26 NSCMarch 2015

Beam and loading details (Figure 1)The beam is a 406 178 60 in S355, which spans 6 m. The maximum lifted load is 3 T, or 30 kN The hoist is assumed to weigh 750 kg, or 7.5 kN The wheels are assumed to be at 300 mm centres, and to be located very close to the edge of the flange ( = 0.1)

ULS checksLTB resistanceThe design bending moment, My,Ed , depends on the design value of the point load. BS EN 1991-3 prescribes several design combinations conditions to be considered, with amplification factors depending on the type of hoist, hoist speed, static and dynamic test loads etc (see Table 2.2 and Table 2.4 of the Standard).

Following this guidance, the design point load is calculated as 61.8 kN As an approximate check, note that 1.35 (30 + 7.5) = 50.6 kN, so with some amplification to allow for dynamic effects, the design point load is of the correct order. Note that the use of 1.35 for the lifted load is prescribed in Table A.1 of BS EN 1991-3 and confirmed by clause NA.2.6 the UK National Annex. The design bending moment is therefore 97.2 kNm, including self weight of the beam. With a central point load, the C1 factor is 1.35 From the Blue Book, Mb,Rd = 215 kNm In fact, clause 6.3.2.2(3) of BS EN 1993-6 allows the benefit of stabilising loads to be taken into account, as explained in Part 1. With loads applied on top of the bottom flange, z = -190.4 mm, as shown in Figure 2 (negative as the loads are applied below the shear centre). If advantage is taken of this effect, Mb,Rd increases to 280 kNm. Even without the benefit of stabilising loads, the LTB resistance is satisfactory. From the Blue Book, the shear resistance is 709 kN. The applied shear is 30.9 kN, which has no impact on the cross sectional moment resistance, Mc,y,Rd. Since the LTB resistance is satisfactory, the cross sectional moment resistance must be satisfactory. For completeness, Mc,y,Rd = 426 kNm, which is significantly greater than 97.2 kNm.

Flange resistanceThe geometry of the applied wheel loads must be established. Dimension m is from the wheel load to the root radius. Dimension n is from the wheel load to the edge of the flange, and relates to the ratio , as given in clause 5.8(4). The dimensions are shown in Figure 3.

Technical

m n

Figure 3: Nomenclature for flange resistance checks

Eurocode verification of a runway beam subject to wheel loads Part 2In Part 1 of this article, Dorota Koschmidder-Hatch of the SCI described the checks covering the design of a runway beam in accordance with BS EN 1993-6. In this Part, a worked example is presented. Readers should refer to Part 1 for nomenclature and detail on the design verifications.

Figure 1: Details of monorail beam

Shear centre

190.4

Figure 2: Application of the wheel loads

27NSCMarch 2015

n = (b tw)/2 = 0.1 (177.9 7.9)/2 = 8.5 mm (expression 5.7, rearranged) m = 0.5 (177.9 7.9) 0.8 10.2 8.5 = 68.3 mm (expression 6.3) Assuming that the wheels are remote from the end of the beam (case (b) of Table 6.2), the length of yield line is established by first calculating the length 4 2 (m + n) and comparing this to the wheel centres. 4 2 (m + n) = 4 2 (68.3 + 8.5) = 434.7 mm Because this is larger than the wheel centres, xw, which were assumed to be 300 mm, the effective length of yield line is given by: leff = 2 2 (m + n) + 0.5 xw = 2 2 (68.3 + 8.5) + (0.5 300) = 367.3 mm The resistance of the flange is reduced by the stress at the midline of the flange, as given by clause 6.7(1). Stress at the midline of the flange is given by:

f,Ed = 97.2 106 (406.4 12.8) 0.5

21600 10-3= 88.6 N/mm2

Design resistance of the bottom flange to a wheel load:

Ft,Rd =f,Ed

fy / M01 -

letf2fy / M04m

2

[ ]( ) = 88.6355/11 -367 12.82 355/14 68.32

[ ]( ) = 73.3 kN 10-3Ft,Rd =

f,Edfy / M0

1 -letf

2fy / M04m

2

[ ]( ) = 88.6355/11 -367 12.82 355/14 68.32

[ ]( ) = 73.3 kN 10-3The applied load is 61.8 / 4 = 15.4 kN, which is satisfactory.

SLS checksDeflectionThe SLS load = 30 + 7.5 = 37.5 kN. This load has not been amplified to allow for dynamic effects. With this load at midspan, the calculated deflection is 3.7 mm. According to case (a) of Table 7.2, the limiting deflection is span/600 or 10.0 mm.

Combined stress checksWith = 0.1, and using the formuale in Table 5.2 (rather than the coefficients in Table 5.3), the calculated local stresses are as follows:

The locations are shown in Figure 4.

The longitudinal stress at the extreme fibre, under the SLS load of 37.5 kN is given by

f,ser,Ed = 37.5 103 6000

4= 52.9 N/mm2

406.4 0.5

21600 104

From the shear resistance of 709 kN taken from the Blue Book, the shear

area, Av can be calculated, since Vpl,Rd =

fyAv( )

M0

3

Therefore, Av = 3459 mm2

The shear stress at SLS is therefore = 5.4 N/mm2

Conservatively assuming that the maximum longitudinal stress, plastic shear stress and local stresses are coincident, the expressions in clause 7.5 can be verified. The sign convention of the local transverse stress is reversed if required to produce the most onerous combined stress result, reflecting that the more onerous position may be on the underside or top side of the bottom flange. At each location, 0, 1 and 2, (see figure 5.6 of BS EN 1993-6) the local longitudinal stress is added to the overall longitudinal stress. Although each position must be verified, for conciseness only the most onerous, position 1 in this case, is shown below.

Location 1x,Ed,ser = 52.9 + 131.8 = 184.7 N/mm2 y,Ed,ser = 31.4 N/mm2 xy,Ed,ser = 5.4 N/mm2

(184.7)2 + 3 (5.4)2 = 185.0 N/mm2 (expression 7.2c)

(184.7)2 + (31.4)2 (184.7) (31.4) + 3 (5.4)2 = 202.4 N/mm2 (expression 7.2d)

The maximum permissible stress is given in clause 7.5 as fyM,ser

is given by

the UK NA to BS EN 1993-6, in clause NA.2.12 as 1.1, (a variation from the recommended value of 1.0) so the maximum permissible stress is 355

1.1 = 322.7 N/mm2

Thus the local stress checks are satisfactory.

Vibration of the bottom flangeDistance between lateral restraints L = 6 mFor simplicity, the inertia of the bottom flange will be taken as half of Iz .Thus the bottom flange inertia = 0.5 1200 104 = 600 104 mm4

The radius of gyration of the flange, iz =600 104

177.9 12.8= 51.3 mm

Slenderness, L/iz = 6000/51.3 = 117 < 250, so vibration is satisfactory.

Search for Advisory Desk articles on newsteelconstruction.comUse the search bar at the top of every page of newsteelconstruction.com to search out Advisory Desk articles by name, number or subject, or list them (most recent first) by hovering over Technical in the main menu and selecting Advisory Desk from the resulting pop-up menu.

Position Stress (N/mm2)

longitudinal transverse

0 11.0 -108.6

1 131.8 31.4

2 124.1 0.0

0

0

1

2

1 2

at the root radius

under the load

at the ange tip

Figure 4: Locations for SLS stress checks

Technical

24 NSCFebruary 2015

Technical

Before the Eurocodes were introduced, BS 2853 covered design and testing of overhead runway beams. Following revision in 2011, BS 2853 now only provides guidance on testing overhead runway beams. BS EN 1993-6:2007 (EC3-6) covers the design of steel crane supporting structures, which includes overhead runway beams, while guidance on determining actions induced by cranes is given in BS EN 1991-3. This article focuses on crane runway beams supporting either a monorail hoist block travelling on the bottom flange (see Figure 1) or an underslung crane, which is also supported on the bottom flange of the beam. The guidance in this article covers beams with parallel flanges, though EC3-6 also includes information for beams with tapered flanges. The bottom flange is subject to a complex state of stress, experiencing direct stresses from the global bending, but also local stresses around the wheel positions, which vary with the proximity of the hoist to the end of the beam. Figure 2 shows a typical situation, with a four wheeled hoist. The local resistance of the flange is based on nominal yield lines, shown in the plan.

Eurocode verification of a runway beam subject to wheel loads Part 1Dorota Koschmidder-Hatch of the SCI describes the design of runway beams carrying an underslung hoist or crane to BS EN 1993-6 in particular the verification of the bottom flange at ULS and SLS. Part 1 describes the requirements of the Standard. Part 2 will include a worked example.

Runway beam

Hoist block

Figure 1: Crane runway beam supporting a monorail hoist block

xe xw

Fz,Ed F z,Ed F z,Ed F z,Ed

b

nm

Wheel loads

Yield lines

n

m

m + n

m + n

r

a

Figure 2: Four-wheel hoist

25NSCFebruary 2015

1. ULTIMATE LIMIT STATEAt the ultimate limit state (ULS), runway beams must be verified for bending due to vertical loads in combination with the effect of lateral loads. Because the lateral loads are applied eccentrically to the shear centre of the beam, they cause minor axis bending, but also apply a torque to the section. EC3-6 clause 6.3.2.3(1) recommends that the combination of lateral torsional buckling, minor axis bending and torque be verified using an interaction expression given in Annex A. The UK National Annex to EC3-6 endorses this approach. In a runway beam with an underslung hoist or crane, the vertical loads are applied below the shear centre, at the bottom flange. This is a stabilising load, as the vertical loads act in opposition to the movement of the compression flange. Clause 6.3.2.2(3) allows this benefit to be taken, but requires that the loads should be assumed to be applied no lower than the top surface of the bottom flange. This limit is because a swinging load could reduce the beneficial effect of the stabilising load. To calculate Mcr for a stabilising load, the free software LTBeam

1 could be used, or the formula given in NCCI document SN0032. It is conservative to ignore the beneficial stabilising effect. In addition to the usual ULS checks, clause 2.7(2) requires that the bottom flange of the beam be verified. The bottom flange experiences a combination of direct stresses from overall bending, combined with local stresses from the wheels. Clause 2.7(2) directs designers to clause 6.7 to verify the bottom flange.

1.1 Verification of bottom flange at ULSClause 6.7 provides expression 6.2 to verify the bottom flange, as shown below.

Ft,Rd =f,Ed

fy / M01 -

letf2fy / M04m

2

[ ]( ) The resistance is based on the length of a yield line, leff , which is given in Table 6.2 of EC3-6 for various locations of a wheel. Wheels close to a free end have a lower effective length; wheels adjacent to a welded closer plate (a full depth end plate) have a higher effective length and consequently a greater resistance. Designers should note that the resistance is based on the

plastic modulus,

letf2

4 , which means that a check of the flange at

SLS is also necessary. The influence of the direct stress is seen

in the reduction factor

f,Edfy / M0

1 -2

[ ]( ) , where f,ed is the tensile stress at the midline of the flange. The reduction may be considerable, but because runway beams are subject to relatively onerous deflection limits (which may dominate the design), the bending stress may be lower than usually found in ordinary beams.

2. SERVICEABILITY LIMIT STATEEC3-6 has a series of deflection limits, for the runway beams and the supporting structure, vertically and horizontally to minimise vibrations and to avoid an excessive slope for the hoist when travelling along the runway beam. In addition, clause 2.7 requires that the stresses in the bottom flange be checked at SLS. Because the ULS check of the flange uses the plastic modulus, a check at SLS is particularly important. The SLS checks of the bottom flange are covered in clause 7.5, which combines direct stresses, shear stresses and local stresses. 2.1 Local stresses due to wheel loadsLocal stresses are to be determined from clause 5.8, which provides a simple approach to calculate local longitudinal and transverse stresses at three locations in the flange, as shown in Figure 3

Stresses are to be determined at:Position 0, at the junction between the

flange and the root radiusPosition1, under the wheels, andPosition 2, at the tip of the flange.The local longitudinal and transverse

stresses are given by:ox,Ed = cx Fz,Ed / t12 (for local longitudinal

bending stress)oy,Ed = cy Fz,Ed / t12 (for local transverse

bending stress) In the formulae, coefficients cx and cy are taken from tables, depending on the lateral spacing of the wheels with respect to the flange width. The formulae are valid as long as the wheels are more than 1.5b from the end of the beam (b is the flange width). Expressions are given to calculate cx and cy , (which appear to be the result of curve fitting) for both parallel and tapered flanges. In the common case, when the wheels are located close to the tips of the flanges (the lateral spacing of the wheels is 90% of the beam width) the expressions are replaced with single values for cx and cy but these values are simply the product of the rather more complicated expressions. The results are valid if the wheels are spaced no less than 1.5b longitudinally; if closer the calculated stresses must be superposed. The situation is more complicated close to the end of a beam (within 1.5b), where there is no continuity of the flange. An expression is offered, or the alternative of reinforcing the flange as shown in Figure 4.

2.2 Combined stressesClause 7.5 provides five expressions to verify combined stresses at SLS. The local stresses must be included in the verifications. In the following expressions (taken from EC3-6), the stresses x,Ed,ser and y,Ed,ser are the sum of the global stress and local stress. Ed,ser fy / M,ser Ed,ser

fy

3M,ser

x,Ed,ser + 3 y,Ed,ser fy /M,ser ( )2 ( )2

x,Ed,ser + y,Ed,ser - x,Ed,ser y,Ed,ser + 3 y,Ed,ser fy /M,ser ( )2 ( )2 ( )( ) ( )2

where x,Ed,ser = global,x,Ed,ser + ox,Ed,serand y,Ed,ser = global,y,Ed,ser + oy,Ed,ser

Technical

n

Fz,Ed

F z,Ed

z

y

10 2

Figure 3: Flange locations for SLS stress verification

b

tf tf

= b

Figure 4: Reinforced beam end

26

26 NSCFebruary 2015

On page T-4 of SCI P358[1], Table G.1 Note 4 states that for double notched beams, the remaining depth of web is taken as the end plate length. This is misleading and provides no information on single notched beams. This AD explains what notch dimensions were assumed and how the quoted shear resistances were calculated for single and double notched beam.

Notch dimensionsFor single notched beams, the notch depth was taken as the larger of 50 mm or the clearance n as given in SCI P363[2] (Blue Book). For most beams therefore, the notch aligns with the top of the end plate, set 50 mm below the top of the beam. For large beams, where the thickness of the flange plus root is greater than 50 mm, it is assumed that the end plate is lowered to clear the root, and the notch depth is correspondingly increased. For doubly notched beams, the upper notch follows the rules given above for single notches. The lower notch similarly follows these rules for large and medium sized beams. For 406 140 and smaller, the lower notch depth is simply taken as 25 mm. The rules are given in the figure above.

Calculation of shear resistanceWhen compiling the resistance tables (Tables G.4 & G.5), the first step was to determine the maximum notch length which could accommodate the shear resistance quoted for the beam without a notch. In many cases, the

maximum notch length was zero, or some small dimension which had no practical benefit. In these cases, a reasonable notch length was set as 100 mm and the resistance back-calculated (using an iterative process) for this geometry. In this process, the applied shear was increased until the applied moment at the notch equalled the moment resistance. An iterative process was required as the moment resistance is reduced in the presence of high shear; the reduction varies with the applied shear. In the resistance tables, if the maximum length is quoted as 100 mm, it will be associated with a reduced shear resistance, indicating that the process above has been followed. For lengths longer than 100 mm, the resistance will be that for an un-notched beam. Occasionally for double notched beams, where N/A is shown in the shear resistance column, it indicates that after the notches have been removed (following

the guidance given above) the remaining depth of web is less than the depth of the end plate. In these cases the resistance of a non-standard connection will have to be determined by calculation. In many cases, the dimensions of the supporting beam may dictate the size of the notch. In these cases the resistance will have to be determined by calculation.

References:[1] SCI P358 Joints in Steel Construction: Simple

Joints to Eurocode 3. (2014) [2] SCI P363 Steel Building Design: Design Data.

(Updated 2013).

Contact: David Brown Tel: 01344 636525Email: advisory@steel-sci.com

Notch dimensions in the Green Book

Advisory Desk

Continued from p25 Eurocode verification of a runway beam subject to wheel loads Part 1

AD 386 Clarification of notch dimensions and shear resistances in SCI P358 (Green Book on Simple Joints)

Greater of 50 mm and clearance

Greater of 50 mm and clearance

Greater of 50 mm and clearance For 406 178 and larger

25 mm For 406 140 and smaller

n n

n

Singlenotch

Doublenotch

M,ser is to be taken as 1.1, according to the UK National Annex. EC3-6 does not indicate where precisely stresses should be checked at positions 0, 1 and 2. At the extreme fibres on the underside of the flange, the global bending stress x,Ed,ser is at a maximum, as is the local transverse bending stress oy,Ed,ser , but the shear stress is zero. At other locations, the shear stress will be combined with a reduced global bending stress. It is conservative simply to combine maximum stresses, especially as the shear stress based on clause 6.2.6 of BS EN 1993-1-1 is likely to be small.

2.3 Vibration of the bottom flangeA further serviceability requirement concerning runway beams is the need to avoid noticeable lateral vibration of the bottom flange. Clause 7.6 of EC3 6 recommends that the slenderness ratio of the bottom flange L/iz should be limited to 250, where iz is the radius of gyration of the bottom flange and L is the distance between lateral restraints.

1. LTBeam software, available from www.cticm.com2. SN003 Elastic critical moment for lateral torsional buckling,

available from www.steel-ncci.co.uk

25