Che materia stai cercando?

Anteprima

### ESTRATTO DOCUMENTO

SU(1 (

(4) For eccentricity in single-sided partial penetration butt welds, see 4.12.

/  E E

The larger of 0,75 and 0,75

we 1

For build-up members in tension:

/  W W

The smallest of 16 and 16 and 200 mm

1 1

For build-up members in compression or shear:

 W W E

/ 12 and 12 and 0,25 and 200 mm

The smallest of 2 1

## )LJXUH,QWHUPLWWHQWILOOHWZHOGV

3OXJZHOGV

(1) Plug welds may be used:

to transmit shear,

– to prevent the buckling or separation of lapped parts, and

– to inter-connect the components of built-up members

but should not be used to resist externally applied tension.

(2) The diameter of a circular hole, or width of an elongated hole, for a plug weld should be at least 8 mm

more than the thickness of the part containing it.

(3) The ends of elongated holes should either be semi-circular or else should have corners which are

rounded to a radius of not less than the thickness of the part containing the slot, except for those ends

which extend to the edge of the part concerned.

SU(1 (

(4) The thickness of a plug weld in parent material up to 16 mm thick should be equal to the thickness of

the parent material. The thickness of a plug weld in parent material over 16 mm thick should be at

least half the thickness of the parent material and not less than 16 mm.

(5) The centre to centre spacing of plug welds should not exceed the value necessary to prevent local

buckling, see Table 3.3.

)ODUHJURRYHZHOGV

(1) For solid bars the design throat thickness of flare groove welds, when fitted flush to the surface of the

solid section of the bars, is defined in Figure 4.2. The definition of the design throat thickness of flare

groove welds in rectangular hollow sections is given in 7.3.1(7).

a

## )LJXUH(IIHFWLYHWKURDWWKLFNQHVVRIIODUHJURRYHZHOGVLQVROLGVHFWLRQV

:HOGVZLWKSDFNLQJV

(1) In the case of welds with packing, the packing should be trimmed flush with the edge of the part that is

to be welded.

(2) Where two parts connected by welding are separated by packing having a thickness less than the leg

length of weld necessary to transmit the force, the required leg length should be increased by the

thickness of the packing.

(3) Where two parts connected by welding are separated by packing having a thickness equal to, or

greater than, the leg length of weld necessary to transmit the force, each of the parts should be

connected to the packing by a weld capable of transmitting the design force.

'HVLJQUHVLVWDQFHRIDILOOHWZHOG

/HQJWKRIZHOGV O

(1) The effective length of a fillet weld should be taken as the length over which the fillet is full-size.

This maybe taken as the overall length of the weld reduced by twice the effective throat thickness a.

Provided that the weld is full size throughout its length including starts and terminations, no reduction

in effective length need be made for either the start or the termination of the weld.

(2) A fillet weld with an effective length less than 30 mm or less than 6 times its throat thickness,

whichever is larger, should not be designed to carry load.

(IIHFWLYHWKURDWWKLFNQHVV

(1) The effective throat thickness, a, of a fillet weld should be taken as the height of the largest triangle

(with equal or unequal legs) that can be inscribed within the fusion faces and the weld surface,

measured perpendicular to the outer side of this triangle, see Figure 4.3.

(2) The effective throat thickness of a fillet weld should not be less than 3 mm.

SU(1 (

(3) In determining the design resistance of a deep penetration fillet weld, account may be taken of its

additional throat thickness, see Figure 4.4, provided that preliminary tests show that the required

penetration can consistently be achieved.

)LJXUH7KURDWWKLFNQHVVRIDILOOHWZHOG

)LJXUH7KURDWWKLFNQHVVRIDGHHSSHQHWUDWLRQILOOHWZHOG

'HVLJQ5HVLVWDQFHRIILOOHWZHOGV

*HQHUDO

(1) The design resistance of a fillet weld should be determined using either the Directional method given

in 4.5.3.2 or the Simplified method given in 4.5.3.3.

'LUHFWLRQDOPHWKRG

(1) In this method, the forces transmitted by a unit length of weld are resolved into components parallel

and transverse to the longitudinal axis of the weld and normal and transverse to the plane of its throat.

$D$ should be taken as = .

(2) The design throat area w w eff

(3) The location of the design throat area should be assumed to be concentrated in the root.

(4) A uniform distribution of stress is assumed on the throat section of the weld, leading to the normal

stresses and shear stresses shown in Figure 4.5, as follows:

is the normal stress perpendicular to the throat

– is the normal stress parallel to the axis of the weld

– is the shear stress (in the plane of the throat) perpendicular to the axis of the weld

– is the shear stress (in the plane of the throat) parallel to the axis of the weld.

SU(1 (

)LJXUH6WUHVVHVRQWKHWKURDWVHFWLRQRIDILOOHWZHOG

(5) The normal stress parallel to the axis is not considered when verifying the design resistance of the

weld.

(6) The design resistance of the fillet weld will be sufficient if the following are both satisfied:

## I I

2 2 2 0,5

+ 3 ( + )] / ( ) and / ... (4.1)

[ u w M2 u M2

where:

I is the nominal ultimate tensile strength of the weaker part joined;

u

is the appropriate correlation factor taken from Table 4.1.

w

(7) Welds between parts with different material strength grades should be designed using the properties of

the material with the lower strength grade.

7DEOH&RUUHODWLRQIDFWRU IRUILOOHWZHOGV

w

Standard and steel grade Correlation factor w

(1 (1 (1

S 235 S 235 H S 235 H 0,8

S 235 W

S 275 S 275 H

S 275 H 0,85

S 275 N/NL S 275 NH/NLH

S 275 NH/NLH

S 275 M/ML S 275 MH/MLH

S 355 S 355 H

S 355 N/NL S 355 H S 355 NH/NLH 0,9

S 355 NH/NLH

S 355 M/ML S 355 MH/MLH

S 355 W

S 420 N/NL S 420 MH/MLH 1,0

S 420 M/ML

S 460 N/NL S 460 NH/NLH

S 460 M/ML S 460 NH/NLH 1,0

S 460 MH/MLH

S 460 Q/QL/QL1

6LPSOLILHGPHWKRGIRUGHVLJQUHVLVWDQFHRIILOOHWZHOG

(1) Alternatively to 4.5.3.2 the design resistance of a fillet weld may be assumed to be adequate if, at

every point along its length, the resultant of all the forces per unit length transmitted by the weld

satisfy the following criterion:

)

) ... (4.2)

w,Ed w,Rd

SU(1 (

where:

) is the design value of the weld force per unit length;

w,Ed

) is the design weld resistance per unit length.

5

w, d

(2) Independent of the orientation of the weld throat plane to the applied force, the design resistance per

should be determined from:

unit length F

w,Rd

) I

= a ... (4.3)

w,Rd vw.d

where:

I is the design shear strength of the weld.

vw.d I

(3) The design shear strength of the weld should be determined from:

vw.d

I / 3

## X

I = ... (4.4)

vw.d β γ

Z 0 2

where:

I and are defined in 4.5.3(7).

u w

'HVLJQUHVLVWDQFHRIILOOHWZHOGVDOOURXQG

(1) The design resistance of a fillet weld all round should be determined using one of the methods given in

4.5.

'HVLJQUHVLVWDQFHRIEXWWZHOGV

)XOOSHQHWUDWLRQEXWWZHOGV

(1) The design resistance of a full penetration butt weld should be taken as equal to the design resistance

of the weaker of the parts connected, provided that the weld is made with a suitable consumable which

will produce all-weld tensile specimens having both a minimum yield strength and a minimum tensile

strength not less than those specified for the parent metal.

3DUWLDOSHQHWUDWLRQEXWWZHOGV

(1) The design resistance of a partial penetration butt weld should be determined using the method for a

deep penetration fillet weld given in 4.5.2(3).

(2) The throat thickness of a partial penetration butt weld should not be greater than the depth of

penetration that can be consistently achieved, see 4.5.2(3).

7EXWWMRLQWV

(1) The design resistance of a T-butt joint, consisting of a pair of partial penetration butt welds reinforced

by superimposed fillet welds, may be determined as for a full penetration butt weld (see 4.7.1) if the

total nominal throat thickness, exclusive of the unwelded gap, is not less than the thickness t of the

part forming the stem of the tee joint, provided that the unwelded gap is not more than (W / 5) or 3 mm,

whichever is less, see Figure 4.6(a).

(2) The design resistance of a T-butt joint which does not meet the requirements given in 4.7.3(1) should

be determined using the method for a fillet weld or a deep penetration fillet weld given in 4.5

depending on the amount of penetration. The throat thickness should be determined in conformity with

the provisions for both fillet welds (see 4.5.2) and partial penetration butt welds (see 4.7.2).

SU(1 (

D D  W

+

nom,1 nom,2 F  W/5

The smaller of and 3 mm

nom

)LJXUH(IIHFWLYHIXOOSHQHWUDWLRQRI7EXWWZHOGV

'HVLJQUHVLVWDQFHRISOXJZHOGV

) of a plug weld (see 4.3.5) should be taken as:

(1) The design resistance w,Rd

) = f A , ... (4.5)

w,Rd vw,d w

where

f is the design shear strength of a weld given in 4.5.3.3(4).

vw.d

A is the design throat area and should be taken as the area of the hole.

w

'LVWULEXWLRQRIIRUFHV

(1) The distribution of forces in a welded connection may be calculated on the assumption of either elastic

or plastic behaviour in conformity with 2.4 and 2.5.

(2) It is acceptable to assume a simplified load distribution within the welds.

(3) Residual stresses and stresses not subjected to transfer of load need not be included when checking the

resistance of a weld. This applies specifically to the normal stress parallel to the axis of a weld.

(4) Welded joints should be designed to have adequate deformation capacity. However, ductility of the

welds should not be relied upon.

(5) In joints where plastic hinges may form, the welds should be designed to provide at least the same

design resistance as the weakest of the connected parts.

(6) In other joints where deformation capacity for joint rotation is required due to the possibility of

excessive straining, the welds require sufficient strength not to rupture before general yielding in the

adjacent parent material. , the weld

(7) If the design resistance of an intermittent weld is determined by using the total length tot

) VHHFigure

shear force per unit length should be multiplied by the factor (H+ 4.7.

w,Ed

SU(1 (

)LJXUH&DOFXODWLRQRIZHOGIRUFHVIRULQWHUPLWWHQWZHOGV

&RQQHFWLRQVWRXQVWLIIHQHGIODQJHV

(1) Where a transverse plate (or beam flange) is welded to a supporting unstiffened flange of an I, H or

other section, see Figure 4.8, and provided that the condition given in 4.10(3) is met, the applied force

perpendicular to the unstiffened flange should not exceed any of the relevant design resistances as

follows:

that of the web of the supporting member of I or H sections as given in 6.2.6.2 or 6.2.6.3 as

– appropriate,

those for a transverse plate on a RHS member as given in Table 7.13,

– that of the supporting flange as given by formula (6.20) in 6.2.6.4.3(1) calculated assuming the

– E , of the flange as given in 4.10(2) or

applied force is concentrated over an effective width, eff

4.10(4) as relevant.”

)LJXUH(IIHFWLYHZLGWKRIDQXQVWLIIHQHG7MRLQW

## E

(2) For an unstiffened I or H section the effective width should be obtained from:

eff

W + V + NW

E 2 7

= ... (4.6a)

eff Z I

where:

## W W I I N

N ( / ) ( / ) but ... (4.6b)

= S

, ,

I S \ I \

I is the yield strength of the flange of the I or H section;

y,f

I is the yield strength of the plate welded to the I or H section.

y,p V

The dimension should be obtained from:

## V= U

for a rolled I or H section: ... (4.6c)

– D

V= 2

for a welded I or H section: ... (4.6d)

SU(1 (

(3) For an unstiffened flange of an I or H section , the following criterion should be satisfied:

## I I E



E ( / ) ... (4.7)

## \ S X S S

eff , ,

where:

I is the ultimate strength of the plate welded to the I or H section.

u,p

b is the width of the plate welded to the I or H section.

p

Otherwise the joint should be stiffened.

(4) For other sections such as box sections or channel sections where the width of the connected plate is

E should be obtained from:

similar to the width of the flange, the effective width eff

## E W NW

E = 2W + 5W but + 5 ... (4.8)

eff w f eff w f

127(For hollow sections, see Table 7.13.

## E

E , the welds connecting the plate to the flange need to be designed to transmit the

(5) Even if eff p W I

E assuming a uniform stress distribution.

design resistance of the plate P P y,P M0

/RQJMRLQWV

(1) In lap joints the design resistance of a fillet weld should be reduced by multiplying it by a reduction

to allow for the effects of non-uniform distribution of stress along its length.

factor Lw

(2) The provisions given in 4.11 do not apply when the stress distribution along the weld corresponds to

the stress distribution in the adjacent base metal, as, for example, in the case of a weld connecting the

flange and the web of a plate girder. should be taken as given by:

(3) Generally in lap joints longer than 150D the reduction factor Lw Lw.1

í/ 

= 1,2 /(150D) but ... (4.9)

Lw.1 j Lw.1

where:

/ is the overall length of the lap in the direction of the force transfer.

j

(4) For fillet welds longer than 1,7 metres connecting transverse stiffeners in plated members, the

may be taken as given by:

reduction factor Lw Lw.2

í/ DQG 

= 1,1 /17 but ... (4.10)

Lw.2 w Lw.2 Lw.2

where:

/ is the length of the weld (in metres).

w

(FFHQWULFDOO\ORDGHGVLQJOHILOOHWRUVLQJOHVLGHGSDUWLDOSHQHWUDWLRQEXWWZHOGV

(1) Local eccentricity should be avoided whenever it is possible.

(2) Local eccentricity (relative to the line of action of the force to be resisted) should be taken into account

in the following cases:

Where a bending moment transmitted about the longitudinal axis of the weld produces tension at

– the root of the weld, see Figure 4.9(a);

Where a tensile force transmitted perpendicular to the longitudinal axis of the weld produces a

– bending moment, resulting in a tension force at the root of the weld, see Figure 4.9(b).

SU(1 (

(3) Local eccentricity need not be taken into account if a weld is used as part of a weld group around the

perimeter of a structural hollow section. e

e

(a) Bending moment produces tension at the (b) Tensile force produces tension at the root of

root of the weld the weld

)LJXUH6LQJOHILOOHWZHOGVDQGVLQJOHVLGHGSDUWLDOSHQHWUDWLRQEXWWZHOGV

$QJOHVFRQQHFWHGE\RQHOHJ (1) In angles connected by one leg, the eccentricity of welded lap joint end connections may be allowed for by adopting an effective cross-sectional area and then treating the member as concentrically loaded. (2) For an equal-leg angle, or an unequal-leg angle connected by its larger leg, the effective area may be taken as equal to the gross area. (3) For an unequal-leg angle connected by its smaller leg, the effective area should be taken as equal to the gross cross-sectional area of an equivalent equal-leg angle of leg size equal to that of the smaller leg, when determining the design resistance of the cross-section, see EN 1993-1-1. However when determining the design buckling resistance of a compression member, see EN 1993-1-1, the actual gross cross-sectional area should be used. :HOGLQJLQFROGIRUPHG]RQHV (1) Welding may be carried out within a length 5t either side of a cold-formed zone, see Table 4.2, provided that one of the following conditions is fulfilled: the cold-formed zones are normalized after cold-forming but before welding; – U/W-ratio the satisfy the relevant value obtained from Table 4.2. SU(1 ( 7DEOH&RQGLWLRQVIRUZHOGLQJFROGIRUPHG]RQHVDQGDGMDFHQWPDWHULDO Maximum thickness (mm) Fully killed Generally Strain due to cold r/t Aluminium-killed forming (%) Predominantly Where fatigue steel static loading predominates  (Al   any any any   any 16 any   24 12 24   12 10 12   8 8 10   4 4 6 SU(1 ($QDO\VLVFODVVLILFDWLRQDQGPRGHOOLQJ

*OREDODQDO\VLV

*HQHUDO

(1) The effects of the behaviour of the joints on the distribution of internal forces and moments within a

structure, and on the overall deformations of the structure, should generally be taken into account, but

where these effects are sufficiently small they may be neglected.

(2) To identify whether the effects of joint behaviour on the analysis need be taken into account, a

distinction may be made between three simplified joint models as follows:

simple, in which the joint may be assumed not to transmit bending moments;

– continuous, in which the behaviour of the joint may be assumed to have no effect on the analysis;

– semi-continuous, in which the behaviour of the joint needs to be taken into account in the

– analysis.

(3) The appropriate type of joint model should be determined from Table 5.1, depending on the

classification of the joint and on the chosen method of analysis.

(4) The design moment-rotation characteristic of a joint used in the analysis may be simplified by

adopting any appropriate curve, including a linearised approximation (e.g. bi-linear or tri-linear),

provided that the approximate curve lies wholly below the design moment-rotation characteristic.

7DEOH7\SHRIMRLQWPRGHO

Method of global Classification of joint

analysis

Elastic Nominally pinned Rigid Semi-rigid

Rigid-Plastic Nominally pinned Full-strength Partial-strength

Semi-rigid and partial-strength

Elastic-Plastic Nominally pinned Rigid and full-strength Semi-rigid and full-strength

Rigid and partial-strength

Type of Simple Continuous Semi-continuous

joint model

(ODVWLFJOREDODQDO\VLV

(1) The joints should be classified according to their rotational stiffness, see 5.2.2.

(2) The joints shall have sufficient strength to transmit the forces and moments acting at the joints

resulting from the analysis. 6

(3) In the case of a semi-rigid joint, the rotational stiffness corresponding to the bending moment

j

0 0

0 should generally be used in the analysis. If does not exceed 2/3 the initial rotational

j,Ed j,Ed j,Rd

6

stiffness may be taken in the global analysis, see Figure 5.1(a).

j,ini 6 / in the analysis, for all

(4) As a simplification to 5.1.2(3), the rotational stiffness may be taken as j,ini

0

values of the moment , as shown in Figure 5.1(b), where is the stiffness modification

j,Ed

coefficient from Table 5.2. 6 is given in 6.3.1.

(5) For joints connecting H or I sections j

SU(1 (

M

M j j

j,Rd j,Rd

2/3 M j,Ed

j,Rd

## M

j,Ed S η

S /

j,ini φ

φ j,ini

0  0 0  0

a) 2/3 b)

j,Ed j,Rd j,Ed j,Rd

)LJXUH5RWDWLRQDOVWLIIQHVVWREHXVHGLQHODVWLFJOREDODQDO\VLV

7DEOH6WLIIQHVVPRGLILFDWLRQFRHIILFLHQW

Other types of joints

(beam-to-beam

Beam-to-column

Type of connection joints joints, beam splices,

column base joints)

Welded 2 3

Bolted end-plate 2 3

Bolted flange cleats 2 3,5

Base plates - 3

5LJLGSODVWLFJOREDODQDO\VLV

(1) The joints should be classified according to their strength, see 5.2.3.

0

(2) For joints connecting H or I sections is given in 6.2.

j,Rd

(3) For joints connecting hollow sections the method given in section 7 may be used.

(4) The rotation capacity of a joint shall be sufficient to accommodate the rotations resulting from the

analysis.

(5) For joints connecting H or I sections the rotation capacity should be checked according to 6.4.

(ODVWLFSODVWLFJOREDODQDO\VLV

(1) The joints should be classified according to both stiffness (see 5.2.2) and strength (see 5.2.3).

6 φ

0 is given in 6.2, is given in 6.3.1 and is given in 6.4.

(2) For joints connecting H or I sections j,Rd j Cd

(3) For joints connecting hollow sections the method given in section 7 may be used.

(4) The moment rotation characteristic of the joints should be used to determine the distribution of

internal forces and moments.

(5) As a simplification, the bi-linear design moment-rotation characteristic shown in Figure 5.2 may be

should be obtained from Table 5.2.

SU(1 (

M j

M j,Rd

S /

j,ini 1

Cd

)LJXUH6LPSOLILHGELOLQHDUGHVLJQPRPHQWURWDWLRQFKDUDFWHULVWLF

*OREDODQDO\VLVRIODWWLFHJLUGHUV

(1) The provisions given in 5.1.5 apply only to structures whose joints are verified according to section 7.

(2) The distribution of axial forces in a lattice girder may be determined on the assumption that the

(3) Secondary moments at the joints, caused by the rotational stiffnesses of the joints, may be neglected

both in the design of the members and in the design of the joints, provided that both of the following

conditions are satisfied:

the joint geometry is within the range of validity specified in Table 7.1, Table 7.8, Table 7.9 or

– Table 7.20 as appropriate;

the ratio of the system length to the depth of the member in the plane of the lattice girder is not

– less than the appropriate minimum value. For building structures, the appropriate minimum value

may be assumed to be 6. Larger values may apply in other parts of EN 1993.

(4) The moments resulting from transverse loads (whether in-plane or out-of-plane) that are applied

between panel points, should be taken into account in the design of the members to which they are

applied. Provided that the conditions given in 5.1.5(3) are satisfied:

the brace members may be considered as pin-connected to the chords, so moments resulting from

– transverse loads applied to chord members need not be distributed into brace members, and vice

versa;

the chords may be considered as continuous beams, with simple supports at panel points.

(5) Moments resulting from eccentricities may be neglected in the design of tension chord members and

brace members. They may also be neglected in the design of connections if the eccentricities are

within the following limits:

íG H G ... (5.1a)

– 0 0

íK H K ... (5.1b)

– 0 0

where:

H is the eccentricity defined in Figure 5.3;

G is the diameter of the chord;

0

K is the depth of the chord, in the plane of the lattice girder.

0

(6) When the eccentricities are within the limits given in 5.1.5(5), the moments resulting from the

eccentricities should be taken into account in the design of compression chord members. In this case

the moments produced by the eccentricity should be distributed between the compression chord

SU(1 (

,/ /

members on each side of the joint, on the basis of their relative stiffness coefficients , where is

the system length of the member, measured between panel points.

(7) When the eccentricities are outside the limits given in 5.1.5(5), the moments resulting from the

eccentricities should be taken into account in the design of the connections and the compression chord

members. In this case the moments produced by the eccentricity should be distributed between all the

,/ .

members meeting at the joint, on the basis of their relative stiffness coefficients

(8) The stresses in a chord resulting from moments taken into account in the design of the chord, should

## N N

N , and used in the design of the

also be taken into account in determining the factors m n p

connections, see Table 7.2 to Table 7.5, Table 7.10 and Table 7.12 to Table 7.14.

(9) The cases where moments should be taken into account are summarized in Table 5.3.

7DEOH $OORZDQFHIRUEHQGLQJPRPHQWV Source of the bending moment Type of component Secondary effects Transverse loading Eccentricity Compression chord Yes Tension chord No Not if 5.1.5(3) Yes is satisfied Brace member No Connection Not if 5.1.5(5) is satisfied SU(1 ( &ODVVLILFDWLRQRIMRLQWV *HQHUDO (1) The details of all joints shall fulfil the assumptions made in the relevant design method, without adversely affecting any other part of the structure. (2) Joints may be classified by their stiffness (see 5.2.2) and by their strength (see 5.2.3). &ODVVLILFDWLRQE\VWLIIQHVV *HQHUDO (1) A joint may be classified as rigid, nominally pinned or semi-rigid according to its rotational stiffness, 6 with the classification boundaries given in 5.2.2.5. by comparing its initial rotational stiffness j,ini 127(Rules 6 for joints connecting H or I sections are given in 6.3.1. for the determination of j,ini 6 for joints connecting hollow sections are not given in this Rules for the determination of j,ini Standard. (2) A joint may be classified on the basis of experimental evidence, experience of previous satisfactory performance in similar cases or by calculations based on test evidence. 1RPLQDOO\SLQQHGMRLQWV (1) A nominally pinned joint shall be capable of transmitting the internal forces, without developing significant moments which might adversely affect the members or the structure as a whole. (2) A nominally pinned joint shall be capable of accepting the resulting rotations under the design loads. 5LJLGMRLQWV (1) Joints classified as rigid may be assumed to have sufficient rotational stiffness to justify analysis based on full continuity. 6HPLULJLGMRLQWV (1) A joint which does not meet the criteria for a rigid joint or a nominally pinned joint should be classified as a semi-rigid joint. 127(Semi-rigid joints provide a predictable degree of interaction between members, based on the design moment-rotation characteristics of the joints. (2) Semi-rigid joints should be capable of transmitting the internal forces and moments. &ODVVLILFDWLRQERXQGDULHV (1) Classification boundaries for joints other than column bases are given in 5.2.2.1(1) and Figure 5.4. SU(1 ( (2) Column bases may be classified as rigid provided the following conditions are satisfied: in frames where the bracing system reduces the horizontal displacement by at least 80 % and – where the effects of deformation may be neglected λ  if ... (5.2a) – 0 λ λ 6  (, / if 0,5 < < 3,93 and - 1 ) / ; ... (5.2b) – j,ini c c 0 0 λ  6 (, / if and / . ... (5.2c) – j,ini c c 0 6 (, / otherwise if / . ... (5.2d) – j,ini c c where: λ is the slenderness of a column in which both ends are assumed to be pinned; 0 / , , are as given in Figure 5.4. c c 6 N (, / Zone 1: rigid, if / j,ini b b b where N = 8 for frames where the bracing system b reduces the horizontal displacement by at least 80 % N = 25 for other frames, provided that in every b *)  . /. 0,1 storey b c Zone 2: semi-rigid All joints in zone 2 should be classified as semi-rigid. Joints in zones 1 or 3 may optionally also be treated as semi-rigid. φ 6  (, / Zone 3: nominally pinned, if / j,ini b b *) . For frames where /. < 0,1 the joints b c should be classified as semi-rigid. Key: . , is the mean value of // for all the beams at the top of that storey; b b b . , is the mean value of // for all the columns in that storey; c c c , is the second moment of area of a beam; b , is the second moment of area of a column; c / is the span of a beam (centre-to-centre of columns); b / is the storey height of a column. c )LJXUH&ODVVLILFDWLRQRIMRLQWVE\VWLIIQHVV &ODVVLILFDWLRQE\VWUHQJWK *HQHUDO (1) A joint may be classified as full-strength, nominally pinned or partial strength by comparing its design 0 with the design moment resistances of the members that it connects. When moment resistance j,Rd classifying joints, the design resistance of a member should be taken as that member adjacent to the joint. 1RPLQDOO\SLQQHGMRLQWV (1) A nominally pinned joint shall be capable of transmitting the internal forces, without developing significant moments which might adversely affect the members or the structure as a whole. SU(1 ( (2) A nominally pinned joint shall be capable of accepting the resulting rotations under the design loads. 0 is not greater than (3) A joint may be classified as nominally pinned if its design moment resistance j,Rd 0,25 times the design moment resistance required for a full-strength joint, provided that it also has sufficient rotation capacity. )XOOVWUHQJWKMRLQWV (1) The design resistance of a full strength joint shall be not less than that of the connected members. (2) A joint may be classified as full-strength if it meets the criteria given in Figure 5.5. 3DUWLDOVWUHQJWKMRLQWV (1) A joint which does not meet the criteria for a full-strength joint or a nominally pinned joint should be classified as a partial-strength joint. a) Top of column 0 0 Either j,Rd b,p 5G M 0 0 j,Sd or j,Rd c,p 5G b) Within column height 0 0 Either j,Rd b,p 5G M  0 0 j,Sd or j,Rd c,p 5G Key: 0 is the design plastic moment resistance of a beam; b,p 5G 0 is the design plastic moment resistance of a column. c,p 5G )LJXUH)XOOVWUHQJWKMRLQWV 0RGHOOLQJRIEHDPWRFROXPQMRLQWV (1) To model the deformational behaviour of a joint, account should be taken of the shear deformation of the web panel and the rotational deformation of the connections. 0 0 and , (2) Joint configurations should be designed to resist the internal bending moments b1,Ed b2,Ed 1 1 9 9 normal forces and and shear forces and applied to the connections by the b1,Ed b2,Ed b1,Ed b2,Ed connected members, see Figure 5.6. 9 in the web panel should be obtained using: (3) The resulting shear force wp,Ed í0 í 9 í9 9 = (0 )/z )/2 ... (5.3) wp,Ed b1,Ed b2,Ed c1,Ed c2,Ed where: ] is the lever arm, see 6.2.7. (4) To model a joint in a way that closely reproduces the expected behaviour, the web panel in shear and each of the connections should be modelled separately, taking account of the internal moments and forces in the members, acting at the periphery of the web panel, see Figure 5.6(a) and Figure 5.7. (5) As a simplified alternative to 5.3(4), a single-sided joint configuration may be modelled as a single joint, and a double-sided joint configuration may be modelled as two separate but inter-acting joints, one on each side. As a consequence a double-sided beam-to-column joint configuration has two moment-rotation characteristics, one for the right-hand joint and another for the left-hand joint. SU(1 ( (6) In a double-sided, beam-to-column joint each joint should be modelled as a separate rotational spring, as shown in Figure 5.8, in which each spring has a moment-rotation characteristic that takes into account the behaviour of the web panel in shear as well as the influence of the relevant connection. (7) When determining the design moment resistance and rotational stiffness for each of the joints, the possible influence of the web panel in shear should be taken into account by means of the and , where: transformation parameters 1 2 is the value of the transformation parameter for the right-hand side joint; 1 is the value of the transformation parameter for the left-hand side joint. 2 127(The and are used directly in 6.2.7.2(7) and 6.3.2(1). They transformation parameters 1 2 are also used in 6.2.6.2(4) and 6.2.6.3(4) in connection with Table 6.3 to obtain the reduction factor for shear. 0 0 and based on the values of the beam moments and at (8) Approximate values for 1 2 b1,Ed b2,Ed the periphery of the web panel, see Figure 5.6(a), may be obtained from Table 5.4. a) Values at periphery of web panel b) Values at intersection of member centrelines Direction of forces and moments are considered as positive in relation to equations (5.3) and (5.4) ## )LJXUH)RUFHVDQGPRPHQWVDFWLQJRQWKHMRLQW ## N N b2,Ed b1,Ed ## V V b2,Ed b1,Ed ## M M b2,Ed b1,Ed a) Shear forces in web panel b) Connections, with forces and moments in beams ## )LJXUH)RUFHVDQGPRPHQWVDFWLQJRQWKHZHESDQHODWWKHFRQQHFWLRQV SU(1 ( 1 3 2 [ [ [ Single-sided joint configuration Double-sided joint configuration ## -RLQW ## -RLQWOHIWVLGH ## -RLQWULJKWVLGH )LJXUH0RGHOOLQJWKHMRLQW and based on the values of the beam (9) As an alternative to 5.3(8), more accurate values of 1 2 0 0 moments and at the intersection of the member centrelines, may be determined from j,b1,Ed j,b2,Ed the simplified model shown in Figure 5.6(b) as follows: 0 0  1− / = ... (5.4a) ## M E (G M E (G 1 , 2 , , 1 , 0 0  1− / = ... (5.4b) ## M E (G M E (G 2 , 1 , , 2 , where: 0 is the moment at the intersection from the right hand beam; j,b1,Ed 0 is the moment at the intersection from the left hand beam. j,b2,Ed (10) In the case of an unstiffened double-sided beam-to-column joint configuration in which the depths of the two beams are not equal, the actual distribution of shear stresses in the column web panel should be taken into account when determining the design moment resistance. SU(1 ( 7DEOH$SSUR[LPDWHYDOXHVIRUWKHWUDQVIRUPDWLRQSDUDPHWHU

Type of joint configuration Action Value of

§

0

b1,Ed

0 0

= = 0 *)

b1,Ed b2,Ed

0 0 §

/ > 0

b1,Ed b2,Ed

0 0 §

/ < 0

b1,Ed b2,Ed

0 0 §

+ = 0

b1,Ed b2,Ed

)

* In this case the value of is the exact value rather than an approximation.

SU(1 (

6WUXFWXUDOMRLQWVFRQQHFWLQJ+RU,VHFWLRQV

*HQHUDO

%DVLV

(1) This section contains design methods to determine the structural properties of joints in frames of any

type. To apply these methods, a joint should be modelled as an assembly of basic components, see

1.3(1).

(2) The basic components used in this Standard are identified in Table 6.1 and their properties should be

determined in accordance with the provisions given in this Standard. Other basic components may be

used provided their properties are based on tests or analytical and numerical methods supported by

tests, see EN 1990.

127(The design methods for basic joint components given in this Standard are of general

application and can also be applied to similar components in other joint configurations. However the

specific design methods given for determining the design moment resistance, rotational stiffness and

rotation capacity of a joint are based on an assumed distribution of internal forces for joint

configurations indicated in Figure 1.2. For other joint configurations, design methods for determining

the design moment resistance, rotational stiffness and rotation capacity should be based on appropriate

assumptions for the distribution of internal forces.

6WUXFWXUDOSURSHUWLHV

'HVLJQPRPHQWURWDWLRQFKDUDFWHULVWLF

(1) A joint may be represented by a rotational spring connecting the centre lines of the connected

members at the point of intersection, as indicated in Figure 6.1(a) and (b) for a single-sided beam-to-

column joint configuration. The properties of the spring can be expressed in the form of a design

0

moment-rotation characteristic that describes the relationship between the bending moment j,Ed

φ

applied to a joint and the corresponding rotation between the connected members. Generally the

Ed

design moment-rotation characteristic is non-linear as indicated in Figure 6.1(c).

(2) A design moment-rotation characteristic, see Figure 6.1(c) should define the following three main

structural properties:

moment resistance;

– rotational stiffness;

– rotation capacity.

127(In certain cases the actual moment-rotation behaviour of a joint includes some rotation due to

such effects as bolt slip, lack of fit and, in the case of column bases, foundation-soil interactions. This

can result in a significant amount of initial hinge rotation that may need to be included in the design

moment-rotation characteristic.

(3) The design moment-rotation characteristics of a beam-to-column joint shall be consistent with the

assumptions made in the global analysis of the structure and with the assumptions made in the design

of the members, see EN 1993-1-1.

(4) The design moment-rotation characteristic for joints and column bases of I and H sections as obtained

from 6.3.1(4) may be assumed to satisfy the requirements of 5.1.1(4) for simplifying this characteristic

for global analysis purposes.

SU(1 (

'HVLJQ0RPHQWUHVLVWDQFH 0 , which is equal to the maximum moment of the design

(1) The design moment resistance j,Rd

moment-rotation characteristic, see Figure 6.1(c), should be taken as that given by 6.1.3(4)

5RWDWLRQDOVWLIIQHVV , which is the secant stiffness as indicated in Figure 6.1(c), should be taken as

(1) The rotational stiffness S

j 6

that given by 5.1.1(4). For a design moment-rotation characteristic this definition of applies up to

j

φ 0 0

the rotation at which first reaches , but not for larger rotations, see Figure 6.1(c). The

Xd j,Ed j,Rd

6

initial rotational stiffness , which is the slope of the elastic range of the design moment-rotation

j,ini

characteristic, should be taken as that given by 6.1.3(4).

5RWDWLRQFDSDFLW\ φ

(1) The design rotation capacity of a joint, which is equal to the maximum rotation of the design

Cd

moment-rotation characteristic, see Figure 6.1(c), should be taken as that given by 6.1.3(4).

M j S j,ini

M j,Rd

M J,Ed

90° 1

φ M j,Ed

Ed S φ

j

φ φ φ

Ed Xd Cd

/LPLWIRU6

## M

a) Joint b) Model c) Design moment-rotation characteristic

## )LJXUH'HVLJQPRPHQWURWDWLRQFKDUDFWHULVWLFIRUDMRLQW

%DVLFFRPSRQHQWVRIDMRLQW

(1) The design moment-rotation characteristic of a joint should depend on the properties of its basic

components, which should be among those identified in 6.1.3(2).

(2) The basic joint components should be those identified in Table 6.1, together with the reference to the

application rules which should be used for the evaluation of their structural properties.

(3) Certain joint components may be reinforced. Details of the different methods of reinforcement are

given in 6.2.4.3 and 6.2.6.

(4) The relationships between the properties of the basic components of a joint and the structural

properties of the joint should be those given in the following clauses:

for moment resistance in 6.2.7 and 6.2.8;

– for rotational stiffness in 6.3.1;

– for rotation capacity in 6.4.

SU(1 (

7DEOH%DVLFMRLQWFRPSRQHQWV

Reference to application rules

Component Design Stiffness Rotation

Resistance coefficient capacity

9

## (G

Column web panel 6.2.6.1 6.3.2 6.4(4)

1 in shear 9

## (G

Column web 6.4(5)

In transverse and

2 6.2.6.2 6.3.2

compression 6.4(6)

)

)

## W(G

Column web 6.2.6.3 6.3.2 6.4(5)

3 in transverse

tension )

## W(G

Column flange

4 6.2.6.4 6.3.2 6.4(7)

in bending )

## W(G

End-plate 6.2.6.5 6.3.2 6.4(7)

5 in bending )

## W(G

Flange cleat

6 6.2.6.6 6.3.2 6.4(7)

in bending

SU(1 (

Reference to application rules

Component Design Stiffness Rotation

Resistance coefficient capacity

Beam or column

7 flange and web 6.2.6.7 6.3.2 *)

in compression )

## F(G

Beam web )

8 6.2.6.8 6.3.2 *)

## W(G

in tension ) )

in tension:

W(G W(G - EN 1993-1-1

Plate

in tension or

9 6.3.2 *)

in compression:

compression - EN 1993-1-1

) )

F(G F(G With column flange:

- 6.2.6.4

Bolts with end-plate: 6.3.2 6.4(7)

10 - 6.2.6.5

in tension )

W(G with flange cleat:

- 6.2.6.6

Bolts

11 3.6 6.3.2 6.4(2)

in shear )

)

## E(G

Bolts

in bearing 3.6 6.3.2 *)

12 (on beam flange,

column flange, )

end-plate or cleat)

## E(G

*) No information available in this part.

SU(1 (

Reference to application rules

Component Design Stiffness Rotation

Resistance coefficient capacity

Concrete

13 in compression 6.2.6.9 6.3.2 *)

including grout

Base plate

14 in bending under 6.2.6.10 6.3.2 *)

compression

Base plate in

15 6.2.6.11 6.3.2 *)

bending under

tension

Anchor bolts

16 6.2.6.12 6.3.2 *)

in tension

Anchor bolts

17 6.2.2 *) *)

in shear

Anchor bolts

18 6.2.2 *) *)

in bearing

19 Welds 4 6.3.2 *)

6.2.6.7 6.3.2 *)

20 Haunched beam

*) No information available in this part.

SU(1 (

'HVLJQ5HVLVWDQFH

,QWHUQDOIRUFHV

(1) The stresses due to the internal forces and moments in a member may be assumed not to affect the

design resistances of the basic components of a joint, except as specified in 6.2.1(2) and 6.2.1(3).

(2) The longitudinal stress in a column should be taken into account when determining the design

resistance of the column web in compression, see 6.2.6.2(2).

(3) The shear in a column web panel should be taken into account when determining the design resistance

of the following basic components:

column web in transverse compression, see 6.2.6.2;

– column web in transverse tension, see 6.2.6.3.

6KHDUIRUFHV

(1) In welded connections, and in bolted connections with end-plates, the welds connecting the beam web

should be designed to transfer the shear force from the connected beam to the joint, without any

assistance from the welds connecting the beam flanges.

(2) In bolted connections with end-plates, the design resistance of each bolt-row to combined shear and

tension should be verified using the criterion given in Table 3.4, taking into account the total tensile

force in the bolt, including any force due to prying action.

127(As a simplification, bolts required to resist in tension may be assumed to provide their full

design resistance in tension when it can be shown that the design shear force does not exceed the sum

of:

a) the total design shear resistance of those bolts that are not required to resist tension and;

b) (0,4/1,4) times the total design shear resistance of those bolts that are also required to resist

tension.

(3) In bolted connections with angle flange cleats, the cleat connecting the compression flange of the

beam may be assumed to transfer the shear force in the beam to the column, provided that:

## J

the gap between the end of the beam and the face of the column does not exceed the thickness

– W of the angle cleat;

a

the force does not exceed the design shear resistance of the bolts connecting the cleat to the

– column;

the web of the beam satisfies the requirement given in EN 1993-1-5, section 6.

(4) The design shear resistance of a joint may be derived from the distribution of internal forces within

that joint, and the design resistances of its basic components to these forces, see Table 6.1.

(5) In base plates if no special elements for resisting shear are provided, such as block or bar shear

connectors, it should be demonstrated that either the design friction resistance of the base plate, see

6.2.2(6), or, in cases where the bolt holes are not oversized, the design shear resistance of the anchor

bolts, see 6.2.2(7), is sufficient to transfer the design shear force. The design bearing resistance of the

block or bar shear connectors with respect to the concrete should be checked according to EN 1992.

) between base plate and grout should be derived

(6) In a column base the design friction resistance f,Rd

as follows:

& 1

) = ... (6.1)

f,Rd f,d c,Ed

where:

SU(1 (

& is the coefficient of friction between base plate and grout layer. The following values may be

f,d used: &

for sand-cement mortar = 0,20

– f,d &

for other types of grout the coefficient of friction should be determined by testing in

– f,d

accordance with EN 1990, Annex D;

1 is the design value of the normal compressive force in the column.

c,Ed

127(If )

the column is loaded by a tensile normal force, = 0.

f,Rd ) should be taken as the smaller of

(7) In a column base the design shear resistance of an anchor bolt vb,Rd

)

) and where

1,vb,Rd 2,vb,Rd

) is the design bearing resistance of the anchor bolt, see 3.6.1

3

8

,

8

/ * V

=

b Σ

" W 3

## HII I

,

1

) is the design tension resistance of a T-stub flange

T,Rd

Q is the prying force γ

Σ

" W I

2

0 0

, 25 /

HII I \ 0

=

p 5G ,

1 0

γ

Σ

" W I

2

0 0

, 25 /

HII I \ 0

=

p 5G , 2 0

γ

Σ

" W I

2

0 0

, 25 /

HII ES \ ES 0

=

bp,Rd ,

1 , 0

Q H Q1,25P

= but

min

) is the design tension resistance of a bolt, see Table 3.4;

t,Rd

) )

is the total value of for all the bolts in the T-stub;

t,Rd t,Rd

 

is the value of for mode 1;

eff,1 eff

 

is the value of for mode 2;

eff,2 eff

## P W

H , and are as indicated in Figure 6.2.

min f

I is the yield strength of the backing plates;

y,bp

W is the thickness of the backing plates;

bp

## H G

= / 4;

w w

G is the diameter of the washer, or the width across points of

w the bolt head or nut, as relevant.

127(In bolted beam-to-column joints or beam splices it may be assumed that prying forces

will develop.

127( In method 2, the force applied to the T-stub flange by a bolt is assumed to be uniformly

concentrated at the centre-line of the bolt. This assumption leads to a higher value for mode 1, but

) and modes 2 and 3 unchanged.

leaves the values for T,1-2,Rd

SU(1 (

,QGLYLGXDOEROWURZVEROWJURXSVDQGJURXSVRIEROWURZV

(1) Although in an actual T-stub flange the forces at each bolt-row are generally equal, when an

equivalent T-stub flange is used to model a basic component listed in 6.2.4.1(1), allowance should be

made for the different in forces at each bolt-row.

(2) When using the equivalent T-stub approach to model a group of bolt rows it may be necessary to

divide the group in to separate bolt-rows and use an equivalent T-stub to model each separate bolt-

row.

(3) When using the T-stub approach to model a group of bolt rows the following conditions should be

satisfied:

a) the force at each bolt-row should not exceed the design resistance determined considering only

that individual bolt-row;

b) the total force on each group of bolt-rows, comprising two or more adjacent bolt-rows within

the same bolt-group, should not exceed the design resistance of that group of bolt-rows.

(4) When determining the design tension resistance of a basic component represented by an equivalent

T-stub flange, the following parameters should be calculated:

a) the maximum design resistance of an individual bolt-row, determined considering only that

bolt-row;

b) the contribution of each bolt-row to the maximum design resistance of two or more adjacent

bolt-rows within a bolt-group, determined considering only those bolt-rows.

 should be taken as equal to the effective length

(5) In the case of an individual bolt-row eff eff

tabulated in 6.2.6 for that bolt-row taken as an individual bolt-row.

 should be taken as the sum of the effective lengths

(6) In the case of a group of bolt-rows eff eff

tabulated in 6.2.6 for each relevant bolt-row taken as part of a bolt-group.

%DFNLQJSODWHV

(1) Backing plates may be used to reinforce a column flange in bending as indicated in Figure 6.3.

(2) Each backing plate should extend at least to the edge of the column flange, and to within 3 mm of the

toe of the root radius or of the weld.

(3) The backing plate should extend beyond the furthermost bolt rows active in tension as defined in

Figure 6.3. ) should be determined using

(4) Where backing plates are used, the design resistance of the T-stub T,Rd

the method given in Table 6.2.

H 1

K ES K 

H ES bp eff,1

H G

bp

1 %DFNLQJSODWH

## )LJXUH&ROXPQIODQJHZLWKEDFNLQJSODWHV

SU(1 (

(TXLYDOHQW7VWXELQFRPSUHVVLRQ

(1) In steel- to-concrete joints, the flange of an equivalent T-stub in compression may be used to model

the design resistances for the combination of the following basic components:

the steel base plate in bending under the bearing pressure on the foundation,

– the concrete and/or grout joint material in bearing.

– E

O and the total width of an equivalent T-stub should be such that the design

(2) The total length eff eff

compression resistance of the T-stub is equivalent to that of the basic joint component it represents.

127(The effective length and the effective width of an equivalent T-stub are notional lengths and

may be smaller than or equal to the physical dimensions of the basic joint component it represents.

) should be determined as follows:

(3) The design compression resistance of a T-stub flange C,Rd

## I E O

) = ... (6.4)

C,Rd jd eff eff

where:

E is the effective width of the T-stub flange, see 6.2.5(5) and 6.2.5(6)

eff

O is the effective length of the T-stub flange, see 6.2.5(5) and 6.2.5(6)

eff

I is the design bearing strength of the joint, see 6.2.5(7)

jd

(4) The forces transferred through a T-stub should be assumed to spread uniformly as shown in Figure

6.4(a) and (b). The pressure on the resulting bearing area should not exceed the design bearing

I and the additional bearing width, c, should not exceed:

strength j I

F W 0.5

/ (3 )] ... (6.5)

= [I y j M0

where:

W is the thickness of the T-stub flange;

I is the yield strength of the T-stub flange.

y

(5) Where the projection of the physical length of the basic joint component represented by the T-stub is

## F,

less than the effective area should be taken as indicated in Figure 6.4(a)

(6) Where the projection of the physical length of the basic joint component represented by the T-stub

## F F

exceeds on any side, the part of the additional projection beyond the width should be neglected, see

Figure 6.4(b). F

≤ O

O eff

eff F F

≤ F F

## F

≤ E

E eff

eff

(a) Short projection (b) Large projection

)LJXUH$UHDRIHTXLYDOHQW76WXELQFRPSUHVVLRQ SU(1 ( ## I (7) The design bearing strength of the joint should be determined from: jd ) O I = / (E ) ... (6.6) jd j Rdu eff eff where: is the foundation joint material coefficient, which may be taken as 2/3 provided that the j characteristic strength of the grout is not less than 0,2 times the characteristic strength of the concrete foundation and the thickness of the grout is not greater than 0,2 times the smallest width of the steel base plate. In cases where the thickness of the grout is more than 50 mm, the characteristic strength of the grout should be at least the same as that of the concrete foundation. )$

is the concentrated design resistance force given in EN 1992, where is to be taken as (E

Rdu c0 eff

O ).

eff

'HVLJQ5HVLVWDQFHRIEDVLFFRPSRQHQWV

&ROXPQZHESDQHOLQVKHDU

(1) The design methods given in 6.2.6.1(2) to 6.2.6.1(14) are valid provided the column web slenderness



G/W .

satisfies the condition w

(2) For a single-sided joint, or for a double-sided joint in which the beam depths are similar, the design

9

9 of an unstiffened column web panel, subject to a design shear force , see

shear resistance wp,Rd wp,Ed

5.3(3), should be obtained using:

I $0 , 9 \ ZF YF , 9 = ... (6.7) wp,Rd γ 3 0 0 where:$ is the shear area of the column, see EN 1993-1-1.

vc

(3) The design shear resistance may be increased by the use of stiffeners or supplementary web plates.

(4) Where transverse web stiffeners are used in both the compression zone and the tension zone, the

9

9 may be increased by given

design plastic shear resistance of the column web panel wp,Rd wp,add,Rd

by: 0 0 + 0

4 2 2

S IF 5G S IF 5G S VW 5G

(, , (, , (, ,

9 

9 = but ... (6.8)

## V V

where:

G is the distance between the centrelines of the stiffeners;

s

0 is the design plastic moment resistance of a column flange

p IF5G

0 is the design plastic moment resistance of a stiffener.

p VW5G

127(In welded joints, the transverse stiffeners should be aligned with the corresponding beam

flange.

(5) When diagonal web stiffeners are used the design shear resistance of a column web should be

determined according to EN 1993-1-1.

127( In double-sided beam-to-column joint configurations without diagonal stiffeners on the

column webs, the two beams are assumed to have similar depths.

(6) Where a column web is reinforced by adding a supplementary web plate, see Figure 6.5, the shear area

$may be increased by . If a further supplementary web plate is added on the other side of the vc s wc web, no further increase of the shear area should be made. SU(1 ( (7) Supplementary web plates may also be used to increase the rotational stiffness of a joint by increasing the stiffness of the column web in shear, compression or tension, see 6.3.2(1). (8) The steel grade of the supplementary web plate should be similar to that of the column. E should be such that the supplementary web plate extends at least to the toe of the root (9) The width s radius. should be such that the supplementary web plate extends throughout the effective width (10) The length s of the web in tension and compression, see Figure 6.5. W W of the supplementary web plate should be not less than the column web thickness . (11) The thickness s wc (12) The welds between the supplementary web plate and profile should be designed to resist the applied design forces. W E of a supplementary web plate should be less than 40 . (13) The width s s (14) Discontinuous welds may be used in non corrosive environments. b eff,t ## O s b eff,c a) Layout b b b ## S S S t t t s s s t t t w c w c w c t t s s r+t S 127( Weldability at the corner should be taken into account. b) Examples of cross-section with longitudinal welds ## )LJXUH([DPSOHVRIVXSSOHPHQWDU\ZHESODWHV &ROXPQZHELQWUDQVYHUVHFRPSUHVVLRQ (1) The design resistance of an unstiffened column web subject to transverse compression should be determined from: ω ω ρ ## N E W I N E W I ## ZF HII F ZF ZF \ ZF ZF HII F ZF ZF \ ZF , , , , , , )  ) = but ... (6.9) c,wc,Rd c,wc,Rd γ γ 0 0 0 1 SU(1 ( where: is a reduction factor to allow for the possible effects of interaction with shear in the column web panel according to Table 6.3; E is the effective width of column web in compression eff,c,wc for a welded connection: – W + D + W + V E 2 2 5 ( ) = ... (6.10) ## IE E F eff,c,wc I ## D U D , and are as indicated in Figure 6.6. c c b for bolted end-plate connection: – W + D + W + V + V E 2 2 5 ( ) = ... (6.11) ## IE S IF S eff,c,wc W V is the length obtained by dispersion at 45° through the end-plate (at least and, provided that p p the length of end-plate below the flange is sufficient, up to 2W ). p for bolted connection with angle flange cleats: – W + U + W + V E 2 0 , 6 5 ( ) = ... (6.12) ## D D F eff,c,wc I V U for a rolled I or H section column: – c D V 2 for a welded I or H section column: = – F is the reduction factor for plate buckling: + λ  if = 1,0 ... (6.13a) – S + + + λ λ λ í 2 if > 0,72: = ( / ... (6.13b) – S S S + λ is the plate slenderness: ## S + E G I ## HII F ZF ZF \ ZF λ , , , 0 , 932 = ... (6.13c) S (W 2 ## ZF G K í W U for a rolled I or H section column: = 2 ( + ) – wc c fc c D G K í W 2 for a welded I or H section column: = ( + ) – wc c fc N is a reduction factor and is given in 6.2.6.2(2). wc 7DEOH5HGXFWLRQIDFWRU IRULQWHUDFWLRQZLWKVKHDU Reduction factor Transformation parameter   0 0,5 = 1 í í 0,5 < < 1 = + 2 (1 ) (1 ) 1 1 = 1 = 1 í í 1 < < 2 = + ( ( ) 1 2 1 = 2 = 2 1 1 = = 1 2 + E W$ + E W $2 2 1 1 , 3 ( / ) 1 5 , 2 ( / ) ## HII F ZF ZF YF HII F ZF ZF YF , , , ,$ is the shear area of the column, see 6.2.6.1;

vc is the transformation parameter, see 5.3(7).

SU(1 (

(2) Where the maximum longitudinal compressive stress due to axial force and bending moment

com,Ed

## I

in the column exceeds 0,7 in the web (adjacent to the root radius for a rolled section or the toe of

y,wc

the weld for a welded section), its effect on the design resistance of the column web in compression

) given by expression (6.9) by a reduction

should be allowed for by multiplying the value of c,wc,Rd

N as follows:

factor wc  I N

when : = 1

– com,Ed y,wc wc σ

− I

I N 1

, 7 /

when > 0,7 : = ... (6.14)

– FRP (G \ ZF

com,Ed y,wc wc , ,

127(Generally N

the reduction factor is 1,0 and no reduction is necessary. It can therefore be

wc

omitted in preliminary calculations when the longitudinal stress is unknown and checked later.

Welded joint Joint with end-plate Joint with angle flange cleats

a) Elevation

b) Rolled column

c) Welded column

)LJXUH7UDQVYHUVHFRPSUHVVLRQRQDQXQVWLIIHQHGFROXPQ

(3) The ‘column-sway' buckling mode of an unstiffened column web in compression illustrated in Figure

6.7 should normally be prevented by constructional restraints.

## )LJXUHµ&ROXPQVZD\¶EXFNOLQJPRGHRIDQXQVWLIIHQHGZHE

(4) Stiffeners or supplementary web plates may be used to increase the design resistance of a column web

in transverse compression.

SU(1 (

(5) Transverse stiffeners or appropriate arrangements of diagonal stiffeners may be used in association

with or as an alternative to, transverse stiffeners in order to increase the design resistance of the

column web in compression.

127(In welded joints, the transverse stiffeners should be aligned with the corresponding beam

flange. In bolted joints, the stiffener in the compression zone should be aligned with the centre of

compression as defined Figure 6.15.

(6) Where an unstiffened column web is reinforced by adding a supplementary web plate conforming with

W if one supplementary web plate is

6.2.6.1, the effective thickness of the web may be taken as 1,5 wc

## W

added, or 2,0 if supplementary web plates are added to both sides of the web. In calculating the

wc for the possible effects of shear stress, the shear area of the web may be reduction factor vc increased only to the extent permitted when determining its design shear resistance, see 6.2.6.1(6). &ROXPQZHELQWUDQVYHUVHWHQVLRQ (1) The design resistance of an unstiffened column web subject to transverse tension should be determined from: ω E I t ## HII W ZF \ ZF , , wc , ) = ... (6.15) t,wc,Rd γ 0 0 where: is a reduction factor to allow for the interaction with shear in the column web panel. E of a column web in tension should be obtained (2) For a welded connection, the effective width eff,t,wc using: W + D + W + V E 2 2 5 ( ) = ... (6.16) ## IE E F eff,t,wc I where: V U for a rolled I or H section column: = – c D V 2 for a welded I or H section column: = – F where: D U D and are as indicated in Figure 6.8 and is as indicated in Figure 6.6. c c b E of column web in tension should be taken as equal (3) For a bolted connection, the effective width eff,t,wc to the effective length of equivalent T-stub representing the column flange, see 6.2.6.4. to allow for the possible effects of shear in the column web panel should be (4) The reduction factor E given in 6.2.6.3(2) or 6.2.6.3(3) as appropriate. determined from Table 6.3, using the value of eff,t,wc (5) Stiffeners or supplementary web plates may be used to increase the design tension resistance of a column web. (6) Transverse stiffeners and/or appropriate arrangements of diagonal stiffeners may be used to increase the design resistance of the column web in tension. 127(In welded joints, the transverse stiffeners should be aligned with the corresponding beam flange. In bolted joints, the stiffener in the compression zone should be aligned with the centre of compression as defined in Figure 6.15. SU(1 ( (7) The welds connecting diagonal stiffeners to the column flange should be fill-in welds with a sealing run providing a combined throat thickness equal to the thickness of the stiffeners. (8) Where an unstiffened column web is reinforced by adding supplementary web plates conforming with 6.2.6.1, the design tension resistance depends on the throat thickness of the longitudinal welds W should be taken as connecting the supplementary web plates. The effective thickness of the web w,eff follows: D W when the longitudinal welds are full penetration butt welds with a throat thickness then: – s ## W W for one supplementary web plate: = 1,5 ... (6.17) – w,eff wc ## W W for supplementary web plates both sides: = 2,0 ... (6.18) – w,eff wc W D  / 2 when the longitudinal welds are fillet welds with a throat thickness then for either – V one or two supplementary web plates: W W for steel grades S 235, S 275 or S 355: = 1,4 ... (6.19a) – w,eff wc ## W W for steel grades S 420 or S 460: = 1,3 ... (6.19b) – w,eff wc

for the possible effects of shear stress, the shear area of a

(9) In calculating the reduction factor vc

column web reinforced by adding supplementary web plates may be increased only to the extent

permitted when determining its design shear resistance, see 6.2.6.1(6).

&ROXPQIODQJHLQWUDQYHUVHEHQGLQJ

6.2.6.4.1 Unstiffened column flange, bolted connection

(1) The design resistance and failure mode of an unstiffened column flange in tranverse bending, together

with the associated bolts in tension, should be taken as similar to those of an equivalent T-stub flange,

see 6.2.4, for both:

each individual bolt-row required to resist tension;

– each group of bolt-rows required to resist tension.

– H P

(2) The dimensions and for use in 6.2.4 should be determined from Figure 6.8.

min

(3) The effective length of equivalent T-stub flange should be determined for the individual bolt-rows and

the bolt-group in accordance with 6.2.4.2 from the values given for each bolt-row in Table 6.4.

SU(1 (

0,8 r m m e

e 0,8 a 2

c c

r c a c e min

e min

a) Welded end-plate narrower than column flange. m

0,8 a 2 e

0,8 r m min

c

c e min

r c a c

b) Welded end-plate wider than column flange.

0,8 r m m e

e 0,8 a 2

c c

r c a c e

e min min

c) Angle flange cleats.

## PLQ F

7DEOH(IIHFWLYHOHQJWKVIRUDQXQVWLIIHQHGFROXPQIODQJH

Bolt-row considered Bolt-row considered as

Bolt-row individually part of a group of bolt-rows

Location Circular patterns Non-circular patterns Circular patterns Non-circular patterns

eff,cp eff,nc eff,cp eff,nc

Inner P S

2 4P + 1,25H 2S

bolt-row The smaller of: The smaller of: The smaller of: The smaller of:

End P P S

+

2 4P + 1,25H 2P + 0,625H + 0,5S

bolt-row P S

## H H

2H

+ 2H + + 0,5S

2P + 0,625H +

1 1 1 1

    

Mode 1: = but = but

eff,1 eff,nc eff,1 eff,cp eff,1 eff,nc eff,1 eff,cp

 

Mode 2: = =

eff,2 eff,nc eff,2 eff,nc

SU(1 (

6.2.6.4.2 Stiffened column flange, joint with bolted end-plate or flange cleats

(1) Transverse stiffeners and/or appropriate arrangements of diagonal stiffeners may be used to increase

the design resistance of the column flange in bending.

(2) The design resistance and failure mode of a stiffened column flange in transverse bending, together

with the associated bolts in tension, should be taken as similar to those of an equivalent T-stub flange,

see 6.2.4, for both:

each individual bolt-row required to resist tension;

– each group of bolt-rows required to resist tension.

(3) The groups of bolt-rows either side of a stiffener should be modelled as separate equivalent T-stub

flanges, see Figure 6.9. The design resistance and failure mode should be determined separately for

each equivalent T-stub. (QGEROWURZDGMDFHQWWRDVWLIIHQHU

## %ROWURZDGMDFHQWWRDVWLIIHQHU

)LJXUH0RGHOOLQJDVWLIIHQHGFROXPQIODQJHDVVHSDUDWH7VWXEV

## H P

(4) The dimensions and for use in 6.2.4 should be determined from Figure 6.8.

min should be determined in accordance with

(5) The effective lengths of an equivalent T-stub flange eff IRUXVHLQTable 6.5

6.2.4.2 using the values for each bolt-row given in Table 6.57KHYDOXHRI

should be obtained from Figure 6.11.

(6) The stiffeners should meet the requirements specified in 6.2.6.1.

SU(1 (

7DEOH(IIHFWLYHOHQJWKVIRUDVWLIIHQHGFROXPQIODQJH

Bolt-row considered Bolt-row considered as

Bolt-row individually part of a group of bolt-rows

Location Circular patterns Non-circular Circular patterns Non-circular patterns

patterns

eff,cp eff,nc eff,cp eff,nc P

## P P P S

2 + í P

to a stiffener + 0,625H)

Other inner P S

2 4P + 1,25H 2S

bolt-row The smaller of: The smaller of: The smaller of: The smaller of:

Other end P P S

+

2 4P + 1,25H 2P + 0,625H + 0,5S

bolt-row H H

## P S

2H

2P + 0,625H +

+ 2H + + 0,5S

1 1 1 1

End bolt-row The smaller of: H P

+

P 1

adjacent to a 2 not relevant not relevant

í P + 0,625H)

P + 2H

stiffener 1     

For Mode 1: = but = but

eff,1 eff,nc eff,1 eff,cp eff,1 eff,nc eff,1 eff,cp

 

For Mode 2: = =

eff,2 eff,nc eff,2 eff,nc

VKRXOGEHREWDLQHGIURPFigure 6.11.

6.2.6.4.3 Unstiffened column flange, welded connection

) of an unstiffened column flange in bending, due to

(1) In a welded joint, the design resistance fc,Rd

tension or compression from a beam flange, should be obtained using:

γ

) /

## HII E IF IE IE 0

= ... (6.20)

γ

fc,Rd , , , 0

where: E

E is the effective breath defined in 4.10 where the beam flange is considered as a plate.

eff,b,fc eff

127(The requirements specified in 4.10(4) and 4.10(6) should be satisfied.

(QGSODWHLQEHQGLQJ

(1) The design resistance and failure mode of an end-plate in bending, together with the associated bolts

in tension, should be taken as similar to those of an equivalent T-stub flange, see 6.2.4 for both:

each individual bolt-row required to resist tension;

– each group of bolt-rows required to resist tension.

(2) The groups of bolt-rows either side of any stiffener connected to the end-plate should be treated as

separate equivalent T-stubs. In extended end-plates, the bolt-row in the extended part should also be

treated as a separate equivalent T-stub, see Figure 6.10. The design resistance and failure mode should

be determined separately for each equivalent T-stub.

H required for use in 6.2.4 should be obtained from Figure 6.8 for that part of the

(3) The dimension min H should be taken as

end-plate located between the beam flanges. For the end-plate extension min

## H

equal to , see Figure 6.10.

x should be determined in accordance with

(4) The effective length of an equivalent T-stub flange eff

6.2.4.2 using the values for each bolt-row given in Table 6.6.

SU(1 (

P P

(5) The values of and for use in Table 6.6 should be obtained from Figure 6.10.

x

b p 5

w eff

5 5

eff eff

e x

m x e

e The extension of the end-plate and the portion

between the beam flanges are modelled as two

separate equivalent T-stub flanges. P

H and in

For the end-plate extension, use x x

## H P

place of and when determining the design

p resistance of the equivalent T-stub flange.

)LJXUH0RGHOOLQJDQH[WHQGHGHQGSODWHDVVHSDUDWH7VWXEV

7DEOH(IIHFWLYHOHQJWKVIRUDQHQGSODWH

Bolt-row considered Bolt-row considered as

Bolt-row individually part of a group of bolt-rows

location Circular patterns Non-circular patterns Circular patterns Non-circular

patterns

eff,cp eff,nc eff,cp eff,nc

Smallest of:

Smallest of: 4P + 1,25H

Bolt-row outside P x x

2 H+2P

x

tension flange +0,625H — —

P Z x x

+

x 0,5E

of beam P p

+ 2H

x 0,5Z+2P +0,625H

x x

First bolt-row P

0,5S +

## P P P

2 + p

below tension í P + 0,625H)

flange of beam

Other inner P H S

2 4P + 1,25 2S

bolt-row

Other end P H P S

2 4P + 1,25 + 2P+0,625H+0,5S

bolt-row     

Mode 1: = but = but

eff,1 eff,nc eff,1 eff,cp eff,1 eff,nc eff,1 eff,cp

 

Mode 2: = =

eff,2 eff,nc eff,2 eff,nc

VKRXOGEHREWDLQHGIURPFigure 6.11.

SU(1 (

)LJXUH9DOXHVRI IRUVWLIIHQHGFROXPQIODQJHVDQGHQGSODWHV

)ODQJHFOHDWLQEHQGLQJ

(1) The design resistance and failure mode of a bolted angle flange cleat in bending, together with the

associated bolts in tension, should be taken as similar to those of an equivalent T-stub flange, see

6.2.4. E

of the equivalent T-stub flange should be taken as 0,5E where is the

(2) The effective length eff a a

length of the angle cleat, see Figure 6.12.

SU(1 (

H P

(3) The dimensions and for use in 6.2.4 should be determined from Figure 6.13.

min

b 5

a eff

5 eff 5 eff

## J  W J W

b) Gap > 0,4

a) Gap a

a

Notes:

- The number of bolt-rows connecting the cleat to the column flange is limited to one;

- The number of bolt-rows connecting the cleat to the beam flange is not limited;

E of the cleat may be different from both the width of the beam flange and the width

- The length a

of the column flange.

## PLQ

%HDPIODQJHDQGZHELQFRPSUHVVLRQ

(1) The design compression resistance of a beam flange and the adjacent compression zone of the beam

web, may be assumed to act at the level of the centre of compression, see 6.2.7. The design

compression resistance of the combined beam flange and web is given by the following expression:

0 K íW

) = / ( ) ... (6.21)

c,fb,Rd c,Rd fb

where:

K is the depth of the connected beam;

0 is the design moment resistance of the beam cross-section, reduced if necessary to allow for

c,Rd 0

shear, see EN 1993-1-1. For a haunched beam may be calculated neglecting the

c,Rd

intermediate flange.

W is the flange thickness of the connected beam.

fb

SU(1 (

If the height of the beam including the haunch exceeds 600 mm the contribution of the beam web to

the design compression resistance should be limited to 20%.

(2) If a beam is reinforced with haunches they should be arranged such that:

the steel grade of the haunch should match that of the member;

– the flange size and the web thickness of the haunch should not be less than that of the member;

– the angle of the haunch flange to the flange of the member should not be greater than 45°;

– V

the length of stiff bearing should be taken as equal to the thickness of the haunch flange parallel

– s

to the beam.

(3) If a beam is reinforced with haunches, the design resistance of beam web in compression should be

determined according to 6.2.6.2.

%HDPZHELQWHQVLRQ

(1) In a bolted end-plate connection, the design tension resistance of the beam web should be obtained

from: γ

## E W I

) /

HII W ZE ZE \ ZE 0

= ... (6.22)

t,wb,Rd , , , 0

E of the beam web in tension should be taken as equal to the effective length

(2) The effective width eff,t,wb

of the equivalent T-stub representing the end-plate in bending, obtained from 6.2.6.5 for an individual

bolt-row or a bolt-group.

&RQFUHWHLQFRPSUHVVLRQLQFOXGLQJJURXW

(1) The design bearing strength of the joint between the base plate and its concrete support should be

determined taking account of the material properties and dimensions of both the grout and the concrete

support. The concrete support should be designed according to EN 1992.

(2) The design resistance of concrete in compression, including grout, together with the associated base

) , should be taken as similar to those of an equivalent T-stub, see 6.2.5.

plate in bending c,pl,Rd

%DVHSODWHLQEHQGLQJXQGHUFRPSUHVVLRQ

(1) The design resistance of a base plate in bending under compression, together with concrete slab on

) , should be taken as similar to those of an equivalent T-stub,

which the column base is placed c,pl,Rd

see 6.2.5.

%DVHSODWHLQEHQGLQJXQGHUWHQVLRQ

(1) The design resistance and failure mode of a base plate in bending under tension, together with the

) , may be determined using the rules given in 6.2.6.5.

associated anchor bolts in tension t,pl,Rd

(2) In the case of base plates prying forces which may develop should not be taken into consideration.

QFKRUEROWLQWHQVLRQ (1) Anchor bolts should be designed to resist the effects of the design loads. They should provide design resistance to tension due to uplift forces and bending moments where appropriate. (2) When calculating the tension forces in the anchor bolts due to bending moments, the lever arm should not be taken as more than the distance between the centroid of the bearing area on the compression side and the centroid of the bolt group on the tension side. SU(1 ( 127(Tolerances on the positions of the anchor bolts should be taken into account if the influence of tolerances is significant. (3) The design resistance of the anchor bolts should be taken as the smaller of the design tension resistance of the anchor bolt, see 3.6, and the design bond resistance of the concrete on the anchor bolt according to EN 1992-1-1. (4) One of the following methods should be used to secure anchor bolts into the foundation: a hook (Figure 6.14(a)), – a washer plate (Figure 6.14(b)), – some other appropriate load distributing member embedded in the concrete, – some other fixing which has been adequately tested and approved. (5) When the bolts are provided with a hook, the anchorage length should be such as to prevent bond failure before yielding of the bolt. The anchorage length should be calculated in accordance with I higher than EN 1992-1-1. This type of anchorage should not be used for bolts with a yield strength yb 2 300 N/mm . (6) When the anchor bolts are provided with a washer plate or other load distributing member, no account should be taken of the contribution of bond. The whole of the force should be transferred through the load distributing device. ## %DVHSODWH ## *URXW ## &RQFUHWHIRXQGDWLRQ (a) Hook (b) Washer plate ## )LJXUH)L[LQJRIDQFKRUEROWV 'HVLJQ0RPHQWUHVLVWDQFHRIEHDPWRFROXPQMRLQWVDQGVSOLFHV *HQHUDO 0 shall satisfy: (1) The applied design moment j,Ed SU(1 ( 0 M (G ,  ... (6.23) 0 M 5G , 0 do not take (2) The methods given in 6.2.7 for determining the design moment resistance of a joint j,Rd 1 account of any co-existing axial force in the connected member. They should not be used if the Ed 1 axial force in the connected member exceeds 5% of the design plastic resistance of its cross- p 5G section. 1 1 in the connected beam exceeds 5% of the design resistance, , the following (3) If the axial force Ed pl,Rd conservative method may be used: 0 1 ## M (G M (G + , ,  ... (6.24) 0 1 M 5G M 5G , , where: 0 is the design moment resistance of the joint, assuming no axial force; j.Rd 1 is the axial design resistance of the joint, assuming no applied moment. j.Rd (4) The design moment resistance of a welded joint should be determined as indicated in Figure 6.15(a). (5) The design moment resistance of a bolted joint with a flush end-plate that has only one bolt-row in tension (or in which only one bolt-row in tension is considered, see 6.2.3(6)) should be determined as indicated in Figure 6.15(b). (6) The design moment resistance of a bolted joint with angle flange cleats should be determined as indicated in Figure 6.15(c). (7) The design moment resistance of a bolted end-plate joint with more than one row of bolts in tension should generally be determined as specified in 6.2.7.2. (8) As a conservative simplification, the design moment resistance of an extended end-plate joint with only two rows of bolts in tension may be approximated as indicated in Figure 6.16, provided that the ) ) does not exceed 3,8) , where is given in Table 6.2. In this case total design resistance Rd t,Rd t,Rd the whole tension region of the end-plate may be treated as a single basic component. Provided that the two bolt-rows are approximately equidistant either side of the beam flange, this part of the end- ) ) . The value of may then plate may be treated as a T-stub to determine the bolt-row force 1,Rd 2,Rd ) ) be assumed to be equal to , and so may be taken as equal to 2) . 1,Rd Rd 1,Rd (9) The centre of compression should be taken as the centre of the stress block of the compression forces. As a simplification the centre of compression may be taken as given in Figure 6.15. (10) A splice in a member or part subject to tension shall be designed to transmit all the moments and forces to which the member or part is subjected at that point. (11) Splices shall be designed to hold the connected members in place. Friction forces between contact surfaces may not be relied upon to hold connected members in place in a bearing splice. (12) Wherever practicable the members should be arranged so that the centroidal axis of any splice material coincides with the centroidal axis of the member. If eccentricity is present then the resulting forces should be taken into account. SU(1 ( Centre of Type of connection Lever arm Force distributions compression ] K W a) Welded connection In line with the = - fb mid thickness K is the depth of of the the connected compression beam flange W is the thickness fb of the beam flange b) Bolted connection with angle In line with the Distance from the flange cleats mid-thickness centre of of the leg of the compression to the angle cleat on bolt-row in tension the compression flange c) Bolted end-plate connection In line with the Distance from the with only one bolt-row active in mid-thickness centre of tension of the compression to the compression bolt-row in tension flange d) Bolted extended end-plate In line with the Conservatively z connection with only two bolt-rows mid-thickness may be taken as active in tension of the the distance from compression the centre of flange compression to a point midway between these two bolt-rows e) Other bolted end-plate In line with the An approximate A more accurate value may connections with two or more bolt- mid-thickness value may be be determined by taking the ] ] rows in tension of the obtained by taking lever arm as equal to eq obtained using the method compression the distance from given in 6.3.3.1. flange the centre of compression to a point midway between the farthest two bolt- rows in tension ## )LJXUH&HQWUHRIFRPSUHVVLRQOHYHUDUP]DQGIRUFHGLVWULEXWLRQVIRU GHULYLQJWKHGHVLJQPRPHQWUHVLVWDQFH0 M5G SU(1 ( )LJXUH6LPSOLILHGPRGHOVIRUEROWHGMRLQWVZLWKH[WHQGHGHQGSODWHV (13) Where the members are not prepared for full contact in bearing, splice material should be provided to transmit the internal forces and moments in the member at the spliced section, including the moments due to applied eccentricity, initial imperfections and second-order deformations. The internal forces and moments should be taken as not less than a moment equal to 25% of the moment capacity of the weaker section about both axes and a shear force equal to 2.5% of the normal force capacity of the weaker section in the directions of both axes. (14) Where the members are prepared for full contact in bearing, splice material should be provided to transmit 25% of the maximum compressive force in the column. (15) The alignment of the abutting ends of members subjected to compression should be maintained by cover plates or other means. The splice material and its fastenings should be proportioned to carry forces at the abutting ends, acting in any direction perpendicular to the axis of the member. In the design of splices the second order effects should also be taken into account. (16) Splices in flexural members should comply with the following: a) Compression flanges should be treated as compression members; b) Tension flanges should be treated as tension members; c) Parts subjected to shear should be designed to transmit the following effects acting together: the shear force at the splice; – the moment resulting from the eccentricity, if any, of the centroids of the groups of fasteners – on each side of the splice; the proportion of moment, deformation or rotations carried by the web or part, irrespective of – any shedding of stresses into adjoining parts assumed in the design of the member or part. %HDPWRFROXPQMRLQWVZLWKEROWHGHQGSODWHFRQQHFWLRQV 0 of a beam-to-column joint with a bolted end-plate connection (1) The design moment resistance j,Rd may be determined from: Σ K ) 0 = ... (6.25) U WU 5G j,Rd , ## U where: ) U is the effective design tension resistance of bolt-row ; ## U t ,Rd K U is the distance from bolt-row to the centre of compression; ## U U is the bolt-row number. SU(1 ( 127(In a bolted connection with more than one bolt-row in tension, the bolt-rows are numbered starting from the bolt-row farthest from the centre of compression. (2) For bolted end-plate connections, the centre of compression should be assumed to be in line with the centre of the compression flange of the connected member. ) for each bolt-row should be determined in sequence, (3) The effective design tension resistance tr,Rd starting from bolt-row 1, the bolt-row farthest from the centre of compression, then progressing to bolt-row 2, etc. U ) for bolt-row the effective design tension resistance of all (4) When determining the value of U t ,Rd other bolt-rows closer to the centre of compression should be ignored. ## U ) of bolt-row should be taken as its design tension (5) The effective design tension resistance U t ,Rd ) as an individual bolt-row determined from 6.2.7.2(6), reduced if necessary to satisfy resistance t,Rd the conditions specified in 6.2.7.2(7), (8) and (9). U ) of bolt-row ,taken as an individual bolt-row, should (6) The effective design tension resistance tr,Rd be taken as the smallest value of the design tension resistance for an individual bolt-row of the following basic components: ) the column web in tension - see 6.2.6.3; – t,wc,Rd ) the column flange in bending - see 6.2.6.4; – t,fc,Rd ) the end-plate in bending - see 6.2.6.5; – t,ep,Rd ) the beam web in tension - see 6.2.6.8. – t,wb,Rd U ) of bolt-row should, if necessary, be reduced below (7) The effective design tension resistance U t ,Rd ) the value of given by 6.2.7.2(6) to ensure that, when account is taken of all bolt-rows up to and t,Rd U the following conditions are satisfied: including bolt-row ) 9 the total design resistance / - with from 5.3(7) - see 6.2.6.1; – t,Rd wp,Rd ) the total design resistance does not exceed the smaller of: – t,Rd ) the design resistance of the column web in compression - see 6.2.6.2; – c,wc,Rd ) the design resistance of the beam flange and web in compression - see 6.2.6.7. – c, fb,Rd ## U ) of bolt-row should, if necessary, be reduced below (8) The effective design tension resistance U t ,Rd ) the value of given by 6.2.7.2(6), to ensure that the sum of the design resistances taken for the t,Rd U bolt-rows up to and including bolt-row that form part of the same group of bolt-rows, does not exceed the design resistance of that group as a whole. This should be checked for the following basic components: ) the column web in tension - see 6.2.6.3; – t,wc,Rd ) the column flange in bending - see 6.2.6.4; – t,fc,Rd ) the end-plate in bending - see 6.2.6.5; – t,ep,Rd ) the beam web in tension - see 6.2.6.8. – t,wb,Rd ) [ (9) Where the effective design tension resistance of one of the previous bolt-rows is greater than tx,Rd ) ) U , then the effective design tension resistance for bolt-row should be reduced, if 1,9 U t,Rd t ,Rd necessary, in order to ensure that: ) K K ) / ... (6.26) tr,Rd tx,Rd r x where: [ K is the distance from bolt-row to the centre of compression; x SU(1 ( [ is the bolt-row farthest from the centre of compression that has a design tension resistance ) greater than 1,9 . t,Rd 127( The National Annex may give other situations where equation (6.26) is relevant. (10) The method described in 6.2.7.2(1) to 6.2.7.2(9) may be applied to a bolted beam splice with welded end-plates, see Figure 6.17, by omitting the items relating to the column. ## )LJXUH%ROWHGEHDPVSOLFHVZLWKZHOGHGHQGSODWHV 'HVLJQ5HVLVWDQFHRIFROXPQEDVHVZLWKEDVHSODWHV *HQHUDO (1) Column bases should be of sufficient size, stiffness and strength to transmit the axial forces, bending moments and shear forces in columns to their foundations or other supports without exceeding the load carrying capacity of these supports. (2) The design bearing strength between the base plate and its support may be determined on the basis of a uniform distribution of compressive force over the bearing area. For concrete foundations the bearing I given in 6.2.5(7). strength should not exceed the design bearing strength, jd , (3) For a column base subject to combined axial force and bending the forces between the base plate and its support can take one of the following distribution depending on the relative magnitude of the applied axial force and bending moment: In the case of a dominant compressive axial force, full compression may develop under both – column flanges as shown in Figure 6.18(a). In the case of a dominant tensile force, full tension may develop under both flanges as shown in – Figure 6.18(b). In the case of a dominant bending moment compression may develop under one column flange – and tension under the other as shown in Figure 6.18(c) and Figure 6.18(d). (4) Base plates should be designed using the appropriate methods given in 6.2.8.2 and 6.2.8.3. (5) One of the following methods should be used to resist the shear force between the base plate and its support: Frictional design resistance at the joint between the base plate and its support. – The design shear resistance of the anchor bolts. – The design shear resistance of the surrounding part of the foundation. If anchor bolts are used to resist the shear forces between the base plate and its support, rupture of the concrete in bearing should also be checked, according to EN 1992. SU(1 ( Where the above methods are inadequate special elements such as blocks or bar shear connectors should be used to transfer the shear forces between the base plate and its support. ## N N Ed Ed M M Ed Ed ] ] ] ] C,l C,r T,l T,r ] ] a) Column base connection in case of a b) Column base connection in case of a dominant compressive normal force dominant tensile normal force ## N N Ed Ed ## M M Ed Ed ] ] ] ] C,l T,r T,l C,r ] ] c) Column base connection in case of a d) Column base connection in case of a dominant bending moment dominant bending moment ## )LJXUH'HWHUPLQDWLRQRIWKHOHYHUDUP]IRUFROXPQEDVHFRQQHFWLRQV &ROXPQEDVHVRQO\VXEMHFWHGWRD[LDOIRUFHV 1 of a symmetric column base plate subject to an axial compressive force (1) The design resistance, j,Rd , ) applied concentrically may be determined by adding together the individual design resistance of C,Rd the three T-stubs shown in Figure 6.19 (Two T-stubs under the column flanges and one T-stub under the column web.) The three T-stubs should not be overlapping, see Figure 6.19. The design resistance of each of these T-stubs should be calculated using the method given in 6.2.5. 7VWXE 7VWXE 7VWXE 2 1 3 )LJXUH1RQRYHUODSSLQJ7VWXEV &ROXPQEDVHVVXEMHFWHGWRD[LDOIRUFHVDQGEHQGLQJPRPHQWV 0 of a column base subject to combined axial force and moment (1) The design moment resistance j,Rd should be determined using the method given in Table 6.7 where the contribution of the concrete portion just under the column web (T-stub 2 of Figure 6.19) to the compressive capacity is omitted. The following parameters are used in this method: ) is the design tension resistance of the left hand side of the joint - see 6.2.8.3(2) – T,l,Rd ) is the design tension resistance of the right hand side of the joint - see 6.2.8.3(3) – T,r,Rd ) is the design compressive resistance of the left hand side of the joint - see 6.2.8.3(4) – C,l,Rd ) is the design compressive resistance of the right hand side of the joint - see 6.2.8.3(5) – C,r,Rd SU(1 ( ) (2) The design tension resistance of the left side of the joint should be taken as the smallest values T,l,Rd of the design resistance of following basic components: ) the column web in tension under the left column flange - see 6.2.6.3; – t,wc,Rd ) the base plate in bending under the left column flange - see 6.2.6.11. – t,pl,Rd ) of the right side of the joint should be taken as the smallest values (3) The design tension resistance T,r,Rd of the design resistance of following basic components: ) the column web in tension under the right column flange - see 6.2.6.3; – t,wc,Rd ) the base plate in bending under the right column flange - see 6.2.6.11. – t,pl,Rd ) (4) The design compressive resistance of the left side of the joint should be taken as the smallest C,l,Rd values of the design resistance of following basic components: ) the concrete in compression under the left column flange - see 6.2.6.9; – c,pl,Rd ) the left column flange and web in compression - see 6.2.6.7. – c,fc,Rd ) of the right side of the joint should be taken as the smallest (5) The design compressive resistance C,r,Rd values of the design resistance of following basic components: ) the concrete in compression under the right column flange - see 6.2.6.9; – c,pl,Rd ) the right column flange and web in compression - see 6.2.6.7. – c,fc,Rd ] ] ] ] (6) For the calculation of , , , see 6.2.8.1. T,l C,l T,r C,r 7DEOH'HVLJQPRPHQWUHVLVWDQFH0 RIFROXPQEDVHV M5G ] 0 Loading Lever arm Design moment resistance j,Rd Left side in tension ]= ] + ] 1 H ] 1  H -] > 0 and > and T,l C,r Ed T,l Ed C,r Right side in compression ) ] − ) ] 7 5G & U 5G , 1 , , , The smaller of and ] H + ] H − / 1 / 1 & U 7 , , 1 Left side in tension ]= ] + ] 1 H ] 1 H  > 0 and 0 < < > 0 and -] < T,l T,r Ed T,l Ed T,r Right side in tension The smaller of The smaller of ) ] ) ] ) ] ) ] 7 5G 7 U 5G 7 5G 7 5G , 1 , , , , 1 , , 1 , and and ] H + ] H − ] H + ] H − / 1 / 1 / 1 / 1 7 U 7 7 7 ## U , , 1 , , 1 Left side in compression ]= ] + ] 1 H -] 1  H ] > 0 and and > C,l T,r Ed T,r Ed C,l Right side in tension − ) ] ) ] & 5G 7 U 5G , 1 , , , The smaller of and ] H + ] H − / 1 / 1 7 & ## U , , 1 Left side in compression ]= ] + ] 1  H ] 1  H  and 0 < < and -] < C,l C,r Ed C,l Ed C,r Right side in compression The smaller of The smaller of − ) ] − ) ] − ) ] − ) ] & 5G & U 5G & 5G & U 5G , 1 , , , , 1 , , , and and ] H + ] H − ] H + ] H − / 1 / 1 / 1 / 1 & U & & U & , , 1 , , 1 0 1 > 0 is clockwise, > 0 is tension Ed Ed 0 0 5G ## (G H = = 1 1 5G ## (G SU(1 ( 5RWDWLRQDOVWLIIQHVV %DVLFPRGHO (1) The rotational stiffness of a joint should be determined from the flexibilities of its basic components, ## N each represented by an elastic stiffness coefficient obtained from 6.3.2. ## L 127(These elastic stiffness coefficients are for general application. (2) For bolted end-plate connections with more than one row of bolts in tension, the stiffness coefficients N for the related basic components should be combined. For beam-to-column joints and beam splices ## L a method is given in 6.3.3 and for column bases a method is given in 6.3.4. (3) In a bolted connection with more than one bolt-row in tension, as a simplification the contribution of any bolt-row may be neglected, provided that the contributions of all other bolt-rows closer to the centre of compression are also neglected. The number of bolt-rows retained need not necessarily be the same as for the determination of the design moment resistance. 1 in the connected member does not exceed 5% of the design (4) Provided that the axial force Ed 1 6 resistance of its cross-section, the rotational stiffness of a beam-to-column joint or beam p j 5G 0 0 less than the design moment resistance of the joint, may be obtained splice, for a moment j,Ed j,Rd with sufficient accuracy from: (] 2 6 = ... (6.27) j 1 µ N ## L L where: L N is the stiffness coefficient for basic joint component ; ## L ] is the lever arm, see 6.2.7;  6 6 is the stiffness ratio / , see 6.3.1(6); j,ini j  127(The 6 of the joint is given by expression (6.27) with = 1,0. initial rotational stiffness j,ini 0 6 of a column base, for a moment less than the design moment (5) The rotational stiffness j j,Ed 0 resistance of the joint, may be obtained with sufficient accuracy from 6.3.4. j,Rd  (6) The stiffness ratio should be determined from the following: 0  0 if : – j,Ed j,Rd  = 1 ... (6.28a) 0 0 0 if 2/3 < : – j,Rd j,Ed j,Rd Ψ 0 0  ( 1 , 5 / ) = ... (6.28b) M (G M 5G , , is obtained from Table 6.8. in which the coefficient SU(1 ( 7DEOH9DOXHRIWKHFRHIILFLHQW Type of connection Welded 2,7 Bolted end-plate 2,7 Bolted angle flange cleats 3,1 Base plate connections 2,7 (7) The basic components that should be taken into account when calculating the stiffness of a welded beam-to-column connection and a bolted angle flange cleat are given in Table 6.9. Similarly, the basic components for a bolted end-plate connection and a base plate are given in Table 6.10. In both of these N ,for the basic components are defined in Table 6.11. tables the stiffness coefficients, L (8) For beam-to-column end plate joints the following procedure should be used for obtaining the joint ] N , and the equivalent lever arm, , of the connection stiffness. The equivalent stiffness coefficient, HT HT should be obtained from 6.3.3. The stiffness of the joint should then be obtained from 6.3.1(4) based ## N on the stiffness coefficients,N (for the connection), (for the column web in shear),and with the HT ], ] . lever arm, taken equal to the equivalent lever arm of the connection, HT 7DEOH-RLQWVZLWKZHOGHGFRQQHFWLRQVRUEROWHGDQJOHIODQJHFOHDW ## FRQQHFWLRQV N Beam-to-column joint with Stiffness coefficients to be taken ## L welded connections into account ## N N N Single-sided ; ; 1 2 3 ## N N Double-sided – Moments equal and opposite ; 2 3 ## N N N Double-sided – Moments unequal ; ; 1 2 3 N Beam-to-column joint with Stiffness coefficients to be taken ## L Bolted angle flange cleat connections into account ## N N N N N N N N ) ) Single-sided ; ; ; ; ; ; * ; ** 1 2 3 4 6 10 11 12 ## N N N N N N N ) ) Double-sided – Moments equal and opposite ; ; ; ; ; * ; ** 2 3 4 6 10 11 12 ## N N N N N N N N ) ) Double-sided – Moments unequal ; ; ; ; ; ; * ; ** 1 2 3 4 6 10 11 12 ## N *) Two coefficients, one for 11 each flange; ## N **) Four coefficients, one for 12 each flange and one for each cleat. Moments unequal Moments equal and opposite SU(1 ( 7DEOH-RLQWVZLWKEROWHGHQGSODWHFRQQHFWLRQVDQGEDVHSODWHFRQQHFWLRQV ## N Beam-to-column joint with Number of bolt-rows in Stiffness coefficients to ## L bolted end-plate connections tension be taken into account ## N N N N N N One ; ; ; ; ; 1 2 3 4 5 10 Single-sided N N N Two or more ; ; 1 2 eq ## N N N N N One ; ; ; ; 2 3 4 5 10 Double sided – Moments equal and opposite N N Two or more ; 2 eq ## N N N N N N One ; ; ; ; ; 1 2 3 4 5 10 Double sided – Moments unequal N N N Two or more ; ; 1 2 eq N Number of bolt-rows in Stiffness coefficients to ## L Beam splice with bolted end-plates tension be taken into account ## N N N One [left]; [right]; 5 5 10 Double sided - Moments equal and opposite N Two or more eq N Number of bolt-rows in Stiffness coefficients to ## L Base plate connections tension be taken into account ## N N N One ; ; 13 15 16 Base plate connections N N N ; and for each bolt 13 15 16 Two or more row 6WLIIQHVVFRHIILFLHQWVIRUEDVLFMRLQWFRPSRQHQWV (1) The stiffness coefficients for basic joint component should be determined using the expressions given in Table 6.11. SU(1 ( 7DEOH6WLIIQHVVFRHIILFLHQWVIRUEDVLFMRLQWFRPSRQHQWV ## N Component Stiffness coefficient i Unstiffened, stiffened &ROXPQZHE single-sided joint, or a double-sided joint in SDQHOLQVKHDU which the beam depths are similar

0

,

38 9&

N N 

= =

1 β 1

]

] is the lever arm from Figure 6.15;

is the transformation parameter from 5.3(7).

&ROXPQZHELQ unstiffened stiffened

0

, 7 HII F ZF ZF

, ,

N N 

= =

2 2

## G F

E is the effective width from 6.2.6.2

eff,c,wc

stiffened or unstiffened bolted connection with stiffened welded connection

&ROXPQZHELQ a single bolt-row in tension or unstiffened

WHQVLRQ welded connection

0

, 7 HII W ZF ZF

, ,

N N 

= =

3 3

## G F

E is the effective width of the column web in tension from 6.2.6.3. For a joint with a

eff,t,wc E should be taken as equal to the smallest of the

single bolt-row in tension, eff,t,wc

effective lengths (individually or as part of a group of bolt-rows) given for this

eff

bolt-row in Table 6.4 (for an unstiffened column flange) or Table 6.5 (for a

stiffened column flange).

" W 3

&ROXPQIODQJH 0

,

9 HII F

## N I

=

LQEHQGLQJ 4 P 3

(for a single is the smallest of the effective lengths (individually or as part of a bolt group) for

eff

bolt-row in this bolt-row given in Table 6.4 for an unstiffened column flange or Table 6.5 for a

tension) stiffened column flange;

P is as defined in Figure 6.8;

" W 3

(QGSODWHLQ 0

,

9 S

## HII

N =

EHQGLQJ 5 P 3

(for a single is the smallest of the effective lengths (individually or as part of a group of bolt-

eff

bolt-row in rows) given for this bolt-row in Table 6.6;

tension) P is generally as defined in Figure 6.11, but for a bolt-row located in the extended part

## P

P P , where is as defined in Figure 6.10.

of an extended end-plate = x x

" W 3

)ODQJHFOHDWLQ 0

,

9 HII D

N =

EHQGLQJ 6 P 3

is the effective length of the flange cleat from Figure 6.12;

eff

P is as defined in Figure 6.13.

SU(1 (

N

Component Stiffness coefficient i

%ROWVLQWHQVLRQ $/ N 1 , 6 / = preloaded or non-preloaded (for a single V E 10 bolt-row) / is the bolt elongation length, taken as equal to the grip length (total thickness of b material and washers), plus half the sum of the height of the bolt head and the height of the nut. *) %ROWVLQVKHDU non-preloaded preloaded ## Q G I 2 16 E XE N N  ## N (or ) = = 11 17 11 (G 0 16 G is the nominal diameter of an M16 bolt; M16 Q is the number of bolt-rows in shear. b %ROWVLQ *) non-preloaded preloaded ## EHDULQJ Q N N G I 24 (for each E E W X  ## N N N = (or ) = M 12 12 18 component ( on which the N H N = is the distance from the bolt-row to the free bolts bear) b b1 b ## N ## N but edge of the plate in the direction of load b b2 ## N H G = 0,25 / + 0,5 transfer; b1 b  N I is the ultimate tensile strength of the steel on but b1 u N S G which the bolt bears; = 0,25 / + 0,375 b2 b S N  but is the spacing of the bolt-rows in the direction b2 b ## W G N = 1,5 / of load transfer; t j M16  N W is the thickness of that component. but t j ( E O ## &RQFUHWHLQ F HII HII ## N FRPSUHVVLRQ = 13 ( 1 , 275 (including E is the effective width of the T-stub flange, see 6.2.5(3); grout) eff O is the effective length of the T-stub flange, see 6.2.5(3). eff  ## N 3ODWHLQ = 14 EHQGLQJXQGHU This coefficient is already taken into consideration in the calculation of the stiffness FRPSUHVVLRQ coefficient k 13 **) **) %DVHSODWHLQ with prying forces without prying forces EHQGLQJXQGHU " W " W 3 3 0 , 85 0 , 425 ## WHQVLRQ S S ## HII HII ## N N = = 15 15 ## P P 3 3 (for a single O bolt row in is the effective length of the T-stub flange, see 6.2.5(3); eff ## W tension) is the thickness of the base plate; p P is the distance according to Figure 6.8. **) **)$QFKRUEROWVLQ with prying forces without prying forces

WHQVLRQ $/$ /

1

, 6 / 2

, 0 /

= =

## V E V E

16 16

L is the anchor bolt elongation length, taken as equal to the sum of 8 times the

b nominal bolt diameter, the grout layer, the plate thickness, the washer and half of

the height of the nut.

*) provided that the bolts have been designed not to slip into bearing at the load level concerned

P $3 8 , 8 V /  **) prying forces may develop, if b O W 3 HII SU(1 ( ## O F 127( E and the distance should be taken as 1,25 times the base plate When calculating eff eff thickness. 127(Backing 6 of the joint. plates should be assumed not to affect the rotational stiffness j 127(For ZHOGV ) the stiffness coefficient should be taken as equal to infinity. This ## (N 19 6 . component need not be taken into account when calculating the rotational stiffness j ## EHDPZHELQWHQVLRQ SODWHLQWHQVLRQ 127(For EHDPIODQJHDQGZHELQFRPSUHVVLRQ ), (N ), ## (N 7 8 ## RU FRPSUHVVLRQ KDXQFKHG EHDPV (N ), (N ), the stiffness coefficients should be taken as equal to 9 20 infinity. These components need not be taken into account when calculating the rotational stiffness 6 . j 127(Where VXSSOHPHQWDU\ZHESODWH a is used, the stiffness coefficients for the relevant basic ## N N to should be increased as follows: joint components 1 3 N$

for the column web panel in shear should be based on the increased shear area from

– 1 vc

6.2.6.1(6);

N for the column web in compression should be based on the effective thickness of the web

– 2

from 6.2.6.2(6);

N for the column web in tension, should be based on the effective thickness of the web from

– 3

6.2.6.3(8).

(QGSODWHFRQQHFWLRQVZLWKWZRRUPRUHEROWURZVLQWHQVLRQ

*HQHUDOPHWKRG

(1) For end-plate connections with two or more bolt-rows in tension, the basic components related to all

N determined

of these bolt-rows should be represented by a single equivalent stiffness coefficient eq

from: ∑ N K

## HII U U

,

U

N = ... (6.29)

eq ] HT

where: U

K is the distance between bolt-row and the centre of compression;

## U

N U

is the effective stiffness coefficient for bolt-row taking into account the stiffness coefficients

## U

eff, N for the basic components listed in 6.3.3.1(4) or 6.3.3.1(5) as appropriate;

## L

] is the equivalent lever arm, see 6.3.3.1(3).

eq U

N for bolt-row should be determined from:

(2) The effective stiffness coefficient eff, U

1

N = ... (6.30)

eff, U 1

∑ N ,

## L L U

where:

N L U

is the stiffness coefficient representing component relative to bolt-row .

## LU

PAGINE

130

PESO

3.47 MB

AUTORE

PUBBLICATO

+1 anno fa

### DESCRIZIONE APPUNTO

The following terms and definitions apply:
– basic component (of a joint): Part of a joint that makes a contribution to one or more of its structural properties.
– connection: location at which two or more elements meet. For design purposes it is the assembly of
the basic components required to represent the behaviour during the transfer of the relevant internal
forces and moments at the connection.
– connected member: any member that is joined to a supporting member or element.
– joint: zone where two or more members are interconnected. For design purposes it is the assembly of
all the basic components required to represent the behaviour during the transfer of the relevant internal forces and moments between the connected members. A beam-to-column joint consists of a web panel and either one connection (single sided joint configuration) or two connections (double sided joint configuration).
– joint configuration: type or layout of the joint or joints in a zone within which the axes of two or more inter-connected members intersect.
– rotational capacity: the angle through which the joint can rotate without failing.
– rotational stiffness: the moment required to produce unit rotation in a joint.
– structural properties (of a joint): resistance to internal forces and moments in the connected members, rotational stiffness and rotation capacity.
– uniplanar joint: in a lattice structure a uniplanar joint connects members that are situated in a single plane.

DETTAGLI
Corso di laurea: Corso di laurea in ingegneria civile
SSD:
A.A.: 2011-2012

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher Atreyu di informazioni apprese con la frequenza delle lezioni di Tecnica delle costruzioni e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Mediterranea - Unirc o del prof D'assisi Ricciardelli Francesco.

Acquista con carta o conto PayPal

Scarica il file tutte le volte che vuoi

Paga con un conto PayPal per usufruire della garanzia Soddisfatto o rimborsato

Recensioni
Ti è piaciuto questo appunto? Valutalo!

Appunto

Dispensa

Appunto

Appunto