmode2.............................................................. 11701.12 kN

Fmode3................................................................ 508.32 kN


PI*mc +P.............................................................162.83 mmOther Pattern for Row 2

2*mc + 0.625*Ec +0.5*P............................................... 686.88 mm


3.7. Column's Web In Tension - Full Results

twc,eff................................................................ 50.00 mm

Bolt Row 1


Omega................................................................... 1.00

FtwbRd............................................................... 2027.76 kN

Group of bolts from row 2 to row 1Effective


14/23

Length...................................................... 325.66mm

Omega................................................................... 1.00

Fmin................................................................. 5255.03 kN

Fmin-FtRd(2)............................................................0.00 kN

Final Strength FtwcRd (1)............................................ 2027.76 kN

Bolt Row 2Effective

Length...................................................... 125.66mm

Omega................................................................... 1.00

FtwbRd...........................................................

.... 2027.76 kN

Final Strength FtwcRd (2)................. 1000000000000000000000000000000.00 kN

3.8. End Plate in Bending - Full Results

Bolt Row 1 (Other End Bolt Row)Geometrical Parameters

Ec.................................................................... 955.00 mm

Ep..................................................................... 30.00 mm

Emin................................................................... 30.00 mm

ex...................................................................... 0.00 mm

Mp..................................................................... 34.34 mm

Mxp.................................................................... 94.34 mm

P..................................................................... 100.00 mm

m................................................................

...... 34.34 mmn................................................................

...... 30.00 mm


2*PI*Mp............................................................... 215.78 mmOther Pattern for Row 1

4*Mp +


15/23

1.25*Ep........................................................174.87 mm

Mpl1,Rd.............................................................. 8818.15 kNmm

Mpl2,Rd.............................................................. 8818.15 kNmm

Fmode1............................................................... 1027.06 kN

Fmode2................................................................ 511.10 kN

Fmode3................................................................ 508.32 kN


PI*Mp +P.............................................................

207.89 mmOther Pattern for Row 1

2*Mp + 0.625*Ep +0.5*p............................................... 137.44 mm

Group of bolts from row 2 to row 1Effective Length Circular

Pattern..................................... 415.78 mmEffective Length Other

Pattern........................................ 276.61 mm

Mpl1,Rd............................................................. 13948.23 kNmm

Mpl2,Rd............................................................. 13948.23 kNmm

Fmode1............................................................... 1624.57 kN

Fmode2................................................................ 907.57 kN

Fmode3............................................................... 1016.64 kN

Fmin.................................................................. 907.57 kN

Fmin-FtRd(2)..........................................................399.25 kN

Final Strength FtepbRd (1)............................................ 399.25 kN

Bolt Row 2 (First Bolt Row Below Tensioned Flange of Beam)Geometrical Parameters

Ec.................................................................... 955.00 mm

Ep..................................................................... 30.00 mm


16/23

Emin................................................................... 30.00 mm

ex...................................................................... 0.00 mm

Mp..................................................................... 34.34 mm

Mxp.................................................................... 94.34 mm

P..................................................................... 100.00 mm

m...................................................................... 34.34 mm

n...................................................................... 30.00 mm

Effective Lengths Calculation as Individual Bolt RowLamda1...........................................................

....... 0.53Lamda2...........................................................

....... 1.16

alpha................................................................... 5.14Circular Pattern for Row 2


alfa*Mp............................................................... 176.61 mm

Mpl1,Rd.............................................................. 8905.62 kNmm

Mpl2,Rd.............................................................. 8905.62 kNmm

Fmode1............................................................... 1037.25 kN

Fmode2................................................................ 513.82 kN

Fmode3................................................................ 508.32 kN


PI*Mp +P.............................................................207.89 mm

Other Pattern for Row 20.5*p + alfa*Mp - (2*Mp +

0.625*Ep)................................... 139.17 mm


3.9. Beams Web In Tension - Full Results


17/23

Bolt Row 1Effective

Length...................................................... 174.87mm

FtwbRd................................................................ 564.36 kN

Group of bolts from row 2 to row 1Effective

Length...................................................... 276.61mm

Fmin.................................................................. 892.69 kN

Fmin-FtRd(2)..........................................................384.37 kN

Final Strength FtwbRd (1)............................................. 384.37 kN

Bolt Row 2Effective

Length...................................................... 176.61mm

FtwbRd................................................................ 569.96 kN

Final Strength FtwbRd (2)............................................. 569.96 kN

3.10. End Plate in Bending - Full Results (Mz)

Bolt Row 1 (First Internal Row)Effective Lengths Calculation as Individual Bolt Row

Lamda1.................................................................. 1.16

Lamda2.................................................................. 0.53

alpha................................................................... 4.45Circular Pattern for Row 1

2*PI*Mp..........................................................

..... 215.78 mmOther Pattern for Row 1

alfa*Mp............................................................... 152.83 mm

Mpl1,Rd.............................................................. 7706.48 kNmm

Mpl2,Rd.............................................................. 7706.48 kNmm

Fmode1...........................................................


18/23

..... 770.65 kNFmode2...........................................................

..... 306.63 kNFmode3...........................................................

..... 254.16 kN

Fmin.................................................................. 254.16 kN


Bolt Row 2 (Last Internal Row)Effective Lengths Calculation as Individual Bolt Row

Lamda1.................................................................. 1.47

Lamda2.................................................................. 0.53

alpha................................................................... 4.45

Circular Pattern for Row 22*PI*Mp..........................................................

..... 215.78 mmOther Pattern for Row 2

alfa*Mp............................................................... 152.83 mm

Mpl1,Rd.............................................................. 7706.48 kNmm

Mpl2,Rd.............................................................. 7706.48 kNmm

Fmode1................................................................ 770.65 kN

Fmode2................................................................ 306.63 kN

Fmode3................................................................ 254.16 kN

Fmin.................................................................. 254.16 kN


3.11. Column's Flange in Bending - Full Results (Mz)

Bolt Row 1 (Generic Bolt Row)Geometrical Parameters

Mc..................................................................... 20.00 mm

Nc..................................................................... 25.00 mm



19/23


PI*Mp +2*e1..........................................................122.83 mm

Mpl1,Rd............................................................. 24775.74 kNmm

Mpl2,Rd............................................................. 24775.74 kNmm

Fmode1............................................................... 2477.57 kN

Fmode2................................................................ 691.77 kN

Fmode3................................................................ 254.16 kN

Fmin.................................................................. 254.16 kN


Bolt Row 2 (Generic Bolt Row)Geometrical Parameters

Mc..................................................................... 20.00 mm

Nc..................................................................... 25.00 mm



PI*Mp +2*e1..........................................................122.83 mm

Mpl1,Rd............................................................. 24775.74 kNmm

Mpl2,Rd............................................................. 24775.74 kNmm

Fmode1............................................................... 2477.57 kN

Fmode2................................................................ 691.77 kN

Fmode3................................................................ 254.16 kN

Fmin.................................................................. 254.16 kN



20/23

3.12. Strength Results (My)

Beam's flange and web in compressionFc,fb,Rd( 1).................... 654.651 kN

End plate in bendingFt,ep,Rd( 1).................................... 399.246 kN

FailureModes..............................................................2

Beam's web in tensionFt,wb,Rd( 1)................................... 384.367 kN

Tension resistance Ftr,Rd of bolt-row1.............................. 240.78 kN

Beam's flange and web in compressionFc,fb,Rd( 2)................... 1162.971 kN

End plate in bendingFt,ep,Rd( 2).................................... 508.320 kN

FailureModes..............................................................3

Beam's web in tensionFt,wb,Rd( 2)................................... 569.960 kN

Tension resistance Ftr,Rd of bolt-row2.............................. 508.32 kN

Bolt's resistance inTension......................................... 254.160 kN

Beam's flange and web in compression checkenabled....................... YES

Applied momentMy,sd................................................... 85.00 KNm

Moment design resistanceMy,Rd........................................ 118.25 KNm

(My,Sd / My,rd) = (85.00 / 118.25) = 0.72 (My,sd/My,Rd) + (Mz,sd/Mz,Rd) = 0.72 + 0.00 = 0.72 < 1 O.K.

3.15. Strength Results (Vz)

Vz,rd(1)=...........................................................186.851 kN

Vz,rd(2)=............................................................80.686 kN

Bolt's resistance inShear........................................... 141.200 kN

Bolt's resistance inBearing......................................... 612.000 kN

Applied shear

Vz,sd.................................................... 21.11 kNShear design resistanceVz,Rd,b....................................... 267.54 kN

(Vz,Sd / Vz,rd) = (21.11 / 267.54) = 0.08 Connection's Strength in Shear of Major AxisMzsd/Mzrd -> Connection's Strength in Moment of Minor AxisVysd/Vyrd -> Connection's Strength in Shear of Minor AxisBiax.Mom -> Connection's Strength in Biaxial BendingBiax.Shr -> Connection's Strength in Biaxial ShearWelds -> Welds Resistance

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