Section properties

6.2.2.1. Gross cross-section

3-2/clause 6.2.1.1(1)defines the gross cross-section as the whole cross-section ignoring bolt holes but including larger holes, such as a cut-out for a drainage pipe.

6.2.2.2. Net area

Some resistances require consideration of net sections. The ‘net’ area of a steel component is defined in 3-1-1/clause 6.2.2.2(1) as its gross area less appropriate deductions for all holes and other openings. The area of a hole is the maximum area removed from the steel component in cross-section. 3-1-1/clause 6.2.2.2(2) reminds the designer that the countersunk portion of a hole should also be deducted if countersunk bolts are to be used as fasteners, as shown in Fig. 6.2-1.

If fastener holes are not staggered then the net area of the steel component will be the gross area minus the area of all the holes at that section – 3-1-1/clause 6.2.2(3) refers. If the fasteners are staggered then, in accordance with 3-1-1/clause 6.2.2(4), the net area of the steel component will be the greater of the following:

1. The gross area of the steel component minus the area of holes at any cross-section perpendicular to the member axis (e.g. Section 1–1 in Fig. 6.2-2).

2. The gross area of the steel component minus an effective area allowing for staggered holes as follows: t
nd
X s 2 4p  3-1-1/(6.3) where: s is the staggered pitch parallel to the member axis;

p is the spacing of centres of the same two holes measured perpendicular to the member axis;

t is the thickness of the steel component;

n is the number of holes in any diagonal or zig-zag line extending progres- sively across the component;

d is the diameter of the hole.

Surface 2–2 in Fig. 6.2-2 indicates a typical application of expression 3-1-1/(6.3) where n¼ 2. The net area from expression 3-1-1/(6.3) should not be taken greater than the gross area, although other resistance checks effectively stop this from being done.

3-2/clause 6.2.1.1(1) 3-1-1/clause 6.2.2.2(1) 3-1-1/clause 6.2.2.2(2) 3-1-1/clause 6.2.2(3) 3-1-1/clause 6.2.2(4)

Area of countersunk hole

Fig. 6.2-1. Area of countersunk hole

p

s s

Direction of force = ‘member axis’ 1

1 2

2

If expression 3-1-1/(6.3) is applied to an angle or other member with holes on several faces, 3-1-1/clause 6.2.2.2(5) requires p to be measured along the centre of the thickness of the plates when the dimension extends around a corner. If a member is connected eccentrically, this eccentricity needs to be considered. EN 1993-1-8 gives a method for tension connections which is discussed in section 6.2.3 of this guide. Where an unequal angle is connected by way of holes on its smaller leg only, 3-1-8/clause 3.10.3 requires the net area for tension calculations to be based on a fictitious equal angle with leg size based on the smaller of those for the real unequal angle.

6.2.2.3. Effective widths for shear lag

6.2.2.3.1. Shear lag for members in bending at SLS and ULS (additional sub-section) A description of the causes and idealization of shear lag effects is given in section 5.1.1 of this guide. This section describes the calculation procedure for determining effective widths for shear lag at both serviceability limit states (SLS) and ultimate limit states (ULS). 3-2/clause 6.2.2.3(1) makes reference to EN 1993-1-5 for this calculation, both directly and through EN 1993-1-1.

The effect of shear lag is greatest in locations of high shear where the force in the flanges is changing rapidly. Consequently, effective widths for shear lag at intermediate supports will be smaller than those for the span regions. Shear lag must be considered in section design at both SLS and ULS in EN 1993. This is unlike design to BS 5400: Part 34 where it was permissible to neglect shear lag at ULS on the basis that stresses could redistribute across the cross-section with a little plasticity. Different effective widths are however obtained for SLS and ULS in EN 1993-1-5 and the reduction at ULS will typically be quite small because allowance is made for plastic redistribution within the rules of EN 1993-1-5.

Effective widths are calculated as a function of the available width, the distance between points of main beam zero bending moment adjacent to the location considered and the amount of stiffening. The effective width at SLS is given by 3-1-5/clause 3.2.1(1):

beff¼ b0 3-1-5/(3.1) 3-1-1/clause 6.2.2.2(5) 3-2/clause 6.2.2.3(1) 3-1-5/clause 3.2.1(1) b01 b02 C L

Fig. 6.2-3. Definition of b0for internal and outstand flanges

Table 6.2-1. Effective width factors,  from 3-1-5/Table 3.1

K Location for bending -value

0.02 ¼ 1:0 0:02 < k < 0:70 Sagging bending ¼ 1¼ 1 1þ 6:4k2 Hogging bending ¼ 2¼ 1 1þ 6:0
k
1 2500k  þ 1:6k2 >0.07 Sagging bending ¼ 1¼ 1 5:9k Hogging bending ¼ 2¼ 1 8:6k

All k End support 0¼ ð0:55 þ 0:025=kÞ1, but 0< 1

where b0is the physical width available equal to the full width of outstands and half the width

of internal plates between webs as shown in Fig. 6.2-3.  is a factor accounting for width-to- span ratio and stiffening and is found from 3-1-5/Table 3.1, reproduced here as Table 6.2-1, and depends on:

k¼ 0b0=Leand 0¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þAsl b0t

s

where Le represents the distance between points of zero bending moment and can be

determined from 3-1-5/Fig. 3.1 (reproduced as Fig. 6.2-4) provided that adjacent internal spans do not differ by more than 50% and a cantilever span is not longer than half the adjacent span – 3-1-5/clause 3.2.1(2) refers. Asl is the total area of longitudinal stiffeners

in the width b0. Figure 6.2-4 also shows the distribution of effective widths.

The limitations on span length ratios for use of Fig. 6.2-4 are made so that the bending moment distributions within spans are of similar shape to those in Fig. 6.2-4. The simple rules do not cater for other cases such as spans that are permanently hogging. If spans or moment distributions do not comply with the above requirements, then the distance between points of zero bending moment, L_e, should be calculated for the actual moment distribution. This is less desirable for design because analysis will have to be done first with gross cross-section properties to determine the likely distribution of moment.

At ULS, the effective width is much greater than at SLS, due to a certain amount of plastic redistribution, and will often approach the full available width for typical width-to-span ratios. (The difference to previous UK practice is therefore less than first appears.) The effective width at ULS can conservatively be taken as the SLS value or may optimally be calculated according to Note 3 of 3-1-5/clause 3.3(1):

Aeff¼  

Ac;eff Ac;eff 3-1-5/(3.5)

Aeffis used here rather than beffto include the effects of reduction in area from plate buckling

effects as well (see sections 6.2.2.5 and 6.2.2.6 of this guide) but the equation has the effect of reducing the available width in the same way as expression 3-1-5/(3.1) so that beff¼ b0.

The effective area accounting for both plate buckling and shear lag is the effective plate area within the width beff.

Figures 6.2-5 and 6.2-6 show the fraction of the full available width obtained for support and mid-span zones of a multi-span continuous bridge with equal internal spans of L. Results are produced for cases with no longitudinal stiffeners (Fig. 6.2-5) and for an amount of longitudinal stiffeners equal to the deck plate area (Fig. 6.2-6). It can be seen that there is considerably more width available at ULS than at SLS. Also, support zones, where the shear is high, suffer a much greater reduction in effectiveness. Typical values of b₀=L are unlikely to exceed 0.1 so it can be seen that shear lag will not usually have a great effect at ULS. The acting flange width is unlikely to be reduced for most bridges,

3-1-5/clause 3.2.1(2) 3-1-5/clause 3.3(1) β2: Le = 0.25(L1 + L2) β1: Le = 0.85L1 β1: Le = 0.70L2 L1 L2 L3 L1/4 L1/2 L1/4 L2/4 L2/2 L2/4 β2: Le = 2L3 β2 β1 β1 β2 β0

Fig. 6.2-4. Length Lefor continuous beam and distribution of effective s

other than stiffened box girders or steel beam bridges with a common orthotropic deck, as flanges will not generally be sufficiently wide. The values obtained at SLS are, in fact, very similar to those that were obtained from BS 5400: Part 3.4

Where it is necessary to determine a more realistic distribution of longitudinal stress across the width of the flange, as may be required in a check of combined local and global effects in a deck plate, the formulae in 3-1-5/clause 3.2.2 Fig. 3.3 (not reproduced here) may be used to estimate stresses. A typical location where this might be necessary would be in checking a deck plate at a transverse diaphragm between main beams where the deck plate has overall longitudinal direct stress from global bending and is also subjected to a local

0.00 0.20 0.40 0.60 0.80 1.00 0 0.1 0.2 0.3 0.4 0.5 b0/L

Effective width fraction

(a)

SLS ULS

Effective width fraction

0 0.1 0.2 0.3 0.4 0.5 b0/L (b) 0.00 0.20 0.40 0.60 0.80 1.00 SLS ULS

Fig. 6.2-5. No longitudinal stiffeners (0¼ 1): (a) support; (b) mid-span

0.00 0.20 0.40 0.60 0.80 1.00

Effective width fraction

0 0.1 0.2 0.3 0.4 0.5

b0/L

(a)

SLS ULS

Effective width fraction

0.00 0.20 0.40 0.60 0.80 1.00 0 0.1 0.2 0.3 0.4 0.5 b0/L (b) SLS ULS

hogging moment from wheel loads. The use of the formula in EN 1993-1-5 can be beneficial here as the global and local effects in the deck plate do not occur at the same location; the greatest local effects occur in the middle of the plate remote from the webs, while the global longitudinal stresses are greatest adjacent to the webs.