Short Course Worked Example

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Helsinki University of Technology Laboratory of Steel Structures Publications 33 Teknillisen korkeakoulun tersrakennetekniikan laboratorion julkaisuja 31 Espoo 2007 TKK-TER-33

DESIGN OF STRUCTURAL CONNECTIONS TO EUROCODEWorked ExamplesF. Wald

AB

TEKNILLINEN KORKEAKOULU TEKNISKA HGSKOLAN HELSINKI UNIVERSITY OF TECHNOLOGY TECHNISCHE UNIVERSITT HELSINKI UNIVERSITE DE TECHNOLOGIE DHELSINKI

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List of Contents

page 1...Welded connection of tension member ........................................................................... 2...Welds of a fin plate connection ........................................................................................ 3...Welded truss connection ................................................................................................. 4...Welded connection of T cantilever ................................................................................... 5...Bolted connection of tension member ............................................................................. 6...Bolted truss connection .................................................................................................... 7...Bolted slip resistant connection ....................................................................................... 8...Bolted long connection ..................................................................................................... 9...Bolted connection with packing ....................................................................................... 10..Single lap connection with one bolt ................................................................................. 11..Bolted beam splices ......................................................................................................... 12..Beam-to-column welded joint .......................................................................................... 13..Pin connection ................................................................................................................. 14..Simple column base ......................................................................................................... 15..Fixed column base ........................................................................................................... 16..Fin plate connection ......................................................................................................... 17..Header plate connection .................................................................................................. 18..Bolted extended end plate connestion ............................................................................. 19..Extended end plate semirigid joint ................................................................................... 3 4 6 8 10 11 13 14 15 17 18 18 21 25 27 30 32 34 34

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1 Welded Connection of Tension MemberCheck the resistance of the connection of the flat section, shown in Fig. 1.1, loaded in tension by the factored force FSd = 330 kN. The steel is Grade S460N. The material partial safety factors are M 0 = 1,10 and M 2 = 1,25 .10 6 3 3 80 3 330 kN

170

Fig. 1.1 Drawing of the connection_____________________________________________________________________________________________________

The structural welds should be (i) longer than 40 mm, and (ii) longer than 6 aw = 6 3 = 18 mm. Both of these are satisfied. The full length of the weld can be taken into account in the strength calculation, because 150 aw = 50 3 = 450 mm > 170 mm . Longitudinal welds In the longitudinal welds is = = 0 . Based on the fillet welds resistance fu f 2 2 2 and + 3 + // u

aw

_ I

(

)

II _ I

w M 2

M2

is the shear strain

1,4 aw

Fig. 1.2 fu .IIFSd

II .Rd =

3 w M 2

The design resistance is FII .w .Rd = II .Rd awII 2 LwII = .Front weld The equation for the resistance may be at the front weld

550 3 1,0 1,25

II

3 2 170 = 259,1 103 N

LwII

awII

Fig. 1.3

( II .Rd = 0 and = =

w22

) rewritten:Lw aw

w

FSd

w fu + 3 w . w M 2 2 2

2

Fig. 1.4

The front weld design strain is

w .Rd =

fu

w M 2 2

.

The design resistance of the front weld is

3

F.w .Rd = w .Rd aw Lw =

550 1,0 1,25 2

3 80 = 74,7 103 N

Connection resistance The connection resistance isFw .Rd = FII .w .Rd + F.w .Rd = 259,1 + 74,7 = 333,8 kN > FSd = 330 kN .

The connection resistance is satisfactory.P 6 - 300 x 800 80 x 10 - 1 500 3 3 3 170 Steel S460N J2 Scale: 1 : 10

Fig. 1.5 Design drawing of the connection_____________________________________________________________________________________________________

Note: 1) The weld resistance may conservatively be checked independent of the loading direction as follows: Fw .Rd = fu aw Lw = 550 3 ( 2 170 + 80 ) 1,0 1,25 3 = 320,0 10 3 N < FSd = 330 kN . The welds are not satisfactory uder this model. 2) The tension resistance of a member is Nu .Rd = A fy = 80 10 460 = 334,5 103 N > 330 kN . 1,10 The tension resistance is satisfactory.

w M 2

3

M0

2 Welds of a Fin Plate ConnectionVSd = 250 kN

Check the resistance of the fillet-welded connection of the fin plate, shown in Fig. 5.2.1. The connection is subject to the vertical factored force VSd = 250 kN, acting at an eccentricity e = 60 mm. The steel is Grade S235, and the material partial safety factors are M 0 = 1,15 and M 2 = 1,50 .

4 L = 300 e = 60 tp =15

Fig. 2.1 Drawing of the connection The structural welds should be (i) longer than 40 mm, and (ii) longer than 6 au = 6 4 = 24 mm. Both of these are satisfied. The full length of the weld can be taken into account in the strength calculation, because 150 aw = 50 4 = 600 mm > 300 mm . The shear stress perpendicular to the weld cross-section is

4

II =

VSd 250 103 = = 104,2 MPa . aw 2 L 4 2 300

The maximum normal stress parallel to the weld cross-section, based on an elastic distribution of bending stresses is

w =

VSd e M 250 103 60 = = = 125,0 MPa , Wel .w 2 aw L2 2 4 300 2 6 6

which may be decomposed (see Fig. 5.2.2) into the shear across the critical plane (the weld throat) and the normal stress perpendicular to this plane:

= = w

w2

=

125 2

= 88,4 MPa .V Sd 104,2 88,4 88,4

II

L

e

II

_I

_ I

Fig. 2.2Check of the weld design resistance:

2 2 2 + 3 + // = 88,4 2 + 3 88,4 2 + 104,2 2 = 252,6 MPa M Sd = 250 10 3 60 = 15 10 6 Nmm . The interaction of bending and shear need not be checked, because the shear resistance is more than double the shear force acting: 53110 3 / 2 = 266 10 3 N > 250 kN .

3) The elastic distribution of stresses in the welds is used because the above is an elastic check of the fin-plate connection. A plastic check of the welds may be performed, based on the expression VSd e M w = = . W pl .w 2 aw L24

3 Welded Truss ConnectionConnect the tension member of the double equal-leg angle section 2 L 50x5 to the plate P 10 by welds, shown in Fig. 3.1. The steel is Grade S275, and the material partial safety factors are M 0 = 1,10 , M 2 = 1,25 .3 FSd 3 100 P10 - 100 2 L 50 x 5

Fig. 3.1 Drawing of the connection______________________________________________________________________________________________________

The tension member resistance (area of a angle A = 480 mm2) is N pl .Rd = A fy = 2 480 275 = 240,0 103 N . 1,10

M0

Weld at connected leg At the connected flange of the angle may be provided as a fillet weld thicker than 3 mm, and thinner than 3 2 = 4 ,2 < 5 mm . The the force in the weld by the connected leg is

Fw .b =

N pl .Rd e . 2 b

b

e

The weld shear resistance is limited by

w .b =

Fw .b fu aw .b Lb w M 2

3

,

Fig. 3.2

6

which can be rewritten asN pl .Rd e w M 2 3 240 10 3 14,0 0 ,85 1,25 3 Lb = = = 47,9 mm 2 b fu aw .b 2 50 430 31,41 aw.b

Provide Lb = 50 mm.

ab

Fig. 3.3

Weld at free leg The force in the weld by the free leg

. . //.aa

Fw .a =

N pl .Rd ( b e ) 240 ( 50 14 ) = = 86,4 kN . 2 2 50 b

the length may be estimated as L y 2 ,5 Lb a b / a a 150 mm . The shear stress in the weld

II .a

F 86,4 103 = w .a = = 192,0 MPa , 3 150 aw .a La

b

//.bFig. 3.4

The bending moment due to the eccentricity of weld isM w .a = FSd / 2 b 240 0,05 = = 1,5 kNm . 2 2 8

The bending stress is

.a = .a =

M w .a

1

2 2 aw .a La 6

=

1,5 10 6 6 2 3 1502

= 94,3 MPa .

The check of stresses:2 2 2 .a + 3 .a + II .a = 94,3 2 + 3 94,3 2 + 192,0 2 =

(

)

(

)

= 382,3 MPa < fu 420 = 336 MPa . 1,25

fu

w M 2

=

430 = 404 MPa 0,85 1,25

= 67,7MPa N pl .Rd = 229 ,6 kN , 1,10 which is satisfactory.

M0

4 Welded connection of T cantileverCheck the resistance of the welded connection of the cantilever of the T section, shown in Fig. 4.1. The plate is P 10. The column is IPE 300. The connection is subject to the factored force FSd = 25 kN. The steel is Grade S275. The weld is designed 3 mm. The partial safety factor is Mw = 1,50 .

FSd = 25 kN 3 5 P 10 - 350 x 110 300 IPE 300Fig. 4.1 Drawing of the connection

P 10 - 350 x 120

____________