3. Members

3.1. Tension

3.1.1. Column Web in Tension

Design resistance of an unstiffened column web in transverse tension according to EN 1993-1-8, 6.2.6.3:

𝐹𝑡,𝑤𝑐,𝑅𝑑 = 𝜔 𝑥 𝑏𝑒𝑓𝑓,𝑡,𝑤𝑐 𝑥 𝑡𝑤𝑐 𝑥 𝑓𝑦,𝑤𝑐

𝛾𝑀0

ω – reduction factor to allow for the interaction with shear in the column web panel, calculated according to the transformation parameter β (EN 1993-1-8 Table 6.3). Where β value is calculated based on design bending moment (MEd or MEd_Left and MEd_Right ) depending on the joint configuration.

For example, for a single-sided connection (moment end plate) with one bending moment β = 1

beff,t,wc – the effective width of column web in tension;

twc – column web thickness

For a welded connection:

𝑏𝑒𝑓𝑓,𝑡,𝑤𝑐=𝑡𝑓𝑏 + 2√2𝑎𝑏 + 5(𝑡𝑓𝑐 + 𝑠)

where:

for a rolled I or H section column: s = rc

for a welded I or H section column: s = √2𝑎𝑐

tfb – beam flange thickness;

tfc – column flange thickness;

ac – weld thickness between the secondary beam flange and end plate;

rc – root radius;

For a bolted end-plate connection: beff,t,wc of column web in tension should be taken as equal to the effective length of equivalent T-stub representing the column flange, see 6.2.6.4

𝑏𝑒𝑓𝑓,𝑡,𝑤𝑐 = 𝑡𝑓𝑏 + 2√2𝑎𝑝 + 5(𝑡𝑓𝑐 + 𝑠) + 𝑠𝑝

sp – the length obtained by dispersion at 45° through the end-plate

For a moment end plate connection:

𝐹𝑡,𝑤𝑐,𝑅𝑑 = 𝑏𝑒𝑓𝑓,𝑡,𝑤𝑐 𝑥 𝑡𝑤𝑐 𝑥 𝑓𝑦,𝑤𝑐

𝛾𝑀0

If

𝐹𝑡,1,𝑅𝑑 ≤ 𝐹𝑡,2,𝑅𝑑 → 𝑏𝑒𝑓𝑓,𝑡,𝑤𝑐 = 𝑙𝑒𝑓𝑓,1

𝐹𝑡,1,𝑅𝑑 > 𝐹𝑡,2,𝑅𝑑 → 𝑏𝑒𝑓𝑓,𝑡,𝑤𝑐 = 𝑙𝑒𝑓𝑓,2

Where

Ft1,Rd , Ft2,Rd – tension resistances of the plate for the first and second mode of failure;

leff,1 – the effective length for the first mode of failure (minimum between effective length of the circular or non-circular failure pattern);

leff,2 – the effective length for the second mode of failure (non-circular failure pattern);

3.1.2. Beam Web in Tension

In a bolted end-plate connection, the design tension resistance of the beam web, according to EN 1993-1-8, 6.2.6.8 should be obtained from:

𝐹𝑡,𝑤𝑏,𝑅𝑑 = 𝜔 𝑥 𝑏𝑒𝑓𝑓,𝑡,𝑤𝑏 𝑥 𝑡𝑤𝑏 𝑥 𝑓𝑦,𝑤𝑏

𝛾𝑀0

beff,t,wb – the effective width of the beam web in tension; it is equal to the effective length of equivalent T-stub representing the end-plate in bending for an individual bolt-row or bolt-group.

twb – beam web thickness;

twb = min( tbeam, thaunch, tst)

For for a moment end plate connection:

For groups with stiffeners:

𝐹𝑡,𝑤𝑏,𝑅𝑑 = 𝑏𝑒𝑓𝑓,𝑡𝑟,𝑤𝑏 𝑥 𝑡𝑠𝑡 𝑥 𝑓𝑦,𝑠𝑡

𝛾𝑀0

For groups without stiffeners:

𝐹𝑡,𝑤𝑏,𝑅𝑑 = 𝑏𝑒𝑓𝑓,𝑡𝑟,𝑤𝑏 𝑥 𝑡𝑤𝑏 𝑥 𝑓𝑦,𝑏

𝛾𝑀0

For first bolt row outside tensioned flange or haunch:

𝐹𝑡,𝑤𝑏,𝑅𝑑 = ℎ𝑠𝑡𝑥 𝑡𝑠𝑡 𝑥 𝑓𝑦,𝑠𝑡

𝛾𝑀0+

𝑏𝑓𝑏𝑥𝑡𝑓𝑏

2 𝑥

𝑓𝑦,𝑏

𝛾𝑀0

For other bolt row outside tensioned flange or haunch (only with stiffener):

𝐹𝑡,𝑤𝑏,𝑅𝑑 = 𝑏𝑒𝑓𝑓,𝑡𝑟,𝑤𝑏 𝑥 𝑡𝑠𝑡 𝑥 𝑓𝑦,𝑠𝑡

𝛾𝑀0

For first row below tensioned beam flange rows:

𝐹𝑡,𝑤𝑏,𝑅𝑑 = 𝐿𝑤 𝑥 𝑡𝑤𝑏 𝑥 𝑓𝑦,𝑏

𝛾𝑀0+

𝑏𝑓𝑏𝑥𝑡𝑓𝑏

2𝑥

𝑓𝑦,𝑏

𝛾𝑀0

For end and inner bolt rows:

𝐹𝑡,𝑤𝑏,𝑅𝑑 = 𝑏𝑒𝑓𝑓,𝑡𝑟,𝑤𝑏 𝑥 𝑡𝑤𝑏 𝑥 𝑓𝑦,𝑏

𝛾𝑀0

If

𝐹𝑡,1,𝑅𝑑 ≤ 𝐹𝑡,2,𝑅𝑑 → 𝑏𝑒𝑓𝑓,𝑡,𝑤𝑏 = 𝑙𝑒𝑓𝑓,1

𝐹𝑡,1,𝑅𝑑 > 𝐹𝑡,2,𝑅𝑑 → 𝑏𝑒𝑓𝑓,𝑡,𝑤𝑏 = 𝑙𝑒𝑓𝑓,2

Where

Ft1,Rd , Ft2,Rd – tension resistances of the plate for the first and second mode of failure;

leff,1 – the effective length for the first mode of failure (minimum between effective length of the circular or non-circular failure pattern);

leff,2 – the effective length for the second mode of failure (non-circular failure pattern);

3.1.3. Tension Yielding Verification

- verification for Clip Angle and Gusset -

Check relation: NEd ≤ Npl,Rd;

The design plastic resistance on axial force is calculated according to EN 1993-1-1 6.2.4:

𝑁𝑝𝑙,,𝑅𝑑 =𝑛 𝑥 𝐴 𝑥 𝑓𝑦

𝛾𝑀0;

Where,

n – number of objects solicited in the same direction;

A – profile gross area;

Note: For a (gusset) plate, the tension verification area A is calculated as follows: 𝐴 = 𝑡𝑝 𝑥 ℎ30

where:

tp – the plate thickness;

h30 – the plate length obtained with a 30° angle diffusion from the bolts on diagonal.

See also the picture below:

3.1.3. Tension Ultimate Verification

- verification for Clip Angle and Gusset -

Check relation: NEd ≤ Nu,Rd;

For sections with holes, the design ultimate resistance of the net cross-section is calculated

according to EN 1993-1-1 6.2.3:

𝑁𝑢,𝑅𝑑 = 0.9 𝑥 𝑛𝑜𝑏𝑗𝑥 𝐴𝑛𝑒𝑡 𝑥 𝑓𝑢

𝛾𝑀2

Note 1: The design ultimate resistance for angles connected by a single row of bolts in one leg is

calculated according to EN 1993-1-8 3.10.3:

For 1 bolt:

𝑁𝑢,𝑅𝑑 =2 𝑥 (𝑒2− 0.5 𝑥 𝑑0,𝑣) 𝑥 𝑡𝑝 𝑥 𝑓𝑢

𝛾𝑀2;

For 2 bolts:

𝑁𝑢,𝑅𝑑 =𝛽2 𝑥 𝐴𝑛𝑒𝑡 𝑥 𝑓𝑢

𝛾𝑀2;

For 3 or more bolts:

𝑁𝑢,𝑅𝑑 =𝛽3 𝑥 𝐴𝑛𝑒𝑡 𝑥 𝑓𝑢

𝛾𝑀2;

where:

nobj – number of objects solicited in the same direction;

Anet – profile net area;

β2, β3 – reduction factors depending on the pitch p1, as given in EN 1993-1-8 Table 3.8;

d0,v – hole diameter on the v direction

Note 2: For a (gusset) plate, the net area Anet is calculated as follows:

𝐴𝑛𝑒𝑡 = (ℎ30 − 𝑛𝑏,𝑣𝑥𝑑0,𝑣) 𝑥 𝑡𝑝

where:

tp – plate thickness;

nb,v – number of bolt rows;

3.2. Compression

3.2.1. Column web in transverse compression

Check relation: Fc,wc,Ed ≤ Fc,wc,Rd

The resistance of the column web in transverse compression according to EN 1993-1-8, 6.2.6.2 is equal to the web crushing or the buckling resistance, whichever is the smallest:

𝐹𝑐,𝑤𝑐,𝑅𝑑 = min (𝜔 𝑥 𝑘𝑤𝑐 𝑥 𝑏𝑒𝑓𝑓,𝑐,𝑤𝑐 𝑥 𝑡𝑤𝑐 𝑥 𝑓𝑦,𝑤𝑐

𝛾𝑀0 ; 𝜔 𝑥 𝑘𝑤𝑐 𝑥 𝜌 𝑥 𝑏𝑒𝑓𝑓,𝑐,𝑤𝑐 𝑥 𝑡𝑤𝑐 𝑥

𝑓𝑦,𝑤𝑐

𝛾𝑀1 )

The design force of column web in transverse compression is determined as follows:

𝐹𝑐,𝑤𝑐,𝐸𝑑 = |𝑀𝐸𝑑

ℎ𝑓−

𝑁𝐸𝑑

2|

Fc,wc,Ed is the design force of the column web in transverse compression

hf is the moment arm between the resultant tensile force and the resultant compressive force

where:

𝑏𝑒𝑓𝑓,𝑐,𝑤𝑐 = 𝑡𝑓𝑏 + 2√2𝑎𝑝 + 5(𝑡𝑓𝑐 + 𝑠) + 𝑠𝑝

𝑠𝑝 ≤ 2𝑡𝑝

For a rolled I or H section column: s = rc

For a welded I or H section column: s = √2𝑎𝑐

ω – reduction factor to allow for the interaction with shear in the column web panel, calculated according to the transformation parameter β (EN 1993-1-8 Table 6.3).

kwc – reduction factor, allowing for coexisting longitudinal compressive stress in the column (EN 1993-1-8 6.2.6.2(2))

ρ – reduction factor for plate buckling (EN 1993-1-8 6.2.6.2(1))

beff,t,wc – the effective width of column web in tension;

σ com,Ed – the maximum longitudinal compression stress due to axial force and bending moment in the column web (adjacent to the root radius for a rolled section or the toe of the weld for a welded section)

𝜎𝑐𝑜𝑚,𝐸𝑑 = 𝑀𝐸𝑑

𝑊𝑒𝑙+

𝑁𝐸𝑑

𝐴

𝜎𝑐𝑜𝑚,𝐸𝑑 ≤ 0.7 𝑥𝑓𝑦,𝑤𝑐 => 𝑘𝑤𝑐 = 1

𝜎𝑐𝑜𝑚,𝐸𝑑 > 0.7 𝑥𝑓𝑦,𝑤𝑐 => 𝑘𝑤𝑐 = 1.7 − 𝜎𝑐𝑜𝑚,𝐸𝑑

𝑓𝑦,𝑤𝑐

Depending on the plate slenderness λp, the reduction factor is determined as follows:

𝜆𝑝 ≤ 0.72 => ρ =1.0

𝜆𝑝 > 0.72 => ρ = 𝜆𝑝−0.2

𝜆𝑝2

Where: 𝜆𝑝 = 0.932 √𝑏𝑒𝑓𝑓,𝑐,𝑤𝑐 𝑥 𝑑 𝑥 𝑓𝑦,𝑤𝑐

𝐸 𝑥 𝑡𝑤𝑐2

d – column straight portion of the web;

E – modulus of elasticity of the column;

For a rolled profile I or H section column : 𝑑 = ℎ𝑐 − 2 𝑥 ( 𝑡𝑓𝑐 + 𝑟𝑐);

For a welded I or H section column: 𝑑 = ℎ𝑐 − 2 𝑥 ( 𝑡𝑓𝑐 + √2𝑎𝑐);

Note: Whenever the column is provided with stiffeners, the column web resistance will be calculated by adding the compressed stiffeners resistance (see chapter 5.2.2 Compression).

3.2.2. Beam web and flange compression

Compression resistance of the beam is calculated according to EN 1993-1-8, 6.2.6.7:

𝐹𝑐,𝑓𝑏,𝑅𝑑 = 𝑀𝑐,𝑅𝑑

(ℎ − 𝑡𝑓𝑏 )

Mc,Rd is the design moment resistance of the beam cross-section;

Wc,pl is the plastic section modulus;

Wc,el is the elastic section modulus;

h is the depth of the section; for a haunched beam, it is the depth of the fabricated section;

tfb is the flange thickness of the connected beam; for a haunched beam, it is the thickness of the haunch flange;

The design bending moment about one main axis of a cross-section is given in EN1993-1-1. 6.2.5, and is determined as follows:

For class 1 or 2 : 𝑀𝑐,𝑅𝑑 = 𝑊𝑐,𝑝𝑙 𝑥 𝑓𝑦

𝛾𝑀0

For class 3: 𝑀𝑐,𝑅𝑑 = 𝑊𝑐,𝑒𝑙 𝑥 𝑓𝑦

𝛾𝑀0

For class 4: 𝑀𝑐,𝑅𝑑 = 𝑊𝑐,𝑒𝑓𝑓 𝑥 𝑓𝑦

𝛾𝑀0

Note: The plastic and elastic section modulus are calculated for the section from the end plate face (including the haunches and reinforcement plates, if they exist).

The presence of reinforcement stiffeners (compressed flange stiffeners) has impact on compression resistance of the beam, but also in other parts of the calculation (e.g.: center of rotation, bolt-rows positioning, T-stub calculation, web plate reference length (EN 1993-1-8, 6.2.6.1 - figure 6.5).

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%. For example, if the resistance of

the beam flange is 𝑡𝑓𝑏 𝑥 𝑏𝑓𝑏 𝑥 𝑓𝑦,𝑓𝑏, then 𝐹𝑐,𝑓𝑏,𝑅𝑑 ≤ 𝑡𝑓𝑏 𝑥 𝑏𝑓𝑏 𝑥 𝑓𝑦,𝑓𝑏

𝛾𝑀0.

The design resistance of a haunched beam in compression according to EN 1993-1-8 6.2.6.7(3) should be determined as follows:

𝐹𝑐,ℎ𝑏,𝑅𝑑 =𝐹𝑐,𝑤𝑏,𝑅𝑑

𝑡𝑎𝑛𝛼

The design resistance of the beam web to transverse compression (according to EN 1993-1-8 6.2.6.2):

𝐹𝑐,𝑤𝑏,𝑅𝑑 = 𝜔 𝑥 𝑘𝑤𝑏 𝑥 𝜌 𝑥 𝑏𝑒𝑓𝑓,𝑐,𝑤𝑏 𝑥 𝑡𝑤𝑏 𝑥 𝑓𝑦,𝑤𝑏

𝛾𝑀1

The effective width of the beam web in compression:

𝑏𝑒𝑓𝑓,𝑐,𝑤𝑏 = 𝑡𝑓𝑏

𝑠𝑖𝑛𝛼+ 5 (𝑡𝑓𝑏 + 𝑟𝑏 )

The other parameters from Fc,wb,Rd expression: ω, ρ, kwb should be calculated similarly to the resistance of the column web in transverse compression Fc,wc,Rd

3.2.3. Compression Yielding Verification

- verification for Clip Angle and Gusset -

Check relation: NEd ≤ Npl,Rd;

The design plastic resistance on the axial force is calculated according to EN 1993-1-1 6.2.4:

𝑁𝑝𝑙,,𝑅𝑑 =𝑛 𝑥 𝐴 𝑥 𝑓𝑦

𝛾𝑀0;

Where,

n – number of objects solicited in the same direction;

A – profile gross area;

Note: For a (gusset) plate, the compression verification area A is calculated as follows:

𝐴 = 𝑡𝑝 𝑥 ℎ30 , where

tp – the plate thickness;

h30 – the plate length obtained with 30° angle diffusion from the bolts on diagonal;

See also the picture below:

3.3. Shear

3.3.1. Column Web Panel in Shear

Check relation: Vwp,Ed ≤ Vwp,Rd

The design resistance of the web panel in shear for an unstiffened column Vwp,Rd according to EN 1993-1-8 6.2.6.1:

𝑉𝑤𝑝,,𝑅𝑑 =0.9 𝑥𝑓𝑦,𝑤𝑐𝑥𝐴𝑣𝑐

√3 𝑥 𝛾𝑀0

The expression given above is valid if the column web slenderness satisfies the condition:

𝑑

𝑡𝑤 ≤ 69 𝑥 𝜀

where, the depth of the column web: 𝑑 = ℎ − 2 𝑥 𝑡𝑓𝑐 − 2 𝑥 𝑟

𝜀 = √235

𝑓𝑦,𝑤𝑐

Avc – the shear area of the column

h – column height;

tfc – flange thickness;

r – root radius

tw – web thickness

The design shear force should be obtained:

𝑉𝑤𝑝,𝐸𝑑 = |𝑀𝐸𝑑

ℎ𝑓| + |

𝑁𝐸𝑑

2|

hf – is calculated according to EN 1993-1-8, 6.2.7, Figure 6.15;

Note: The column web panel in shear resistance for a stiffened column is the sum of the column

web panel in shear for the unstiffened column and the stiffener resistance (see chapter 5.2.3)

3.3.2. Shear Yielding Verification

- verification for Moment End Plate and Apex -

Check relation: VEd ≤ Vpl,Rd;

Design plastic shear resistance:

𝑉𝑝𝑙,𝑅𝑑 =𝑛 𝑥𝐴𝑣𝑐𝑥𝑓𝑦,𝑤𝑐

√3 𝑥 𝛾𝑀0

n – the number of connected objects;

Av – end plate gross shear area;

Av =hp x tp ;

VEd – must be used in relations as a projection of the forces on the bolt directions

3.3.3. Shear Ultimate Verification

- verification for Moment End Plate and Apex –

Check relation: VEd ≤ Vu,Rd ;

Design ultimate shear resistance:

𝑉𝑢,𝑅𝑑 =0.9 𝑥 𝑛 𝑥 𝐴𝑣,𝑛𝑒𝑡𝑥𝑓𝑢

√3 𝑥 𝛾𝑀2

𝐴𝑣,𝑛𝑒𝑡 = (ℎ − 𝑛𝑣𝑥 𝑑0,𝑣) 𝑥 𝑡

Av,net -net shear area;

nv – number of vertical bolt rows;

d0,v – diameter of the hole on vertical direction;

3.3.4.Block Tearing Verification

- verification for Moment End Plate and Apex -

Check relation: VEd ≤ Veff,Rd ;

Design block shear tearing resistance when bolts are centered on members:

𝑉𝑒𝑓𝑓,𝑅𝑑 = 𝑛 𝑥 ( 𝐴𝑛,𝑡 𝑥 𝑓𝑢

𝛾𝑀2+ 𝐴𝑛,𝑣 𝑥

𝑓𝑦

√3 𝑥 𝛾𝑀0

)

Design block shear tearing resistance when bolts are not centered on members:

𝑉𝑒𝑓𝑓,𝑅𝑑 = 𝑛 𝑥 (0.5𝑥 𝐴𝑛,𝑡 𝑥 𝑓𝑢

𝛾𝑀2+ 𝐴𝑛,𝑣 𝑥

𝑓𝑦

√3 𝑥 𝛾𝑀0

)

n – number of end plates;

Net area subjected to tension:

𝐴𝑛,𝑡 = 𝑚𝑖𝑛( [𝑒ℎ,𝑟 + 𝑒ℎ,𝐿 + (𝑛ℎ − 2) 𝑥 𝑝ℎ − (𝑛ℎ − 1) 𝑥 𝑑0,ℎ ]𝑥 𝑡 ; [𝑤 − 𝑒ℎ,𝑟 − 𝑒ℎ,𝐿 − (𝑛ℎ − 1) 𝑥 𝑑0,ℎ ]𝑥 𝑡)

eh,R – edge distance between the last hole and the plate right edge on horizontal direction;

eh,L – edge distance between the last hole and the plate left edge on horizontal direction;

nh – holes number on horizontal direction (from one bolt row);

ph – intermediate distance between hole center on horizontal direction;

d0,h – diameter of the hole on horizontal direction;

bp – end plate width;

t – end plate thickness;

Net area subjected to shear:

𝐴𝑛,𝑣 = 𝑛𝑏𝑐 𝑥 [ℎ − 𝑒𝑣,𝑇 − (𝑛𝑣 − 0.5) 𝑥 𝑑0,𝑣 ]𝑥 𝑡

nbc – coefficient depending of number of bolt columns;

h – end plate height;

evB – edge distance between the first hole from bottom and the bottom plate edge on vertical direction;

nv – holes number on vertical direction (from one bolt column);

d0,v – diameter of the hole on vertical direction;

3.4. Bending

3.4.1. Column Flange in Bending

Equivalent T-Stub Method is used for the Column Flange Bending Resistance and end plate bending resistance:

1. Design resistance of a T-Stub, if the prying effect is not developed, (Lb>Lb*):

𝐹𝑡,𝑅𝑑 = min (𝐹𝑡,1−2,𝑅𝑑; 𝐹𝑡,3,𝑅𝑑 ) EN 1993-1-8, 6.2.4.1 (6)

Tension resistance for the 1-2 failure mode (yield in bending of connection)

𝐹𝑡,1−2,𝑅𝑑 =2𝑥𝑀𝑝𝑙,1,𝑅𝑑

𝑚 EN 1993-1-8, Table 6.2

Tension resistance of the plate/flange for third mode of failure:

𝐹𝑡,3,𝑅𝑑 = ∑𝐹𝑡,𝑅𝑑 = 𝑛𝑥𝐹𝑡,𝑅𝑑 EN 1993-1-8, Table 6.2

Ft,Rd – the design tension resistance of a bolt, according to EN1993-1-8 Table 3.4

∑Ft,Rd – the total value of Ft,Rd for all the bolts in the T-stub;

2. Design resistance of a T-Stub, if the prying effect is developed, (Lb<Lb*):

𝐹𝑡,𝑅𝑑 = min (𝐹𝑡,1,𝑅𝑑; 𝐹𝑡,2,𝑅𝑑 ; 𝐹𝑡,3,𝑅𝑑) EN 1993-1-8, 6.2.4.1 (6)

According to EN 1993-1-8, Table 6.2 the tension resistance of the plate for the 3 mode of failure:

Tension resistance of the plate/flange for the first mode of failure (complete yielding of the connection at bending of the plate/flange):

𝐹𝑡,1,𝑅𝑑 =4𝑥𝑀𝑝𝑙,1,𝑅𝑑 + 2𝑥𝑀𝑏𝑝,𝑅𝑑

𝑚

Tension resistance of the plate for the second mode of failure (yielding of the connection at bending with bolt failure in tension):

𝐹𝑡,2,𝑅𝑑 =2𝑥𝑀𝑝𝑙,2,𝑅𝑑 + ∑𝐹𝑡,𝑅𝑑

𝑚 + 𝑛

Tension resistance of the plate for the third mode of failure (bolt failure):

𝐹𝑡,3,𝑅𝑑 = ∑𝐹𝑡,𝑅𝑑 = 𝑛𝑥𝐹𝑡,𝑅𝑑

Plastic resistances of the plates for the failure modes according to EN 1993-1-8, Table 6.2:

𝑀𝑝𝑙,1,𝑅𝑑 = 0.25𝑥∑𝑙𝑒𝑓𝑓,1𝑥 𝑡𝑓2𝑥

𝑓𝑦

𝛾𝑀0

𝑀𝑝𝑙,2,𝑅𝑑 = 0.25𝑥∑𝑙𝑒𝑓𝑓,2𝑥 𝑡𝑓2𝑥

𝑓𝑦

𝛾𝑀0

Note 1: If there are backing plates:

𝑀𝑝𝑙,1,𝑅𝑑 = 0.25𝑥∑𝑙𝑒𝑓𝑓,1𝑥 𝑡𝑏𝑝2 𝑥

𝑓𝑦,𝑏𝑝

𝛾𝑀0

fy,bp – the yield strength of the backing plates;

tbp – the thickness of the backing plates;

Lb – is the bolt elongation length, taken as equal to the grip length (total thickness of material and washers), plus half the sum of the height of the bolt head and the height of the nut.

𝐿𝑏∗ = 8.8 𝑥

𝑚3𝑥 𝑛𝑟 𝑥 𝐴𝑠

∑𝑙𝑒𝑓𝑓,1 𝑥 𝑡3 EN 1993-1-8, Table 6.11

As tensile stress area of the bolt;

nr number of bolt rows (nr >1, for groups)

Failure patterns effective lengths:

lcp row effective length for a circular failure pattern;

lcp,g group effective length for a circular failure pattern;

lnc row effective length for a non-circular failure pattern;

lnc,g group effective length for a non-circular failure pattern;

leff,1 the effective length for the first mode of failure (minimum between effective length of the circular or non-circular failure pattern);

leff,2 the effective length for the second mode of failure (non-circular failure pattern);

Note 2: There are differences between French (FR) localization (e.g.: member web in tension

exists for outer rows) and other countries. See the availability of member web in tension and end

plate in bending resistances for outer rows/groups presented in the pictures below:

3.4.2. Bending

The design bending moment about one principal axis of a cross-section is given in EN1993-1-1. 6.2.5 and is determined as follows:

For class 1 or 2 : 𝑀𝑐,𝑅𝑑 = 𝑊𝑐,𝑝𝑙 𝑥 𝑓𝑦

𝛾𝑀0

For class 3: 𝑀𝑐,𝑅𝑑 = 𝑊𝑐,𝑒𝑙 𝑥 𝑓𝑦

𝛾𝑀0

For class 4: 𝑀𝑐,𝑅𝑑 = 𝑊𝑐,𝑒𝑓𝑓 𝑥 𝑓𝑦

𝛾𝑀0

Mc,Rd design moment resistance of the beam cross-section;

Wc,pl plastic section modulus;

Wc,el elastic section modulus;

Base Plate. Bending Moment Verification

Check relation: Mj,Ed ≤ Mj,Rd ;

Design moment resistance of a column base Mj,Rd depend on eccentricity.

Load eccentricity: 𝑒 =𝑀𝑗,𝐸𝑑

𝑁𝑗,𝐸𝑑

The tensile force FT is positioned at the centre of anchor bolts.

Compression force Fc is positioned at the centre of the column flange.

The following parameters are used in this method:

The design tension resistance of the left hand side of the joint:

FT,l,Rd = min(Ft,wc,Rd, Ft,pl,Rd)

Ft,wc,Rd – column web in tension under the left column flange;

Ft,pl,Rd – base plate in bending under the left column flange

The design tension resistance FT,r,Rd of the right side of the joint:

FT,r,Rd = min(Ft,wc,Rd, Ft,pl,Rd)

Ft,wc,Rd – column web in tension under the right column flange;

Ft,pl,Rd – base plate in bending under the right column flange;

The design compressive resistance FC,l,Rd of the left side of the joint:

FC,l,Rd = min(Fc,pl,Rd, Fc,fc,Rd)

Fc,pl,Rd – concrete in compression under the left column flange;

Fc,fc,Rd – left column flange and web in compression;

The design compressive resistance FC,r,Rd of the right side of the joint:

FC,r,Rd = min(Fc,pl,Rd, Fc,fc,Rd)

Fc,pl,Rd – concrete in compression under the right column flange;

Fc,fc,Rd – right column flange and web in compression;

Determination of the lever arm z depending on the values of MEd and NEd :

a) Column base connection in case of a dominant compressive normal force;

b) Column base connection in case of a dominant tensile normal force;

c) Column base connection in case of a dominant bending moment;

Design moment resistance Mj,Rd of column bases depending on the loading values of M j,Ed and Nj,Ed

according to EN1993-1-8 6.2.8.3 Table 6.7.

Moment End Plate and Apex Haunch. Bending Moment Verification

The design moment resistance Mj,Rd of a beam-to-column joint with a bolted end-plate connection or bolted beam splices with welded end-plates may be determined from:

𝑀𝑗,𝑅𝑑 = ∑(𝐹𝑡𝑅𝑑𝑥ℎ𝑟)

Ft,Rd – the effective design tension resistance of bolt-row

hr – is the distance from bolt-row to the centre of compression;

r- the bolt row number;

Note: If NEd ≤ 5% NplRd the design moment resistance Mj,Rd of a beam to column joint or beam

splice may be determined as follows: 𝑀𝑗,𝑅𝑑 = ∑(𝐹𝑡𝑅𝑑𝑥ℎ𝑟)

𝑁𝑝𝑙,𝑅𝑑 = 𝐴𝑥𝑓𝑦

𝛾𝑀0

3.5. Buckling

Column Web Buckling

Check relation: Fb,wc,Ed ≤ Fb,wc,Rd ;

Column web buckling design force:

𝐹𝑏,𝑤𝑐,𝐸𝑑 = |𝑀𝐸𝑑

ℎ𝑓−

𝑁𝐸𝑑

2|

hf – distance between resultant tensile force and resultant compressive force

NEd – design axial force

MEd – design bending moment

Column web buckling design resistance:

𝐹𝑏,𝑤𝑐,𝑅𝑑 = 𝜒 𝑥 𝐴 𝑥 𝑓𝑦

𝛾𝑀1 EN 1993-1-1 6.3.1.1

The column web is stiffened, so:

𝜀 = √235

𝑓𝑦,𝑠𝑡

The reduction factor for the relevant buckling curve is:

𝜒 = min (1 ; 1

𝜙+√𝜙2−𝜆2) EN 1993-1-1 6.3.1.2

𝜙 = 0.5𝑥(1 + 𝛼 𝑥 (𝜆 − 0.2) + 𝜆2)

Φ – value to determine the reduction factor;

The imperfection coefficient α is chosen according to EN 1993-1-1, tables 6.1 and 6.2.

𝐴 = 𝐴𝑤𝑒𝑏 = ℎ𝑢𝑛𝑠𝑡𝑖𝑓𝑓𝑥 𝑡𝑤

ℎ𝑢𝑛𝑠𝑡𝑖𝑓𝑓 = ℎ𝐿 + 2𝑥𝑡 + 𝑡𝑓

hL –height of the column section;

t – end plate thickness;

tf – beam flange thickness or the haunch flange thickness( when the haunch beam stiffener is enabled)

Note: When the column web is stiffened area A is calculated by adding the stiffener area to

web area:

𝐴 = 𝐴𝑤𝑒𝑏 + 𝐴𝑠𝑡

𝐴𝑤𝑒𝑏 = ℎ𝑠𝑡𝑖𝑓𝑓𝑥 𝑡𝑤

ℎ𝑠𝑡𝑖𝑓𝑓 = 𝑡𝑠𝑡 + 30 𝑥 𝜀

𝐴𝑠𝑡 = 𝑛𝑠𝑡 𝑥 𝑏𝑠𝑡 𝑥 𝑡𝑠𝑡

hstiff – the height of the section subject to buckling;

tw – thickness of the column web

tst – stiffener thickness;

bst – stiffener width;

nst – number of stiffeners;

I – moment of inertia of section subject to buckling, according to “weak” axis:

Radius of gyration:

𝑖 = √𝐼

𝐴

The stiffeners non dimensional slenderness:

𝜆 =𝐿𝑐𝑟

𝑖 𝑥 𝜆1 EN 1993-1-1 6.3.1.3

λ1 – non dimensional slenderness (limit for elastic buckling);

𝜆1 = π 𝑥 √𝐸

𝑓𝑦

Buckling length:

𝐿𝑐𝑟 = 0.75 𝑥 𝑑𝑐

dc -column straight portion of the web;

For example for a rolled profile:

𝑑𝑐 = ℎ𝑐 − 2𝑥(𝑡𝑓𝑐 − 𝑟𝑐)

hc – column section height;

rc – column inner radius;

tfc – column flange thickness;