Crane Girder Design Procedure

Crane Girder Design to BS 5950-1: 2000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1- Introduction

2- Using CRANEgirder

3- Crane Classes

4- Single or Double Flange Wheels in the End Carriage

5- Impact Factor

6- Crane Girder Section

7- Calculated Weight of the Crane Girder

8- Plastic Modulus of the Section

9- Section Classification of the Compound Girder Section

10- Structural Deployment of Various Section Parts

11- Horizontal Wheel Loads

12- Crabbing Force of Trolley

13- Partial Factors for Loads

14- Load Combinations

15- Vertical Wheel Loads

16- Vertical and Horizontal Deflection

17- Shear Resistance at Supports Fv < Pv 18- Vertical Moment Resistance x-x

19- Horizontal Moment Resistance y-y

20- Web Bearing & Buckling at Support

21- Local Compression under the Wheel

22- UB-Flange to Top Section Weld

23- Reactions on to the Support Structure

24- Cautions & Limitations of Use

25- References 1 2 3

4

5

Crane Girder Design to BS 5950-1: 2000 User Notes An Excel Template for the Design of Crane Girders to BS5950-1:2000 by Dr Shaiq U.R. Khan BEng (Civil), MEng, PhD, PE, CEng, FIStructE

November 2004 Techno Consultants Ltd www.technouk.com

Contents Introduction Using CRANEgirder Crane Classes Single or Double Flange Wheels in the End Carriage Impact Factor Crane Girder Section Calculated Weight of the Crane Girder Plastic Modulus of the Section Section Classification of the Compound Girder Section Structural Deployment of Various Section Parts Horizontal Wheel Loads Crabbing Force of Trolley Partial Factors for Loads Load Combinations Vertical Wheel Loads Vertical and Horizontal Deflection Shear Resistance at Supports Fv < Pv Vertical Moment Resistance x-x Horizontal Moment Resistance y-y Web Bearing & Buckling at Support Local Compression under the Wheel UB-Flange to Top Section Weld Reactions on to the Support Structure Cautions & Limitations of Use References 1- Introduction This Template helps design simply supported crane girders comprising a UB section at its bottom and a PFC, RSC or a Plate section at its top. By omitting the top section, the girder can also be a UB section alone. The compound section of a girder can be Class 1 Plastic, Class 2 Compact or Class 3 Semi-compact sections. Class 4 slender sections as crane girders are outside the scope of this template. BS5950-1: 2000 appear ambiguous for calculating the necessary Zx effective values and it may not be a good idea to use such sections as crane girders. The crane class can be Q1, Q2, Q3 or Q4 as defined in BS 2573-1:1983. The steel grades can be S275, S355 or S460.

The Template allows storing data for up to 100 Crane girders. Any girder data can be recalled, amended and re-stored later to suit design needs. The method of design used is generally based on the Steelwork Design Guide 2. However there is a difference when it comes to deploying section parts for resisting lateral loads. Whereas the Guide ignores the top flange of UB to resist horizontal bending and deflection, this template optionally allows including it in line with a conventional design practice of the past 5. 2- Using CRANEgirder "Home" worksheet allows navigation to all worksheets through its command buttons. To design a Crane Girder, the data input and output is via "Cranegirder" worksheet. Utilising Windows interface, the use of CRANEgirder is self explanatory. All data input is via green colour cells. The user is responsible for values in these cells to make an engineering sense. The result output is via rest of the non-green colour cells At top of the screen, four command buttons allow storing, retrieving and navigating through the stored information. For example using the NEXT and PREVIOUS buttons, data can be viewed in girder sequence numbers. During its use, CRANEgirder keeps an eye on 7 adequacy checks. It reports the outcome at top left corner of the screen in Cell A2. When a girder passes all 7 checks, "All Checks OK" message is displayed. When it is not so, failing check numbers are displayed and the background colour of the cell changes to red. To improve structural usage of the crane girder, eight usage ratios are calculated and a maximum value displayed in upper part of the worksheet. This ratio represents the actual to permitted values on deflection and strength for the chosen girder. 3- Crane Classes The descriptions as per BS2573-1 are: Q1 - Light - hoisting SWL very rarely and, normally light loads Q2 - Moderate - hoisting SWL fairly frequently and, normally moderate loads Q3 - Heavy - hoisting SWL very fairly frequently and, normally heavy loads Q4 - Very heavy - normally hoisting loads close to SWL 4- Single or Double Flange Wheels in the End Carriage Single or double flange wheels can be specified in the end-carriages via a drop down menu. In the case of single flange wheels, the transverse surge is shared by two wheels in one end-carriage of the crane bridge. In the case of double flange wheels (i.e. one flange on each side of the rails), the transverse surge is shared by four wheels in two end-carriages of the crane bridge. Generally, double flanged wheels are assumed in a routine design. 5- Impact Factor For overhead travelling cranes, Cl 2.2.3 of BS 5950-1:2000 states that the impact effects and the vertical and horizontal dynamic loads should be determined in accordance with BS 2573-1.

As stated in Cl 3.1.4 of BS2573-1, the impact factor applies to the motion of the hook load in a vertical direction and covers inertia forces including shock. In order to calculate dynamic wheel loads for Crane girder design, the hook load is multiplied by an impact factor. For example, Table 4 of BS2573-1 gives a value of 1.3 for medium and heavy workshop/warehouse duty cranes. This Template permits using various impact factors. The values that can be selected from a drop down menu are 1.1, 1.25, 1.3, 1.4, 1.5 and 2. The values of 1.1, 1.3, 1.4, 1.5 and 2 are from Table 4 of BS 2573-1. The value of 1.25 is for a traditional design with dynamic effects based on BS 449. 6- Crane Girder Section The Crane girder section can have up to two parts. The bottom section is always a UB. The top section can be a PFC, RSC, Plate or Nil. To select the main UB section, use its drop down menu and click any desired section. To select the top section, again use its drop down menu and scroll down to click any desired PFC, RSC, Plate or a Nil section. The plate section dimensions can be specified by amending h & b dimensions in worksheet PFC. The cells for these dimensions are shown in green colour. To select a Nil section, scroll to very bottom of the drop down list and select Nil. 7- Calculated Weight of the Crane Girder This weight is obtained by multiplying span length and mass/m of the combined section i.e. = L M. It is calculated for information only as the user may need to include the weight of various attachments e.g. crane rails, packing plates, etc. A conversion factor of 1kN = 101.971621297793 kg is used. 8- Plastic Modulus of the Section The plastic modulus Sx is found by considering 5 strips A1 to A5 to represent the combined section. The root radius areas of the sections are ignored for simplicity in calculations. Starting from top, the width of these areas are Dc, (Bb+2Tfc), (Twb+2Tfc), Twb & Bb. The corresponding heights of these strips are Twc, Tfb, (Bc-Twc-Tfb)>=0, (D-Bc-Tfb) & Tfb. The calculation details for Sx are shown in the table. 9- Section Classification of the Compound Girder Section The combined girder section is classified using Cl 3.5.3 and Table (11) of BS5950-1:2000. The dimensions and the limiting width-to-thickness ratios used are shown and described below

Case a - Outstand element of compression flange - rolled section b/T <= 9 Class 1 Plastic b/T <= 10 Class 2 Compact b/T <= 15 Class 3 Semi-compact b/T > 15 Class 4 slender In the above ratios, b=Bb/2 and T=Tfb Case b - Internal element of compression flange bp/tp <= 28 Class 1 Plastic bp/tp <= 32 Class 2 Compact bp/tp <= 40 Class 3 Semi-compact bp/tp > 40 Class 4 slender In the above bo= Bb or IF Dc 13 Class 4 slender In the above bo=Abs(Dc-Bb)/2 and tp=Twc Case d - Web Classification d/t <= 80 Class 1 Plastic d/t <= 100 Class 2 Compact d/t <= 120 Class 3 Semi-compact d/t > 120 Class 4 slender In the above d=Db-2 (Tfb+r) and t=Twb In all of the above ratios, the parameter  = Sqrt(275/py) 10- Structural Deployment of Various Section Parts CRANEgirder offers an option to ignore top flange of the UB to resist horizontal bending and deflections. The Yes/No cell input allows the flange to be ignored or included. To signify this point, the flange resisting lateral loads is shown dotted in the following sketch. When the crane girder has no top element (FFC, RSC or Plate), however, CRANEgirder always includes the UB flange to resist lateral bending and deflection; the Yes/No input is ignored when the UB section alone is acting as the crane girder.

11- Horizontal Wheel Loads These loads act transverse and longitudinal to the crane rails and stem from surge or crabbing. Due to surge or inertia, the horizontal loads are taken as: Transverse load of 10% of the combined weight of the crab & the lifted load Longitudinal load of 5% of the static vertical reactions (i.e. crab + crane + lifted-load) When the cranes are Class Q1 or Q2, the crabbing forces are not considered. For Class Q3 & Q4 cranes, the transverse crabbing forces are obtained from Cl 4.11.2 of BS 5950-1:2000. 12- Crabbing Force of Trolley When the crane is class Q3 or Q4, a crabbing force FR is applied as a single point load to calculate the maximum horizontal moment and deflection. The critical position of this force is at mid span of the Crane girder. As per Cl 4.11.2, the magnitude of FR is: FR = Lc Ww / (40 s) but >= Ww/20 When the crane is class Q1 or Q2, the crabbing force FR is assumed to be zero and the Crane girder is designed for the surge forces only. 13- Partial Factors for Loads Table 2 in Cl 2.4.1.1 of BS 5950-1:2000 specifies the following load factors: 1.6 Vertical crane loads 1.4 Vertical crane loads acting together with horizontal crane loads 1.6 Horizontal crane loads (surge or crabbing) 1.4 Horizontal crane loads acting together with vertical crane loads. When a Crane girder is also subjected to imposed and wind loads, Table 2 of BS 5950-1:2000 gives other load factors. However, these loads are outside the usage of this Template and their factors are not summarised above. 14- Load Combinations Cl 2.4.1.3 of BS 5950-1, specifies the following principal load combinations: Crane Combination 1: Dead, imposed load and vertical crane loads Crane Combination 2: Dead, imposed load and horizontal crane loads

Crane Combination 3: Dead, imposed load, vertical crane loads and horizontal crane loads As discussed in section 20.2.2 of the Steelwork Design Guide2, load combination 2 is meant for the design of Crane girder supports rather than itself. Hence this combination is not considered and only the following two combinations are checked. 1.4 Dead Load + 1.6 Vertical Crane Load 1.4 (Dead Load + Vertical Crane Load + Horizontal Crane Surge/Crabbing) When calculating maximum moment and deflection in the horizontal direction, the surge or crabbing load, whichever causes the maximum effect, is used. 15- Vertical Wheel Loads The maximum unfactored static wheel load is: Wus = Wc / 4 + (Wcap+Wcb) (Lc-ah) / (2 Lc) The maximum unfactored dynamic wheel load is: Ww= Impact-factor Wus 16- Vertical and Horizontal Deflection Using Table 8 of BS 5950-1:2000, the suggested limits for deflections are: Vertical deflection due to static wheel load: Span/600 Horizontal deflection (using top section properties alone) due to horizontal crane loads: Span/500 The formula for vertical deflection due to Crane girder self weight is: 5 Wg L^3 / (384 E Ix) The formula for vertical (and similarly horizontal) deflections due to two equal point loads acting at distances a & c from the supports is: Wus L^3 [ 3(a+c)/L - 4(a^3 + c^3)/L^3 ] / [48 E Ix] The formula for horizontal deflection due to a single crabbing load FR at mid span is: FR L^3 / (48 E Iyfc) When calculating deflections, full combined section is used for the vertical loading & part combined section (comprising PFC/RSC/Plate and optionally top UB flange) for the horizontal loading. 17- Shear Resistance at Supports Fv < Pv Pv = 0.6 py Av = 0.6 py Twb Db 18- Vertical Moment Resistance x-x Lateral-torsional buckling moment capacity Mb is calculated using Cl 4.3.6.3 and Cl 4.3.6.9. A girder section can be Plastic, Compact or Semi-compact nut not slender. When a girder section happens to be slender, Mb calculations become outside the scope of this template and the value of Mb is made equal to zero. Mb= pb Sx for Class 1 Plastic and Class 2 Compact Sections Mb= pb Zx for Class 3 Semi-compact Sections, using the lesser of Zx top and Zx bottom values.

In the above, pb =f(py, LamdaLT) and is obtained from Table 17 of BS 5950-1:2000 and by using Cl 4.3.6.7 to calculate various factors as below: LamdaLT= u v Lamda (Bw)^0.5 Bw=1 for class 1 plastic and Class 2 Compact sections Bw=Zx/Sx for Class 3 Semi-compact sections, using the lesser of the Zx top and Zx bottom values Lamda=Le/ry u = [4 Sx^2 (1-Iy/Ix)/{A^2 hs^2}] v = 1 / [{4N(1-N) + 0.5 (Lamda/x)^2 + sai^2}^0.5 + sai ]^0.5 x = 0.566 hs(A/J)^0.5 hs = Db +Twc/2 -Tfb sai =kn (2N-1) (1 + 0.5 DL/D) where kn=0.8 when N>0.5 and kn=1 when n<0.5 The buckling resistance is checked by using the following two interaction expressions: mx Mx / py Zx + my My / py zy <=1 and mLT MLT / Mb + my My / py Zy <=1 As per Cl 4.11.3, the lateral torsional factor buckling factor mLT is taken as 1. The equivalent uniform moment factors mx and my for flexural buckling are also taken as 1 for simplicity, i.e. the moment gradient is ignored. 19- Horizontal Moment Resistance y-y The horizontal moment is assumed to be resisted by the top section and, if selected, by also including top flange of the bottom UB. It is given by: Mcy = py Zyfc As stated above, full PFC/RSC/Plate and optionally UB-top-flange is included in the value of Zyfc. 20- Web Bearing & Buckling at Support This is checked as per rules given in Cl 4.5.2 and 4.5.3 of BS 5950-1:2000 The data input required is the stiff bearing length b1 at support, the distance be from beam-end to the stiff bearing edge and the nature of beam-end restraint represented by Le/d ratio. The unstiffened web bearing capacity as per Clause 4.5.2.1 is Pbw =(b1 + n k) Twb pyw where n = 2 + 0.6 be / k <=5 ; k = Tf + r for rolled & k = Tf for welded section; The unstiffened web buckling capacity to Cl 4.5.3.2 is: Px = K1 K2 [25e t / Sqrt{(b1+n k) d}] Pbw where K1 is the reduction factor for proximity to the beam end and is given by: K1= (ae + 0.7 d)/(1.4d) <=1 and K2 is the reduction factor for the nature of the beam end restraint given by: K2 = 0.7 d/Le In the above, ae = b1/2 + be when be>=0 and ae = b1/2 + e/2 when be<0 When the flange for applying the reaction or load is effectively restrained against both: a) rotation relative to the web; b) lateral movement relative to the other flange the value of Le/d ratio is 0.7 and the factor K2 becomes equal to 1. Where a) or b) are not met, the Le/d ratio is to be determined as per Cl 4.7.3 for the appropriate conditions of end-restraint.

Using Table 22 of BS 5950-1:2000, various values of Le/d ratios that can be used are summarised in a table below. They can be selected via drop down menu of the input cell.

21- Local Compression under the Wheel As per Cl 4.11.4, the local compressive stress is obtained by load distribution over a length XR given by: XR= 2(HR+Tfc+Twc) <=s The magnitude of this stress is fw = 1.6 Ww/ [XR Twb] 22- UB-Flange to Top Section Weld CRANEgirder does not size or design this weld as in most cases it needs to be continuous nominal size weld. However, it calculates the magnitudes of both the longitudinal and the transverse shears and also their resultants. Using these values, welds can be sized by the user. The horizontal shear in each of the two welds due to vertical reaction is: Rb Ac (Ytop -Cy)/(2Ix) This force acts in longitudinal direction of the Crane girder. In addition, the surge and crabbing actions also cause shear in these welds. Whereas the shear due to surge occurs in both the longitudinal and the transverse direction, the shear due to crabbing is assumed to occur in the transverse direction only. The weld length XR for transferring the surge and crabbing forces from the top-section to the UB-flange is given by: XR= 2(HR+Twc) 23- Reactions on to the Support Structure Unfactored values of these reactions are calculated as maximum for crane girder-1 and corresponding minimum for girder-2 These reactions are due to dead and crane loads acting on supports of the two girders. Their directions are vertical, longitudinal and transverse in relation to the girder span. Two sets of values are calculated for crane reactions. One set is for crabbing and the other for crane surge. To design the support structure, critical set values need to be used. The maximum reaction due to crane crabbing occurs when one carriage wheel is at the support and the other within the girder span at distance s.

The maximum reaction due to crane surge occurs when the two carriage wheels are symmetrically placed at equal distance from a middle support. A static 3D diagram shows the position of crane bridge causing maximum crabbing and surge reactions together with the direction and position of induced reactions. 24- Cautions & Limitations of Use CRANEgirder allows changing of plate sizes towards bottom of the PFC data sheet. Any section change made here applies also to all stored crane girders being recalled later and using the changed section. CRANEgirder allows selecting bottom and top section parts to make a compound crane girder. However, it makes no detailing checks to ensure a logical section. It is therefore the user's responsibility to specify a feasible compound section. As mentioned in the introduction section, CRANEgirder allows inclusion of the top flange of UB to resist lateral bending and displacements. Although a past design practice, this aspect differs from the Steelwork Design Guide2 and gives less conservative results. Storing crane girder data does not save the Excel file to the hard disk. It merely writes information of a crane girder into the Store worksheet. When finishing the use of CRANEgirder, save the Excel file in the usual windows manner. Do not delete contents of cells O1, O2 & O3 as being unprotected for Excel use purposes. They house bottom & top section numbers and crane numbers. 25- References BS 5950: Structural use of steelwork in building BS 5950-1:2000: Code of practice for design - Rolled and welded sections, 2001 Steelwork Design Guide to BS 5950-1:2000, Volume 2, Worked Examples, SCI Publication P326, The Steel Construction Institute, 2003 BS 2573: Rules for the design of cranes BS 2573-1: 1983: Specification, for classification, stress calculations and design criteria for structures, British Standards Institution, 1983 BS 449: The use of structural steel in buildings BS 449-2: 1969: Metric Units British Standards Institution, 1969 Structural Steelwork, Design to Limit State Theory, 2nd Edition, T J MacGinley & T C Ang, ButterworthHeinemann, 1992