The symbol * denotes that the section is Class 4 when fully stressed under axial compression only.
(a) Design resistance for axial force Npl,Rd =
M0 y
Af
where:
A is the gross area of the cross section fy is the yield strength
M0 is the partial factor for cross sections (M0 = 1.0 as given in the National Annex).
(b) Design resistances for bending about the principal axes of the cross section
The design resistances for bending about the major and minor axes, Mc,Rd , Mc,y,Rd and Mc,z,Rd have been calculated as in Section 8.1 using Wpl,y, Wel,y and Wpl,z and Wel,z as appropriate. No values are given for the reduced resistance in the presence of high shear.
6.2.5 (2)
Mc,Rd values for Class 4 cross sections are not given in the tables. For checks of Class 4 cross sections, see BS EN 1993-1-1, 6.2.9.3(2).
If a section is Class 4, the design resistances are calculated based on the section modulus appropriate for a Class 3 section and a reduced design strength such that the section is Class 3. When subject to combined axial compression and bending, elliptical hollow sections are classified for axial compression, which may be more onerous than major axis bending.
The symbol indicates that the section is Class 4 for a given value of NEd/Npl,Rd.
The symbol $ indicates that the section is Class 4 and that it would be overloaded due to compressive axial force alone i.e. the section is Class 4 and NEd Aeff fy for the given value of NEd / Npl,Rd.
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The Class 2 and Class 3 limits for the section subject to bending and compression are the maximum values of NEd / Npl,Rd up to which the section is either Class 2 or Class 3, respectively. The Class 2 limit is given in bold type.
5.5.2 (8)
As an alternative to Equation (6.2) for Class 1 and 2 sections a less conservative criterion may be used as follows:
MEd ≤ MN,Rd Eq (6.31)
Values of MN,Rd are given in the tables.
6.2.9.1(2)
(c) Design moment resistance reduced due to axial force The reduced design resistances for bending have been calculated as follows:
(i) Circular hollow sections
No information is available in BS EN 1993-1-1 or BS EN 1993-1-6 for the resistance of cross sections of circular hollow sections under combined axial force and bending. The values of MN,Rd have been calculated using the methodology adopted in P202 Volume 1 Section properties member capacities[23]. For Class 1 and 2 sections, the expression is as follows:
y pl
Rd
N, W cos n 2 f
M
where:
n = NEd / Npl,Rd.
(ii) Rectangular and square hollow sections For bending about the y-y axis
w Rd
y, pl, Rd y,
N, 1 0 . 5
1 a M n
M but Mpl,y,Rd Eq (6.39)
6.2.9.1(5)
where:
5 . 0 2 but
w
A
t b a A
Mpl,y,Rd is the plastic resistance moment about the y-y axis n is the ratio NEd / Npl,Rd .
Because the values of MN,y,Rd are only valid for Class 1 and Class 2 sections, no values are shown when NEd / Npl,Rd exceeds the limit for a Class 2 section (shown as the symbol ‘ – ’ in the tables).
For square hollow sections, the reduced moment resistance is the same for both axes, and is displayed as MN,Rd.
For bending about the z-z axis
f Rd
z, pl, Rd
z,
N, 1 0 . 5
1 a M n
M
but Mpl,z,Rd Eq (6.40)
6.2.9.1(5)
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where:
A t h
a A 2
f
but 5 0 .
Mpl,z,Rd is the plastic resistance moment about the z-z axis n is the ratio NEd / Npl,Rd
Because the values of M N,z,Rd are only valid for Class 1 and Class 2 sections, no values are shown when NEd / Npl,Rd exceeds the limit for a Class 2 section (shown as the symbol ‘ – ’ in tables).
10.2.2 Member buckling check
Interaction equations (6.61) and (6.62) from BS EN 1993-1-1, 6.3.3(4) must be satisfied for members subject to combined axial compression and bending. To check these interaction equations the following parameters given in (a), (b) and (c) are needed:
(a)
M1 y Rk
N and
M1 z Rk
N
These are given in the tables as Nb,y,Rd and Nb,z,Rd for rectangular hollow sections and elliptical hollow sections, and as Nb,Rd for circular and square hollow sections. They are the compression resistances for buckling about the y-y and the z-z axis respectively. The adjacent n limit (i.e. NEd / Npl,Rd) ensures that the section is not Class 4 and has been calculated as in Section 6.1.
If a section is Class 4, the design resistances are calculated based on the section modulus appropriate for a Class 3 section and a reduced design strength such that the section is Class 3. When subject to combined axial compression and bending, elliptical hollow sections are classified for axial compression, which may be more onerous than major axis bending.
(b)
M1 Rk y, LT
M
This term is given in the table as Mb,Rd for rectangular and elliptical hollow sections.
Values are given for two NEd./ Npl,Rd limits. The higher limit ensures the section is Class 3 and the lower limit (in bold) ensures the section is Class 2, Mb,Rd is calculated accordingly.
See Section 8.1. For circular and square hollow sections, this term is not applicable and is therefore not given in the tables.
(c)
M1 Rk z,
M
Mz,Rk may be based on the elastic or plastic modulus, depending on the section
classification, as shown in Table 6.7 of BS EN 1993-1-1. Values of fyWel,z are given (for Class 4 elliptical hollow sections, a reduced value of fy is used with the elastic modulus).
Values of fyWpl,z are given as Mc,z,Rd (Mc,Rd for CHS) in the tables for cross section resistance check. Values are quoted with M1 = 1.0, as given in the National Annex.
In addition, values of fyWel,y and Npl,Rd are given in the tables for completeness.
According to the National Annex, Annex A of BS EN 1993-1-1 should be used to calculate the interaction factors k for circular, square and rectangular hollow sections.
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The symbol * denotes that the cross section is Class 4 under axial compression only (due to the web becoming Class 4). Under combined axial compression and bending, the class of the cross section depends on the axial force, expressed in terms of n (= NEd / Npl,Rd).
Values of n are given, up to which the cross sections would be Class 2 or Class 3.
The limits in normal and bold type are the maximum values up to which the section is either Class 3 or Class 2, respectively. The tabulated resistances are only valid up to the given NEd / Npl,Rd limit.
For certain rectangular hollow sections, webs and flanges are Class 4. In these cases section resistances provided are based on effective section properties. These sections are indicated by the symbol.
11 BOLTS AND WELDS BS EN 1993-
1-8
11.1 Bolt resistances
The types of bolts covered are:
Classes 4.6, 8.8 and 10.9, as specified in BS EN ISO 4014[27], BS EN ISO 4016[29], BS EN ISO 4017[28] and BS EN ISO 4018[30], assembled with a nut conforming to BS EN ISO 4032[31] or BS EN ISO 4034[32]. Such bolts should be specified as also complying with BS EN 15048[19].
Countersunk non-preloaded bolts as specified in BS 4933[26], assembled with a nut conforming to BS EN ISO 4032[31] or BS EN ISO 4034[32]. Such bolts should be specified as also complying with BS EN 15048[19] and, for grade 8.8 and grade 10.9, with the mechanical property requirements of BS EN ISO 898-1[33].
Preloaded bolts as specified in BS EN 14399[18]. In the UK, either system HR bolts to BS EN 14399-3 or HRC bolts to EN 14399-10 should be used, with appropriate nuts and washers (including direct tension indicators to BS EN 14399-9, where required).
Countersunk bolts to BS EN 14399-7 may alternatively be used. Bolts should be tightened in accordance with BS EN 1090-2[17].
(a) Non Preloaded Hexagon Head bolts and Countersunk bolts For each grade:
The first table gives the tensile stress area, the design tension resistance, the design shear resistance and the minimum thickness of ply passed through in order to avoid failure due to punching shear.
The second table (and where applicable the third table) gives the design bearing resistance for the given bolt configurations.
(i) The values of the tensile stress area As are those given in the relevant product standard.
(ii) The design tension resistance of a bolt is given by:
M2 s ub Rd 2
t,
A f F k
Table 3.4
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where:
k2 = 0.63 for countersunk bolts
= 0.9 for other bolts
fub is the ultimate tensile strength of the bolt from the relevant product standard As is the tensile stress area of the bolt
M2 is the partial factor for bolts ( M2 = 1.25, as given in the National Annex).
(iii) The shear resistance of the bolt is given by:
M2 s ub Rd v
v,
f A
F Table 3.4
where:
v = 0.6 for Classes 4.6 and 8.8 = 0.5 for Class 10.9
fub is the ultimate tensile strength of the bolt As is the tensile stress area of the bolt.
(iv) The punching shear resistance is expressed in terms of the minimum thickness of the ply for which the design punching shear resistance would be equal to the design tension resistance. The value has been derived from the expression for the punching shear resistance given in BS EN 1993-1-8, table 3.4. The minimum thickness is given by:
u m
M2 Rd p, min 0 . 6 d f t B
Table 3.4
where:
Rd t, Rd
p, F
B
Ft,Rd is the design tension resistance per bolt
dm
nut head ; 2
min e 2 s e s
e is the width across points of the bolt head or the nut s is the width across flats of the bolt head or the nut
fu is the ultimate tensile strength of the ply under the bolt head or nut As is the tensile stress area of the bolt.
(v) The bearing resistance of a bolt is given by:
M2 u b Rd 1
b,
f d t
F k Table 3.4
where:
k1
2 . 8 1 . 7 ; 1 . 4 1 . 7 ; 2 . 5 min
0 2 0
2
d p d
e
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e2 is the edge distance measured perpendicular to the direction of load transfer p2 is the gauge measured perpendicular to the direction of load transfer
d0 is the hole diameter
b
; ; 1.0
4 1
; 3 min 3
u ub 0
1 0 1
f f d
p d e
fub is the ultimate tensile strength of the bolt
fu is the ultimate tensile strength of the ply passed through e1 is the end distance measured in the direction of load transfer p1 is the pitch measured in the direction of load transfer
Bearing resistances have been calculated for end distances of e1 = 2d in the second table and e1 =3d in the third table.
The values of e2 in the second table are based on typical connections used in the UK and values of e2 in the third for Class 8.8 and 10.9 bolts table have been chosen to give increased resistances.
The values of pitch, p1 and p2, have been chosen such that resistance values based on them are not more critical than those based on e1 and e2.
Values of e1 e2, p1 and p2 given in the tables have then been rounded up to the nearest 5 mm. Further details about the layout of the bolts are given in AD348.