CivilBay Crane Load and Crane Runway Beam Design v1.0.0 User Manual

Transcription

1 CivilBay Crane Load and Crane Runway Beam Design v1.0.0 User Manual (Alberta, Canada) Web: Tel: Rev Page 1 of 11

2 TABLE OF CONTENTS 1.0 END USER LICENSE AGREEMENT QUICK START DESIGN EXAMPLES... 6 Example 01: Top Running 0 Ton Crane + Runway W Shape with Cap Channel Imperial Unit... 6 Example 0: Top Running 40 Ton Crane + Runway W Shape with Cap Channel Metric Unit Example 03: Top Running 45 Ton Crane + Runway W Shape with Cap Plate Imperial Unit Example 04: Underhung 7.5 Ton Crane + Runway W Shape Metric Unit Example 05: Underhung 7.5 Ton Crane + Runway S Shape Metric Unit REFERENCES Rev Page of 11

3 1.0 END USER LICENSE AGREEMENT 1.1 General This End-User License Agreement ("EULA") is a legal agreement between Don Structural Ltd. ( AUTHOR ) and you, the user of the licensed software ( SOFTWARE ) that accompanies this EULA. You agree to be bound by the terms of this EULA by downloading and/or using the SOFTWARE. If you do not agree to all of the terms of this EULA, please do not download, install and use this SOFTWARE on your computer. 1. License Grant The SOFTWARE is licensed, not sold, to you by AUTHOR for use only under the terms of this License, and AUTHOR reserves any rights not expressly granted to you License Types AUTHOR provides the following types of licenses - Evaluation License (Trial Mode) and Single User License. 1.. Evaluation License The Evaluation License only applies when you obtain a copy of the SOFTWARE for the first time. You may use the Evaluation (Trial) version of the SOFTWARE for a 14-day evaluation period. After the evaluation period, if you want to continue to use the SOFTWARE you must purchase the license from AUTHOR Single User License The Single User License only applies after you have purchased the Single User License from AUTHOR. The Single User License authorizes you to use one copy of the SOFTWARE on a single computer for one year period starting from the date you obtain the license. After one year, if you want to continue to use the SOFTWARE you must renew the license by paying an annual maintenance fee. The annual renewal maintenance fee is 40% of current Single User License price. 1.3 Software Deliverables The licensed SOFTWARE is delivered as Excel spreadsheets compiled as EXE applications. AUTHOR does not provide uncompiled or unprotected native Excel files. You can download all SOFTWARE including user manual in electronic file format from AUTHOR provided website. The AUTHOR does not provide any hard copy or burned CD for the licensed SOFTWARE. 1.4 Software Upgrading The Single User License authorizes you to use one copy of the SOFTWARE on a single computer for one year period starting from the date you obtain the license. During this one year period you can get all available SOFTWARE upgrades without paying additional maintenance fee. After one year, if you want to continue to use the SOFTWARE, you must renew the license by paying an annual maintenance fee. The annual renewal maintenance fee is 40% of current Single User License price. After paying the annual maintenance fee, you can continue to get all available SOFTWARE upgrades free of charge Rev Page 3 of 11

4 1.5 No Refund No refund is given at any time, unless authorized by the AUTHOR under unexpected circumstances. Please contact the AUTHOR to see if you qualify for a refund. 1.6 Disclaimer of Warranty and Liability Licensee of this SOFTWARE acknowledges that Don Structural Ltd., CivilBay.com, its employees and affiliates are not and cannot be responsible for either the accuracy or adequacy of the output produced by the licensed SOFTWARE. Furthermore, Don Structural Ltd., CivilBay.com, its employees and affiliates neither make any warranty expressed nor implied with respect to the correctness of the output prepared by the licensed SOFTWARE. Although Don Structural Ltd. and CivilBay.com have endeavored to produce the licensed SOFTWARE error free the SOFTWARE are not and cannot be certified infallible. The final and only responsibility for analysis, design and engineering documents is the licensees. Accordingly, Don Structural Ltd., CivilBay.com, its employees and affiliates disclaim all responsibility in contract, negligence or other tort for any analysis, design or engineering documents prepared in connection with the use of the licensed SOFTWARE. This disclaimer of warranty constitutes an essential part of this License. Copyright , Don Structural Ltd. and CivilBay.com. All rights reserved Rev Page 4 of 11

5 .0 QUICK START.1 Software Installation After downloading the ZIP file the user can unzip the file and save it to user s computer. User can double click the two EXE files and open them just as normal Excel files. The 14-day trial will start the same date when user tries any of these compiled Excel files. During trial period the software provides full functions except that the user can not save the file, but the user can print the file to printer and get a hard copy of the calculation for verification. The trial period will expire after 14 days. Any time during or after trial period the user can go to to purchase a license. After placing the order, the user shall send his/her Computer ID to author for licensing. The user can get his/her Computer ID by clicking on Contact author button on the pop-up dialog box.. Software Licensing After receiving user s Computer ID, the author will send the user a license key to unlock the trial version. The user shall save the license key file at the same folder where the compiled Excel files locate. The user can copy, save and rename any of the compiled Excel files and use them same as the normal Excel files. All the compiled Excel files will fully function as long as they can find the license key in the same folder. The license key is created using the Computer ID sent by the user and it only works on that computer where the Computer ID is retrieved from..3 Crane Load and Crane Runway Beam Design v1.0.0 Modules Top Running & Underhung Bridge Crane Crane Load & Runway Beam Design.exe Crane load and crane runway beam design as per AISC ASD 9 and LRFD Top Running & Underhung Bridge Crane Crane Load & Runway Beam Design-Metric.exe Crane load and crane runway beam design as per AISC ASD 9 and LRFD 13 using metric unit input Rev Page 5 of 11

6 3.0 DESIGN EXAMPLES Example 01: Top Running 0 Ton Crane + Runway W Shape with Cap Channel Imperial Unit BRIDGE CRANE RUNWAY BEAM PLAN Rev Page 6 of 11

7 CRANE RUNWAY BEAM CONNECTION PLAN Rev Page 7 of 11

8 Rev Page 8 of 11

9 Rev Page 9 of 11

10 Crane Data Imperial Metric Crane capacity 0 US Tons = 40 kips Metric Tons = kn Bridge weight 8.0 kips 1701 kg Trolley + hoist weight 6.1 kips 767 kg Max static wheel load 30.1 kips kn Bridge span S r 61.0 ft m Left min. hook approach S L 4.0 ft 1.19 m Right min. hook approach S R 3.5 ft m Bridge wheel spacing s 1.5 ft m Crane runway beam span L 0 ft m Left runway CL to column CL dist e L.0 ft m Right runway CL to column CL dist e R.0 ft m Crane rail size ASCE 85 ASCE 85 CMAA crane service class Class C Class C Vertical impact factor 5% 5% Crane type Top Running Top Running Crane runway beam size W4x84 + C15x33.9 W610x15 + C380x50 W shape F y 50 ksi 345 MPa Channel cap F y 36 ksi 48 MPa Rev Page 10 of 11

11 1 of 6 BRIDGE CRANE LOAD CALCULATION Bridge crane load calc based on Code Abbreviation CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition CISC Crane Guide AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric CMAA Overhead Traveling Cranes Crane Data suggested value Crane rated capacity W rc = 0.0 [US Ton] = 40.0 [kips] Bridge weight W br = 8.0 [kips] 6.1 = 1701 [kg] Trolley + hoist weight W th =6.1 [kips] 3.6 = 767 [kg] Bridge wheel spacing s = 1.5 [ ft ] 9.8 Max. static wheel load by vendor P max-v = 30.1 [kips] input 0 if vendor data is unknown Crane bridge span S r = 61.0 [ ft ] 61.7 Min. hook approach-left S L = 4.0 [ ft ] 3.1 Min. hook approach-right S R = 3.5 [ ft ] 3.1 Crane runway beam span L = 0.0 [ ft ] Runway CL to col CL dist-left e L =.0 [ ft ] 1.6 Runway CL to col CL dist-right e R =.0 [ ft ] 1.6 Crane column C to C distance S r + e = 65.0 [ ft ] suggested section Runway beam type = W_Shape_Cap_Channel? Runway beam size = W4x84 C15x33.9 size <= W1x6 C1x0.7 Top flange cap plate size width b p = 18.0 [in] thick t p = 0.8 [in] not applicable suggest ASCE 60 U rb = [kip/ft] Crane rail size = ASCE 85 U cr =85 [lbs/yd] = 0.08 [kip/ft] Rail base width B w =5.188 [in] Rail height H t = [in] W section yield strength f wy = 50.0 [ksi] = 345 [MPa] Cap channel or plate yield strength f cy = 36.0 [ksi] = 48 [MPa] CMAA crane service class = Class C? Moderate service Crane type = Top Running? Rev Page 11 of 11

12 Code Reference CISC Crane Guide Vertical load impact factor = 0.5? Table.1 of 6 Crane side thrust load option = Option 1? Table.1 Crane side thrust load can be calculated using one of the following 3 options Option 1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) Option H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) Option 3 H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) 0.4 Lifted Load Conclusion Runway Beam Design Using AISC ASD 9 Overall ratio = 0.38 OK Local buckling OK Bending about X-X Axis ratio = 0.34 OK Bending about Y-Y Axis on Top Flange ratio = 0.10 OK Biaxial Bending on Top Flange ratio = 0.38 OK Shear along Y-Y Axis ratio = 0.3 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.4 OK Runway Beam Lateral Deflection ratio = 0.11 OK Runway Beam Design Using AISC LRFD 13 Overall ratio = 0.46 OK Local buckling OK Biaxial Bending on Top Flange ratio = 0.46 OK Shear along Y-Y Axis ratio = 0.6 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.4 OK Runway Beam Lateral Deflection ratio = 0.11 OK Runway Beam Bottom Flange Local Bending ratio = 0.00 OK Rev Page 1 of 11

13 3 of 6 Crane Load Calculation Code Reference Crane runway + rail selfweight R sw = (U rb + U cr ) x B =.9 [kips] Wheel load by bridge selfwei P br = W br / 4 wheel = 7.0 [kip/per wheel] Side Thrust Load Crane side thrust load calculated by = Option 1 CISC Crane Guide H s1 = 0.4 Lifted Load = 16.0 [kips] Table.1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) = 9. [kips] H s3 = 0.1 (Lifted Load+ Entire Crane Wt) = 7.4 [kips] H st = side thrust load calc using Option 1 =.3 [kip/per wheel] H st1 =H st3 = H st (1 + (B-s) / B) = 3. [kips] H st =H st4 = H st s / B = 1.4 [kips] Tractive Load Table.1 H tr = 0. Max wheel load = 6.0 [kip/per wheel] H tr1 =H tr3 = H tr (1 + (B-s) / B) = 8.3 [kips] H tr =H tr4 = H tr s / B = 3.8 [kips] Vertical Load Case 1 Hook at One Side Min. hook aproach S min = min (S 1, S ) = 3.5 [ ft ] Max wheel load by calc P max-c = [(W rc +W th )x(s r -S min )/ S r ]/ wheel+p br = 8.7 [kip/per wheel] Max. wheel load by vendor P max-v = = 30.1 [kip/per wheel] Max static wheel load P max = max (P max-v, P max-c ) = 30.1 [kip/per wheel] Min wheel load P min = [(W rc +W th )xs min /S r ]/ wheel+p br = 8.3 [kip/per wheel] Rev Page 13 of 11

14 4 of 6 Reaction on runway support R 1 = P max (1 + (B-s) / B) + R sw = 44.3 [kips] R = P max s / B + R sw = 1.7 [kips] R 3 = P min (1 + (B-s) / B) + R sw = 14.4 [kips] R 4 = P min s / B + R sw = 8.1 [kips] Point moment to column center M 1 = R 1 x e R = 88.6 [kip-ft] M = R x e R = 43.5 [kip-ft] M 3 = R 3 x e L = 8.7 [kip-ft] M 4 = R 4 x e L = 16.3 [kip-ft] Case 1 Hook at One Side - Crane Load Summary 3. kips 14.4 kips 8.7 kip-ft 1.4 kips 3.8 kips 8.3 kips 8.1 kips 16.3 kip-ft 88.6 kip-ft 8.3 kips 44.3 kips 3. kips 43.5 kip-ft 1.7 kips 1.4 kips 3.8 kips Note: The crane loads shown above may be reverse if crane hook goes to the other side. When reverse the loads and apply them on building columns, the point moment value may need adjusted if eccentricity e L <> e R Rev Page 14 of 11

15 5 of 6 Case Hook at Center of Bridge Max wheel load P max = P min = (W rc +W br +W th )/4 wheel = 18.5 [kip/per wheel] Reaction on runway support R 1 = R 3 = P max (1 + (B-s) / B) + R sw = 8.4 [kips] R = R 4 = P max s / B + R sw = 14.5 [kips] Point moment to column center M 1 = M 3 = R 1 x max (e L, e R ) = 56.8 [kip-ft] M = R x max (e L, e R ) = 9.0 [kip-ft] Case Hook at Center of Bridge - Load Summary 3. kips 8.4 kips 56.8 kip-ft 1.4 kips 3.8 kips 8.3 kips 14.5 kips 9.0 kip-ft 56.8 kip-ft 8.3 kips 8.4 kips 3. kips 9.0 kip-ft 14.5 kips 1.4 kips 3.8 kips Rev Page 15 of 11

16 Code Reference 6 of 6 Bumper Force at End Frame AISC Design Guide 7 Bumper force to be the greater of 1 Twice the tractive force = 1.0 [kips] % of entire crane weight = 3.7 [kips] Bumper force used for design = 1.0 [kips] Apply longitudinal bumper force to both sides of end frame 1.0 kips 1.0 kips Rev Page 16 of 11

17 1 of 3 CRANE RUNWAY BEAM DESIGN Crane beam design using two codes : AISC LRFD-13 and AISC ASD 9th Edition Code Abbreviation AISC Specification for Structural Steel Buildings AISC LRFD-13 AISC Manual of Steel Construction: Allowable Stress Design 9th Edition ASD 9th Edition CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition CISC Crane Guide AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane Data Crane rated capacity W rc = 0.0 [tonne] = 44.1 [kips] Bridge weight W br = 8.0 [kips] = 1701 [kg] Trolley + hoist weight W th = 6.1 [kips] = 767 [kg] Bridge wheel spacing s = 1.5 [ ft ] = [m] For 4-wheel crane double the vendor provided max static wheel load as input Max static wheel load P max = 30.1 [kips] = [kn] Crane bridge span S r = 61.0 [ ft ] = [m] Left min. hook approach S 1 = 4.0 [ ft ] = 1.19 [m] Right min. hook approach S = 3.5 [ ft ] = [m] Crane runway beam span L = 0.0 [ ft ] = [m] Runway CL to column CL dist e =.0 [ ft ] = [m] Runway beam type W_Shape_Cap_Channel Runway beam size W4x84 C15x33.9 U rb = 0.1 [kip/ft] = 1.7 [kn/m] Crane rail size ASCE 85 U cr = 0.03 [kip/ft] = 0.4 [kn/m] Rev Page 17 of 11

18 Crane Load Calculation CISC Crane Guide Ver. load impact factor α = 1.5 Table.1 Crane side thrust load H s = Option 1 = 9. [kips] Option 1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) of 3 Option H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) Option 3 H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) 0.4 Lifted Load Runway beam span L = 0.0 [ ft ] Bridge wheel spacing s = 1.5 [ ft ] M max = P s L L =4.73 P Runway beam + rail selfwei U = U rb + U cr = [kip/ft] Crane Load for Design per AISC ASD 9th Ed Max ver. load /wheel (no impact) P v = = 30.1 [kips / per wheel] Max hor. load /wheel P h = H s / 4 =.3 [kips / per wheel] Bending moment x-x axis M x = 4.73 xp v x α (impact) + U x L / 8 = 185. [kip-ft] Bending moment y-y axis M y = 4.73 xp h = 10.9 [kip-ft] Shear along y-y axis V x = P v [ 1+ (L - s) / L ]x α (mpact) + UxL/ = 53. [kips] Crane Load for Design per AISC LRFD-13th Ed Wheel load by bridge selfwei P br = W br / 4 = 7.0 [kips] as dead load Wheel load by lift load + trolley P lt = P max - P br = 3.1 [kips] as live load Max factored ver. load /wheel P v = 1. x P br x P lt = 45.4 [kips] impact not included Max factored hor. load /wheel P h = H x 1.6 / 4 = 3.7 [kips] Factor bending moment x-x axis M x = 4.73 xp v x α(impact)+1.xuxl / 8 = 76.8 [kip-ft] Factor bending moment y-y axis M y = 4.73 xp h = 17.4 [kip-ft] Factor shear along y-y axis V x = P v [1+ (L - s) /L]xα(mpact)+1.xUxL/ = 79.7 [kips] Rev Page 18 of 11

19 1 of 5 CRANE RUNWAY BEAM DESIGN - ASD 9 Crane runway design based on Code Abbreviation AISC Manual of Steel Construction: Allowable Stress Design 9th Edition ASD 9th Edition AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane runway beam section W4x84 C15x33.9 W4x84 and C15x33.9 Section Properties Combined Section Overall A = [in ] d all = [in] top y =9.100 [in] bott. y 1 = [in] I x = [in 4 ] I y = [in 4 ] top S = [in 3 ] bott. S 1 = [in 3 ] S y =54.50 [in 3 ] Z x =86.00 [in 3 ] Z y = [in 3 ] r x =9.80 [in] r y = [in] J = 4.71 [in 4 ] C w =0 [in 6 ] W Section d = [in] b f = 9.00 [in] t w =0.470 [in] t f = [in] h = [in] Top Flange A f = [in ] d all / A f =1.450 [in -1 ] r T =4.468 [in] r yt = 4.69 [in] I t =36.09 [in 4 ] S t =48.8 [in 3 ] Z t = [in 3 ] W section yield strength F wy = 50.0 [ksi] = 345 [MPa] C section yield strength F cy = 36.0 [ksi] = 48 [MPa] Runway beam unbraced length L b =40.00 [in] Design Forces Bending moment x-x axis M x = [kip-ft] Bending moment y-y axis M y = [kip-ft] Shear along y-y axis V x =53.0 [kips] Conclusion Overall ratio = 0.38 OK Local buckling OK Bending about X-X Axis ratio = 0.34 OK Bending about Y-Y Axis on Top Flange ratio = 0.10 OK Biaxial Bending on Top Flange ratio = 0.38 OK Shear along Y-Y Axis ratio = 0.3 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.4 OK Runway Beam Lateral Deflection ratio = 0.11 OK Rev Page 19 of 11

20 of 5 Code Reference Design Basis & Assumption AISC Design Guide 7 1. The channel and W section top flange resist the hor. load and the combined section resists the 18.1 on page 56 ver. load. This assumption eliminates the need for an analysis of torsional effects on the combined section and simplifies the analysis.. If A36 channel cap is used on A99 W section then lateral torsional buckling and weak axis on page 57 flexure strength must be calculated based on A36 yield stress. Check Local Buckling Flange of W shape ASD 9th Edition Compact limit λ p = 65 / sqrt (F wy ) = 9.19 Table B5.1 Noncompact limit λ r = 95 / sqrt (F wy ) = b f / t f = 5.86 Compact Web of W shape Compact limit λ p = 640 / sqrt (F wy ) = Table B5.1 Noncompact limit λ r = 760 / sqrt ( 0.66F wy ) = d / t w =51.8 h / t w = Compact W shape classification Compact Flange of Channel This part is applicable Compact limit λ p = 65 / sqrt (F cy ) = Table B5.1 Noncompact limit λ r = 95 / sqrt (F cy ) = b f / t f = 5.3 Compact Web of Channel Compact limit λ p = 640 / sqrt (F cy ) = Table B5.1 Noncompact limit λ r = 760 / sqrt ( 0.66F cy ) = d / t w =37.50 h / t w = 34.5 Compact Channel shape classification Compact Combined section classification Compact OK Check Bending about X-X Axis Tension Allowable tension stress F bx t = 0.6 x F wy = [ksi] Actual tension stress f bx t = M x / S 1 = 10.4 [ksi] ratio = f bx t / F bx t = 0.34 OK Compression Comb sect top flange yield stress F y = 36.0 [ksi] see assumption Comb sect top flange width b f = 15.0 [in] use channel depth if capped with channel Rev Page 0 of 11

21 Code Reference Critical length L c ASD 9th Edition 4 = = [in] Eq F1-76 xb f x10 min, F d y all / A f xfy 3 of 5 76 b f / sqrt( F y ) = = [in] When L b <= L c For compact sect For non-compact sect This part is NOT applicable Not Applicable F bx = 0.66 x F y = 0.00 [ksi] Eq F1-1 Not Applicable b f / t f = Comb Sect max( W b f / t f, C b f / t f ) =5.86 W Sect b f / t f b f F bx = Fy Fy = 0.00 [ksi] Eq F1-3 t f F bx = 0.6 x F y = 0.00 [ksi] Eq F1-5 When L b > L c This part is applicable L b / r T = = Bending coefficient C b = 1.0 to be conservative 510 x10 xc b x = = F y 3 For ( L b / r T ) <= x Applicable Fy L b / r T F bx = Fy 0.6Fy = 1.56 [ksi] Eq F x10 C b For ( L b / r T ) > x Not Applicable 170 x10 Cb F bx = 0.6F y = 0.00 [ksi] Eq F1-7 L / r b T 3 For any value of ( L b / r T ) Applicable 1 x10 C F bx = b 0.6Fy = 1.60 [ksi] Eq F1-8 L xd / A b Allowable compression stress F bx c = = 1.60 [ksi] Actual compression stress f bx c = M x / S =6.05 [ksi] ratio = f bx c / F bx c = 0.8 OK all 3 f Check Bending about Y-Y Axis on Top Flange For compact top flange Applicable F by = 0.75 x F y = 7.00 [ksi] Eq F Rev Page 1 of 11

22 Code Reference For non-compact top flange Not Applicable ASD 9th Edition F by = 0.60 x F y = 0.00 [ksi] Eq F- Allowable compression stress F by c = = 7.00 [ksi] Actual compression stress f by c = M y / S t =.71 [ksi] ratio = f bx c / F bx c = 0.10 OK 4 of 5 Check Biaxial Bending on Top Flange Combined bending stress f bx / F bx + f by / F by = 0.38 OK Eq H1-3 Check Shear along Y-Y Axis Clear dist between trans. stiffeners a = L b = [in] W sect clear dist between flange h = [in] a / h = k v = / (a / h) if a / h <=1 =5.37 F / (a / h) if a / h >1 h / t w =45.87 C v =1.36 For h / t w <= 380 / sqrt ( F y ) Applicable F v = 0.40 x F y = 0.00 [ksi] Eq F4-1 For h / t w > 380 / sqrt ( F y ) Not Applicable F v = ( F y x C v ) /.89 <=0.4 F y = 0.00 [ksi] Eq F4- Allowable shear stress F v = = 0.00 [ksi] Actual shear stress f v = V x / S t =4.70 [ksi] ratio = f v / F v = 0.3 OK Check Web Sidesway Buckling AISC Design Guide 7 Use LRFD 13 instead of ASD 9 to increase web sidesway buckling resistance when flexural page 61 stress in the web is less than 0.66F y (h / t w ) / (L b / b f ) =1.7 >1.7 AISC LRFD-13 Max actual bending stress f b =10.4 [ksi] When f b < (F y / 1.5) = 0.66 F y Applicable C r = 9.6E+05 [ksi] When f b >= (F y / 1.5) = 0.66 F y Not Applicable C r = 0.0E+00 [ksi] R n = 3 3 C r t w t f h / t w 0.4 h L b / b f = NA [kips] Eq J10-7 R a = R n / Ω = R n / 1.76 =NA [kips] P v-impt = P v x α (impact factor) = [kips] ratio = P v-impt / R a = 0.00 OK Rev Page of 11

23 5 of 5 Check Runway Beam Deflection Code Reference Crane serviceability criteria based on CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition Table 4.1 item 14,15 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition page 56 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric Cl Overhead Traveling Cranes CMAA crane service class Class C Moderate service Ver deflection limit (no impact, max wheel load) B v = L / 600 Hor deflection limit (no impact, 10% max wheel load) B h = L / 400 Runway beam span L = [in] Bridge wheel spacing s = [in] a = [in] Pa(3L 4a ) Max deflection at center Δ max = = P / I 4 E I Vertical Deflection Unfactored max ver. wheel load P = 30.1 [kips / per wheel] impact factor NOT included I x = [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = [in] 4 E I Allowable deflection Δ a = L / B v = [in] ratio = Δ max / Δ a = 0.4 OK Lateral Deflection Unfactored max hor. wheel load P =.3 [kips / per wheel] I t =36.1 [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = [in] 4 E I Allowable deflection Δ a = L / B h = [in] ratio = Δ max / Δ a = 0.11 OK Rev Page 3 of 11

24 1 of 7 CRANE RUNWAY BEAM DESIGN - LRFD 13 Crane runway design based on Code Abbreviation AISC Specification for Structural Steel Buildings AISC LRFD-13 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane runway beam section W4x84 C15x33.9 W4x84 and C15x33.9 Section Properties Combined Section Overall A = [in ] d all = [in] top y c =9.100 [in] bott. y t = [in] I x = [in 4 ] I y = [in 4 ] top S xc = [in 3 ] bott. S xt = [in 3 ] S y =54.50 [in 3 ] Z x =86.00 [in 3 ] Z y = [in 3 ] r x =9.80 [in] r y = [in] J = 4.71 [in 4 ] C w =0 [in 6 ] W Section d = [in] b f = 9.00 [in] t w =0.470 [in] t f = [in] h = [in] h c = ( y c - k ) = [in] h 0 = d - t f =3.330 [in] Top Flange A f = [in ] d all / A f =1.450 [in -1 ] r t =4.468 [in] r yt = 4.69 [in] I t =36.09 [in 4 ] S t =48.8 [in 3 ] Z t = [in 3 ] W section yield strength F wy = 50.0 [ksi] = 345 [MPa] C section yield strength F cy = 36.0 [ksi] = 48 [MPa] Runway beam unbraced length L b =40.00 [in] Design Forces Bending moment x-x axis M x = [kip-ft] Bending moment y-y axis M y = [kip-ft] Shear along y-y axis V y =79.7 [kips] Conclusion Overall ratio = 0.46 OK Local buckling OK Biaxial Bending on Top Flange ratio = 0.46 OK Shear along Y-Y Axis ratio = 0.6 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.4 OK Runway Beam Lateral Deflection ratio = 0.11 OK Rev Page 4 of 11

25 of 7 Code Reference Design Basis & Assumption AISC Design Guide 7 1. The channel and W section top flange resist the hor. load and the combined section resists the 18.1 on page 56 ver. load. This assumption eliminates the need for an analysis of torsional effects on the combined section and simplifies the analysis.. If A36 channel cap is used on A99 W section then lateral torsional buckling and weak axis on page 57 flexure strength must be calculated based on A36 yield stress. Check Local Buckling Flange of W shape AISC LRFD-13 Compact limit λ p = 0.38 sqrt (E / F wy ) = 9.15 Table B4.1 Case 1 Noncompact limit λ r = 1.0 sqrt (E / F wy ) = 4.08 b f / t f = 5.86 Compact Web of W shape Compact limit λ p = 3.76 sqrt (E / F wy ) = Table B4.1 Case 9 Noncompact limit λ r = 5.7 sqrt (E / F wy ) = h / t w = Compact W shape classification Compact Flange of Channel This part is applicable Compact limit λ p = 0.38 sqrt (E / F cy ) = Table B4.1 Case 1 Noncompact limit λ r = 1.0 sqrt (E / F cy ) = 8.38 b f / t f = 5.3 Compact Web of Channel (flange cover plate between lines of welds) Compact limit λ p = 1.1 sqrt (E / F cy ) = Table B4.1 Case 1 Noncompact limit λ r = 1.4 sqrt (E / F cy ) = b f (W shape) / t w (C channel) =.55 Compact Channel shape classification Compact Combined section classification Compact ratio = 0.00 OK Check Bending about X-X Axis Calculate R pc λ pw =90.55 λ rw = M yc = S xc F y = 159. [kip-ft] M p = min ( Z x F y, 1.6 S xc F y ) = [kip-ft] λ = h c / t w = 33.3 M p / M yc = = 0.78 For λ <= λ pw Applicable R pc = M p / M yc =0.78 Eq F4-9a Rev Page 5 of 11

26 Code Reference For λ > λ pw Not Applicable AISC LRFD-13 3 of 7 Mp Mp pw Mp R pc = 1 = 0.00 Eq F4-9b M yc M yc rw pw Myc R pc used for design R pc = = 0.78 Calculate R pt M yt = S xt F y = 904. [kip-ft] M p = min ( Z x F y, 1.6 S xt F y ) = [kip-ft] M p / M yt = = 1.3 For λ <= λ pw Applicable R pt = M p / M yc =1.3 Eq F4-15a For λ > λ pw Not Applicable Mp Mp pw Mp R pt = 1 = 0.00 Eq F4-15b M yt M yt rw pw Myt R pt used for design R pt = = 1.3 Calculate F L Sxt / Sxc =0.59 For S xt / S xc >= 0.7 For S xt / S xc < 0.7 Not Applicable F L = 0.7 F y = 0.0 [ksi] Eq F4-6a Applicable F L = max ( F y x (S xt / S xc ), 0.5F y ) = 1.3 [ksi] Eq F4-6b F L used for design F L = = 1.3 [ksi] M n - Compression Flange Yielding M n1 = R pc F y S xc = [kip-ft] Eq F4-1 M n - Lateral Torsional Buckling Runway beam unbraced length L b = = [in] Calculate L p & L r E Lp = 1.1 rt = [in] Eq F4-7 F y E J F L L S xcho r = 1.95 rt Eq F4-8 F S h E J L xc o = [in] Rev Page 6 of 11

27 Code Reference For L b <= L p Not Applicable AISC LRFD-13 M n = = NA [kip-ft] 4 of 7 For L p < L b <= L r Applicable C b = 1.0 to be conservative Lb Lp M n = Cb RpcMyc R pcmyc FL S xc RpcMyc Eq F4- Lr L p For L b > L r Not Applicable = [kip-ft] For I t / I y <= 0.3 J = 0 Not Applicable J = 4.71 [in 4 ] Cb E J Lb F cr = = 0.0 [ksi] Eq F4-5 L S b xcho rt rt M n = F cr S xc <= R pc F y S xc = NA [kip-ft] Eq F4-3 M n - LTB M n = = [kip-ft] M n - Compression Flange Local Buckling For λ <= λ pf λ =5.86 λ pf =9.15 λ rf = 4.08 Applicable M n3 = = NA [kip-ft] For λ pf < λ <= λ rf Not Applicable M n3 pf = R pcm yc R pcm yc FL S xc rf pf = NA [kip-ft] Eq F4-1 M n3 = = NA [kip-ft] M n - Tension Flange Yielding M n4 = R pt F y S xt = [kip-ft] Eq F4-14 M nx = min( M n1, M n, M n3, M n4 ) = [kip-ft] Rev Page 7 of 11

28 Check Bending about Y-Y Axis Code Reference Check top flange compactness, for W check W flange only, for W+Cap Channel check both W and Channel flange 5 of 7 Top flange compactness = Compact AISC LRFD-13 For compact top flange M ny = F y Z t = [kip-ft] Eq F6-1 For noncompact top flange M ny = F y S t = [kip-ft] M ny = = [kip-ft] Check Biaxial Bending on Top Flange Combined bending M x / (Φ M nx ) + M y / (Φ M ny ) = 0.46 OK Eq H1-1b Check Shear along Y-Y Axis Clear dist between trans. stiffeners a = L b = [in] W sect clear dist between flange h = [in] a / h = h / t w =45.87 k v = 5 if h / t w < 60 =5.00 G.1 (b) 5 if a / h > 3.0 or a / h >[60/(h / t w )] / (a / h) T = sqrt(k v E / F y ) = 53.9 For h / t w <= 1.10 T Applicable C v = 1.0 Eq G-3 For 1.10 T < h / t w <= 1.37 T Not Applicable C v = 1.10 x sqrt(k v E / F y ) / (h / t w ) =NA Eq G-4 For h / t w > 1.37 T Not Applicable C v = 1.51 E k v / [ (h / t w ) F y ] =NA Eq G-5 C v used for design C v = = 1.0 ΦV n = 0.9 x 0.6 F y (d t w ) C v = [kips] Eq G-1 ratio = V y / ΦV n = 0.6 OK Rev Page 8 of 11

29 Check Web Sidesway Buckling (h / t w ) / (L b / b f ) =1.7 >1.7 Code Reference AISC LRFD-13 6 of 7 When M u < M y Applicable C r = 9.6E+05 [ksi] When M u >= M y Not Applicable C r = 0.0E+00 [ksi] 3 3 R n = C r t w t f h / t w 0.4 = NA [kips] Eq J10-7 h L b / b f Φ = = 0.85 P v-impt = P v x α (impact factor) = [kips] ratio = P v-impt / ΦR n = 0.00 OK Check Runway Beam Deflection Crane serviceability criteria based on CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition Table 4.1 item 14,15 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition page 56 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric Cl Overhead Traveling Cranes CMAA crane service class Class C Moderate service Ver deflection limit (no impact, max wheel load) B v = L / 600 Hor deflection limit (no impact, 10% max wheel load) B h = L / 400 Runway beam span L = [in] Bridge wheel spacing s = [in] a = [in] Max deflection at center Δ max = Pa (3L 4a ) 4 E I = P / I Vertical Deflection Unfactored max ver. wheel load P = 30.1 [kips / per wheel] impact factor NOT included I x = [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = [in] 4 E I Rev Page 9 of 11

30 Allowable deflection Δ a = L / B v = [in] ratio = Δ max / Δ a = 0.4 OK Code Reference 7 of 7 Lateral Deflection Unfactored max hor. wheel load P =.3 [kips / per wheel] I t =36.1 [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = [in] 4 E I Allowable deflection Δ a = L / B h = [in] ratio = Δ max / Δ a = 0.11 OK Rev Page 30 of 11

31 Example 0: Top Running 40 Ton Crane + Runway W Shape with Cap Channel Metric Unit This is a 35 tonne bridge crane with 5 tonne auxiliary hoist. The bridge has 4 wheels at each side. We need to convert the 4- wheel bridge to equivalent -wheel bridge for analysis. Crane Plan Convert the 4-wheel bridge to equivalent -wheel bridge by consolidating -wheel into a single wheel. For an equivalent -wheel bridge Bridge wheel spacing s = = 4176 mm = m Max static wheel load = kn x = kn Rev Page 31 of 11

32 Crane Elevation Rev Page 3 of 11

33 Crane Data Imperial Metric Crane capacity US Tons = 88. kips 40 Metric Tons = 39.3 kn Bridge weight 64. kips 9130 kg Trolley + hoist weight 8.3 kips 3780 kg Max static wheel load 69.0 kips kn Bridge span S r 10.9 ft m Left min. hook approach S L 4.6 ft m Right min. hook approach S R 4.6 ft 1400 m Bridge wheel spacing s 13.7 ft m Crane runway beam span L 1.3 ft m Left runway CL to column CL dist e L 1.9 ft m Right runway CL to column CL dist e R 1.9 ft m Crane rail size ASCE 85 ASCE 85 CMAA crane service class Class C Class C Vertical impact factor 5% 5% Crane type Top Running Top Running Crane runway beam size W7x84 + C15x33.9 W690x15 + C380x50 W shape F y 50 ksi 345 MPa Channel cap F y 36 ksi 48 MPa Rev Page 33 of 11

34 Crane Runway Beam Connection Runway Beam Size Change to W690x15 + C380x Rev Page 34 of 11

35 Rev Page 35 of 11

36 1 of 6 BRIDGE CRANE LOAD CALCULATION Bridge crane load calc based on Code Abbreviation CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition CISC Crane Guide AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric CMAA Overhead Traveling Cranes Crane Data suggested value Crane rated capacity W rc = 40.0 [Metric Ton] = 39.3 [kn] Bridge weight W br = 9130 [kg] 3136 = 85.5 [kn] Trolley + hoist weight W th =3780 [kg] 3300 = 37.0 [kn] Bridge wheel spacing s = [m] 4.0 Max. static wheel load by vendor P max-v =307.0 [kn] input 0 if vendor data is unknown Crane bridge span S r = [m] 31. Min. hook approach-left S L =1.400 [m] 1.40 Min. hook approach-right S R =1.400 [m] 1.40 Crane runway beam span L = [m] Runway CL to col CL dist-left e L =0.576 [m] 0.65 Runway CL to col CL dist-right e R =0.576 [m] 0.65 Crane column C to C distance S r + e =3.500 [m] suggested section Runway beam type = W_Shape_Cap_Channel? Runway beam size = W690x15 C380x50 size > W610x15 C380x50 Top flange cap plate size width b p = [mm] thick t p = 19.1 [mm] not applicable suggest ASCE 60 U rb = 1.7 [kn/m] Crane rail size = ASCE 85 U cr =85 [lbs/yd] = 0.41 [kn/m] Rail base width B w =13 [mm] Rail height H t = 13 [mm] W section yield strength f wy = 345 [MPa] = 50.0 [ksi] Cap channel or plate yield strength f cy = 48 [MPa] = 36.0 [ksi] CMAA crane service class = Class C? Moderate service Crane type = Top Running? Rev Page 36 of 11

37 Code Reference CISC Crane Guide Vertical load impact factor = 0.5? Table.1 of 6 Crane side thrust load option = Option 1? Table.1 Crane side thrust load can be calculated using one of the following 3 options Option 1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) Option H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) Option 3 H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) 0.4 Lifted Load Conclusion Runway Beam Design Using ASD 89 Overall ratio = 0.81 OK Local buckling OK Bending about X-X Axis ratio = 0.73 OK Bending about Y-Y Axis on Top Flange ratio = 0. OK Biaxial Bending on Top Flange ratio = 0.81 OK Shear along Y-Y Axis ratio = 0.48 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.49 OK Runway Beam Lateral Deflection ratio = 0.5 OK Runway Beam Design Using LRFD 05 Overall ratio = 0.97 OK Local buckling OK Biaxial Bending on Top Flange ratio = 0.97 OK Shear along Y-Y Axis ratio = 0.54 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.49 OK Runway Beam Lateral Deflection ratio = 0.5 OK Runway Beam Bottom Flange Local Bending ratio = 0.00 OK Rev Page 37 of 11

38 3 of 6 Crane Load Calculation Code Reference Crane runway + rail selfweight R sw = (U rb + U cr ) x B = 13.9 [kn] Wheel load by bridge selfwei P br = W br / 4 wheel = 71.4 [kn/per wheel] Side Thrust Load Crane side thrust load calculated by = Option 1 CISC Crane Guide H s1 = 0.4 Lifted Load = [kn] Table.1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) = 85.9 [kn] H s3 = 0.1 (Lifted Load+ Entire Crane Wt) = 71.5 [kn] H st = side thrust load calc using Option 1 = 1.5 [kn/per wheel] H st1 =H st3 = H st (1 + (B-s) / B) = 9.1 [kn] H st =H st4 = H st s / B = 13.8 [kn] Tractive Load Table.1 H tr = 0. Max wheel load = 61.4 [kn/per wheel] H tr1 =H tr3 = H tr (1 + (B-s) / B) = 83.4 [kn] H tr =H tr4 = H tr s / B = 39.4 [kn] Vertical Load Case 1 Hook at One Side Min. hook aproach S min = min (S L, S R ) = [m] Max wheel load by calc P max-c = [(W rc +W th )x(s r -S min )/ S r ]/ wheel+p br = 76.4 [kn/per wheel] Max. wheel load by vendor P max-v = = [kn/per wheel] Max static wheel load P max = max (P max-v, P max-c ) = [kn/per wheel] Min wheel load P min = [(W rc +W th )xs min /S r ]/ wheel+p br = 81.0 [kn/per wheel] Rev Page 38 of 11

39 4 of 6 Reaction on runway support R 1 = P max (1 + (B-s) / B) + R sw = [kn] R = P max s / B + R sw = 11.1 [kn] R 3 = P min (1 + (B-s) / B) + R sw = 13.8 [kn] R 4 = P min s / B + R sw = 65.9 [kn] Point moment to column center M 1 = R 1 x e R = 48.1 [knm] M = R x e R = 11.6 [knm] M 3 = R 3 x e L = 71.3 [knm] M 4 = R 4 x e L = 38.0 [knm] Case 1 Hook at One Side - Crane Load Summary 9.1 kn 13.8 kn 71.3 knm 13.8 kn 39.4 kn 83.4 kn 65.9 kn 38.0 knm 48.1 knm 83.4 kn kn 9.1 kn 11.6 knm 11.1 kn 13.8 kn 39.4 kn Note: The crane loads shown above may be reverse if crane hook goes to the other side. When reverse the loads and apply them on building columns, the point moment value may need adjusted if eccentricity e L <> e R Rev Page 39 of 11

40 5 of 6 Case Hook at Center of Bridge Max wheel load P max = P min = (W rc +W br +W th )/4 wheel = [kn/per wheel] Reaction on runway support R 1 = R 3 = P max (1 + (B-s) / B) + R sw = 56.5 [kn] R = R 4 = P max s / B + R sw = 18.7 [kn] Point moment to column center M 1 = M 3 = R 1 x max (e L, e R ) = [knm] M = R x max (e L, e R ) = 74.1 [knm] Case Hook at Center of Bridge - Load Summary 9.1 kn 56.5 kn knm 13.8 kn 39.4 kn 83.4 kn 18.7 kn 74.1 knm knm 83.4 kn 56.5 kn 9.1 kn 74.1 knm 18.7 kn 13.8 kn 39.4 kn Rev Page 40 of 11

41 6 of 6 Code Reference Bumper Force at End Frame AISC Design Guide 7 Bumper force to be the greater of 1 Twice the tractive force = 1.8 [kn] % of entire crane weight = 35.7 [kn] Bumper force used for design = 1.8 [kn] Apply longitudinal bumper force to both sides of end frame 1.8 kn 1.8 kn Rev Page 41 of 11

42 1 of 3 CRANE RUNWAY BEAM DESIGN Crane beam design using two codes : AISC LRFD 13th Ed and AISC ASD 9th Ed Code Abbreviation AISC Specification for Structural Steel Buildings AISC LRFD-13 AISC Manual of Steel Construction: Allowable Stress Design 9th Edition ASD 9th Edition CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition CISC Crane Guide AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane Data Crane rated capacity W rc = 40.0 [tonne] = 88. [kips] Bridge weight W br = 9130 [kg] = 64. [kips] Trolley + hoist weight W th = 3780 [kg] = 8.3 [kips] Bridge wheel spacing s = [m] = 13.7 [ ft ] For 4-wheel crane double the vendor provided max static wheel load as input Max static wheel load P max = [kn] = 69.0 [kips] Crane bridge span S r = 31.3 [m] = 10.8 [ ft ] Left min. hook approach S 1 = [m] = 4.6 [ ft ] Right min. hook approach S = [m] = 4.6 [ ft ] Crane runway beam span L = [m] = 1.3 [ ft ] Runway CL to column CL dist e = [m] = 1.9 [ ft ] Runway beam type W_Shape_Cap_Channel Runway beam size W690x15 C380x50 U rb = 1.7 [kn/m] = [kip/ft] Crane rail size ASCE 85 U cr = 0.41 [kn/m] = 0.09 [kip/ft] Rev Page 4 of 11

43 Crane Load Calculation CISC Crane Guide Ver. load impact factor α = 1.5 Table.1 Crane side thrust load H s = Option 1 = 19.3 [kips] Option 1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) of 3 Option H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) Option 3 H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) 0.4 Lifted Load Runway beam span L = 1.3 [ ft ] Bridge wheel spacing s = 13.7 [ ft ] M max = P s L L =4.91 P Runway beam + rail selfwei U = U rb + U cr = [kip/ft] Crane Load for Design per AISC ASD 9th Ed Max ver. load /wheel (no impact) P v = = 69.0 [kips / per wheel] Max hor. load /wheel P h = H s / 4 = 4.8 [kips / per wheel] Bending moment x-x axis M x = 4.91 xp v x α (impact) + U x L / 8 = [kip-ft] Bending moment y-y axis M y = 4.91 xp h = 3.71 [kip-ft] Shear along y-y axis V x = P v [ 1+ (L - s) / L ]x α (mpact) + UxL/ = [kips] Crane Load for Design per AISC LRFD 13th Ed Wheel load by bridge selfwei P br = W br / 4 = 16.1 [kips] as dead load Wheel load by lift load + trolley P lt = P max - P br = 53.0 [kips] as live load Max factored ver. load /wheel P v = 1. x P br x P lt = [kips] impact not included Max factored hor. load /wheel P h = H x 1.6 / 4 = 7.7 [kips] Factor bending moment x-x axis M x = 4.91 xp v x α(impact)+1.xuxl / 8 = [kip-ft] Factor bending moment y-y axis M y = 4.91 xp h = [kip-ft] Factor shear along y-y axis V x = P v [1+ (L - s) /L]xα(mpact)+1.xUxL/ = [kips] Rev Page 43 of 11

44 1 of 5 CRANE RUNWAY BEAM DESIGN - ASD 9 Crane runway design based on Code Abbreviation AISC Manual of Steel Construction: Allowable Stress Design 9th Edition ASD 9th Edition AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane runway beam section W690x15 C380x50 W7x84 and C15x33.9 Section Properties Combined Section Overall A = [in ] d all = [in] top y = [in] bott. y 1 = [in] I x = [in 4 ] I y = [in 4 ] top S = [in 3 ] bott. S 1 = [in 3 ] S y =56.00 [in 3 ] Z x = [in 3 ] Z y = [in 3 ] r x = [in] r y = [in] J = 3.8 [in 4 ] C w =0 [in 6 ] W Section d = [in] b f = [in] t w =0.460 [in] t f = [in] h = 4.0 [in] Top Flange A f =16.34 [in ] d all / A f =1.660 [in -1 ] r T =4.558 [in] r yt = [in] I t = [in 4 ] S t =49.03 [in 3 ] Z t = [in 3 ] W section yield strength F wy = 50.0 [ksi] = 345 [MPa] C section yield strength F cy = 36.0 [ksi] = 48 [MPa] Runway beam unbraced length L b =55.91 [in] Design Forces Bending moment x-x axis M x = [kip-ft] Bending moment y-y axis M y = 3.71 [kip-ft] Shear along y-y axis V x = [kips] Conclusion Overall ratio = 0.81 OK Local buckling OK Bending about X-X Axis ratio = 0.73 OK Bending about Y-Y Axis on Top Flange ratio = 0. OK Biaxial Bending on Top Flange ratio = 0.81 OK Shear along Y-Y Axis ratio = 0.48 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.49 OK Runway Beam Lateral Deflection ratio = 0.5 OK Rev Page 44 of 11

45 of 5 Code Reference Design Basis & Assumption AISC Design Guide 7 1. The channel and W section top flange resist the hor. load and the combined section resists the 18.1 on page 56 ver. load. This assumption eliminates the need for an analysis of torsional effects on the combined section and simplifies the analysis.. If A36 channel cap is used on A99 W section then lateral torsional buckling and weak axis on page 57 flexure strength must be calculated based on A36 yield stress. Check Local Buckling Flange of W shape ASD 9th Edition Compact limit λ p = 65 / sqrt (F wy ) = 9.19 Table B5.1 Noncompact limit λ r = 95 / sqrt (F wy ) = b f / t f = 7.78 Compact Web of W shape Compact limit λ p = 640 / sqrt (F wy ) = Table B5.1 Noncompact limit λ r = 760 / sqrt ( 0.66F wy ) = 13.7 d / t w =58.04 h / t w = 5.65 Compact W shape classification Compact Flange of Channel This part is applicable Compact limit λ p = 65 / sqrt (F cy ) = Table B5.1 Noncompact limit λ r = 95 / sqrt (F cy ) = b f / t f = 5.3 Compact Web of Channel Compact limit λ p = 640 / sqrt (F cy ) = Table B5.1 Noncompact limit λ r = 760 / sqrt ( 0.66F cy ) = d / t w =37.50 h / t w = 34.5 Compact Channel shape classification Compact Combined section classification Compact OK Check Bending about X-X Axis Tension Allowable tension stress F bx t = 0.6 x F wy = 30.0 [ksi] Actual tension stress f bx t = M x / S 1 = 1.88 [ksi] ratio = f bx t / F bx t = 0.73 OK Compression Comb sect top flange yield stress F y = 36.0 [ksi] see assumption Comb sect top flange width b f = 15.0 [in] use channel depth if capped with channel Rev Page 45 of 11

46 Code Reference Critical length L c ASD 9th Edition 4 = = [in] Eq F1-76 xb f x10 min, F d y all / A f xfy 3 of 5 76 b f / sqrt( F y ) = = [in] When L b <= L c For compact sect For non-compact sect This part is NOT applicable Not Applicable F bx = 0.66 x F y = 0.00 [ksi] Eq F1-1 Not Applicable b f / t f = Comb Sect max( W b f / t f, C b f / t f ) =7.78 W Sect b f / t f b f F bx = Fy Fy = 0.00 [ksi] Eq F1-3 t f F bx = 0.6 x F y = 0.00 [ksi] Eq F1-5 When L b > L c This part is applicable L b / r T = = Bending coefficient C b = 1.0 to be conservative 510 x10 xc b x = = F y 3 For ( L b / r T ) <= x Applicable Fy L b / r T F bx = Fy 0.6Fy = 1.31 [ksi] Eq F x10 C b For ( L b / r T ) > x Not Applicable 170 x10 Cb F bx = 0.6F y = 0.00 [ksi] Eq F1-7 L / r b T 3 For any value of ( L b / r T ) Applicable 1x10 C F bx = b 0.6Fy = 1.58 [ksi] Eq F1-8 L xd / A b Allowable compression stress F bx c = = 1.58 [ksi] Actual compression stress f bx c = M x / S = 1.87 [ksi] ratio = f bx c / F bx c = 0.60 OK all 3 f Check Bending about Y-Y Axis on Top Flange For compact top flange Applicable F by = 0.75 x F y = 6.97 [ksi] Eq F Rev Page 46 of 11

47 Code Reference For non-compact top flange Not Applicable ASD 9th Edition F by = 0.60 x F y = 0.00 [ksi] Eq F- Allowable compression stress F by c = = 6.97 [ksi] Actual compression stress f by c = M y / S t =5.80 [ksi] ratio = f bx c / F bx c = 0. OK 4 of 5 Check Biaxial Bending on Top Flange Combined bending stress f bx / F bx + f by / F by = 0.81 OK Eq H1-3 Check Shear along Y-Y Axis Clear dist between trans. stiffeners a = L b = [in] W sect clear dist between flange h = 4.0 [in] a / h = k v = / (a / h) if a / h <=1 =5.38 F / (a / h) if a / h >1 h / t w =5.65 C v =1.18 For h / t w <= 380 / sqrt ( F y ) Applicable F v = 0.40 x F y = 0.01 [ksi] Eq F4-1 For h / t w > 380 / sqrt ( F y ) Not Applicable F v = ( F y x C v ) /.89 <=0.4 F y = 0.00 [ksi] Eq F4- Allowable shear stress F v = = 0.01 [ksi] Actual shear stress f v = V x / S t =9.66 [ksi] ratio = f v / F v = 0.48 OK Check Web Sidesway Buckling AISC Design Guide 7 Use LRFD 13 instead of ASD 9 to increase web sidesway buckling resistance when flexural page 61 stress in the web is less than 0.66F y (h / t w ) / (L b / b f ) =.05 >1.7 AISC LRFD 13 Max actual bending stress f b =1.88 [ksi] When f b < (F y / 1.5) = 0.66 F y Applicable C r = 9.6E+05 [ksi] When f b >= (F y / 1.5) = 0.66 F y Not Applicable C r = 0.0E+00 [ksi] R n = 3 3 C r t w t f h / t w 0.4 h L b / b f = NA [kips] Eq J10-7 R a = R n / Ω = R n / 1.76 =NA [kips] P v-impt = P v x α (impact factor) = 86.7 [kips] ratio = P v-impt / R a = 0.00 OK Rev Page 47 of 11

48 5 of 5 Check Runway Beam Deflection Code Reference Crane serviceability criteria based on CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition Table 4.1 item 14,15 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition page 56 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric Cl Overhead Traveling Cranes CMAA crane service class Class C Moderate service Ver deflection limit (no impact, max wheel load) B v = L / 600 Hor deflection limit (no impact, 10% max wheel load) B h = L / 400 Runway beam span L = [in] Bridge wheel spacing s = [in] a = [in] Pa(3L 4a ) Max deflection at center Δ max = = 1.36 P / I 4 E I Vertical Deflection Unfactored max ver. wheel load P = 69.0 [kips / per wheel] impact factor NOT included I x = [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = 0.11 [in] 4 E I Allowable deflection Δ a = L / B v = 0.47 [in] ratio = Δ max / Δ a = 0.49 OK Lateral Deflection Unfactored max hor. wheel load P = 4.8 [kips / per wheel] I t =367.7 [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = 0.16 [in] 4 E I Allowable deflection Δ a = L / B h = [in] ratio = Δ max / Δ a = 0.5 OK Rev Page 48 of 11

49 1 of 7 CRANE RUNWAY BEAM DESIGN - LRFD 13 Crane runway design based on Code Abbreviation AISC Specification for Structural Steel Buildings AISC LRFD 13 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane runway beam section W690x15 C380x50 W7x84 and C15x33.9 Section Properties Combined Section Overall A = [in ] d all = [in] top y c = [in] bott. y t = [in] I x = [in 4 ] I y = [in 4 ] top S xc = [in 3 ] bott. S xt = [in 3 ] S y =56.00 [in 3 ] Z x = [in 3 ] Z y = [in 3 ] r x = [in] r y = [in] J = 3.8 [in 4 ] C w =0 [in 6 ] W Section d = [in] b f = [in] t w =0.460 [in] t f = [in] h = 4.0 [in] h c = ( y c - k ) = [in] h 0 = d - t f =6.060 [in] Top Flange A f =16.34 [in ] d all / A f =1.660 [in -1 ] r t =4.558 [in] r yt = [in] I t = [in 4 ] S t =49.03 [in 3 ] Z t = [in 3 ] W section yield strength F wy = 50.0 [ksi] = 345 [MPa] C section yield strength F cy = 36.0 [ksi] = 48 [MPa] Runway beam unbraced length L b =55.91 [in] Design Forces Bending moment x-x axis M x = [kip-ft] Bending moment y-y axis M y = [kip-ft] Shear along y-y axis V y = [kips] Conclusion Overall ratio = 0.97 OK Local buckling OK Biaxial Bending on Top Flange ratio = 0.97 OK Shear along Y-Y Axis ratio = 0.54 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.49 OK Runway Beam Lateral Deflection ratio = 0.5 OK Rev Page 49 of 11

50 of 7 Code Reference Design Basis & Assumption AISC Design Guide 7 1. The channel and W section top flange resist the hor. load and the combined section resists the 18.1 on page 56 ver. load. This assumption eliminates the need for an analysis of torsional effects on the combined section and simplifies the analysis.. If A36 channel cap is used on A99 W section then lateral torsional buckling and weak axis on page 57 flexure strength must be calculated based on A36 yield stress. Check Local Buckling Flange of W shape AISC LRFD 13 Compact limit λ p = 0.38 sqrt (E / F wy ) = 9.15 Table B4.1 Case 1 Noncompact limit λ r = 1.0 sqrt (E / F wy ) = 4.08 b f / t f = 7.78 Compact Web of W shape Compact limit λ p = 3.76 sqrt (E / F wy ) = Table B4.1 Case 9 Noncompact limit λ r = 5.7 sqrt (E / F wy ) = h / t w = 5.65 Compact W shape classification Compact Flange of Channel This part is applicable Compact limit λ p = 0.38 sqrt (E / F cy ) = Table B4.1 Case 1 Noncompact limit λ r = 1.0 sqrt (E / F cy ) = 8.40 b f / t f = 5.3 Compact Web of Channel (flange cover plate between lines of welds) Compact limit λ p = 1.1 sqrt (E / F cy ) = Table B4.1 Case 1 Noncompact limit λ r = 1.4 sqrt (E / F cy ) = b f (W shape) / t w (C channel) = 4.90 Compact Channel shape classification Compact Combined section classification Compact ratio = 0.00 OK Check Bending about X-X Axis Calculate R pc λ pw =90.53 λ rw = M yc = S xc F y = [kip-ft] M p = min ( Z x F y, 1.6 S xc F y ) = [kip-ft] λ = h c / t w = M p / M yc = = 0.78 For λ <= λ pw Applicable R pc = M p / M yc =0.78 Eq F4-9a Rev Page 50 of 11

51 Code Reference For λ > λ pw Not Applicable AISC LRFD 13 3 of 7 Mp Mp pw Mp R pc = 1 = 0.00 Eq F4-9b M yc M yc rw pw Myc R pc used for design R pc = = 0.78 Calculate R pt Myt = Sxt Fy = [kip-ft] M p = min ( Z x F y, 1.6 S xt F y ) = [kip-ft] M p / M yt = = 1.33 For λ <= λ pw Applicable R pt = M p / M yc =1.33 Eq F4-15a For λ > λ pw Not Applicable Mp Mp pw Mp R pt = 1 = 0.00 Eq F4-15b M yt M yt rw pw Myt R pt used for design R pt = = 1.33 Calculate F L Sxt / Sxc =0.59 For S xt / S xc >= 0.7 For S xt / S xc < 0.7 Not Applicable F L = 0.7 F y = 0.0 [ksi] Eq F4-6a Applicable F L = max ( F y x (S xt / S xc ), 0.5F y ) = 1.1 [ksi] Eq F4-6b F L used for design F L = = 1.1 [ksi] M n - Compression Flange Yielding M n1 = R pc F y S xc = [kip-ft] Eq F4-1 M n - Lateral Torsional Buckling Runway beam unbraced length L b = = [in] Calculate L p & L r E Lp = 1.1 rt = 14.4 [in] Eq F4-7 F y E J F L L S xcho r = 1.95 rt Eq F4-8 F S h E J L xc o = [in] Rev Page 51 of 11

52 Code Reference For L b <= L p Not Applicable AISC LRFD 13 M n = = NA [kip-ft] 4 of 7 For L p < L b <= L r Applicable C b = 1.0 to be conservative Lb Lp M n = Cb RpcMyc R pcmyc FL S xc RpcMyc Eq F4- Lr L p For L b > L r Not Applicable = [kip-ft] For I t / I y <= 0.3 J = 0 Not Applicable J = 3.8 [in 4 ] Cb E J Lb F cr = = 0.0 [ksi] Eq F4-5 L S b xcho rt rt M n = F cr S xc <= R pc F y S xc = NA [kip-ft] Eq F4-3 M n - LTB M n = = [kip-ft] M n - Compression Flange Local Buckling For λ <= λ pf λ =7.78 λ pf =9.15 λ rf = 4.08 Applicable M n3 = = NA [kip-ft] For λ pf < λ <= λ rf Not Applicable M n3 pf = R pcm yc R pcm yc FL S xc rf pf = NA [kip-ft] Eq F4-1 M n3 = = NA [kip-ft] M n - Tension Flange Yielding M n4 = R pt F y S xt = [kip-ft] Eq F4-14 M nx = min( M n1, M n, M n3, M n4 ) = [kip-ft] Rev Page 5 of 11

53 Check Bending about Y-Y Axis Code Reference Check top flange compactness, for W check W flange only, for W+Cap Channel check both W and Channel flange 5 of 7 Top flange compactness = Compact AISC LRFD 13 For compact top flange M ny = F y Z t = [kip-ft] Eq F6-1 For noncompact top flange M ny = F y S t = [kip-ft] M ny = = [kip-ft] Check Biaxial Bending on Top Flange Combined bending M x / (Φ M nx ) + M y / (Φ M ny ) = 0.97 OK Eq H1-1b Check Shear along Y-Y Axis Clear dist between trans. stiffeners a = L b = [in] W sect clear dist between flange h = 4.0 [in] a / h = h / t w =5.65 k v = 5 if h / t w < 60 =5.00 G.1 (b) 5 if a / h > 3.0 or a / h >[60/(h / t w )] / (a / h) T = sqrt(k v E / F y ) = 53.8 For h / t w <= 1.10 T Applicable C v = 1.0 Eq G-3 For 1.10 T < h / t w <= 1.37 T Not Applicable C v = 1.10 x sqrt(k v E / F y ) / (h / t w ) =NA Eq G-4 For h / t w > 1.37 T Not Applicable C v = 1.51 E k v / [ (h / t w ) F y ] =NA Eq G-5 C v used for design C v = = 1.0 ΦV n = 0.9 x 0.6 F y (d t w ) C v = [kips] Eq G-1 ratio = V y / ΦV n = 0.54 OK Rev Page 53 of 11

54 Check Web Sidesway Buckling (h / t w ) / (L b / b f ) =.05 >1.7 Code Reference AISC LRFD 13 6 of 7 When M u < M y Applicable C r = 9.6E+05 [ksi] When M u >= M y Not Applicable C r = 0.0E+00 [ksi] 3 3 R n = C r t w t f h / t w 0.4 = NA [kips] Eq J10-7 h L b / b f Φ = = 0.85 P v-impt = P v x α (impact factor) = [kips] ratio = P v-impt / ΦR n = 0.00 OK Check Runway Beam Deflection Crane serviceability criteria based on CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition Table 4.1 item 14,15 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition page 56 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric Cl Overhead Traveling Cranes CMAA crane service class Class C Moderate service Ver deflection limit (no impact, max wheel load) B v = L / 600 Hor deflection limit (no impact, 10% max wheel load) B h = L / 400 Runway beam span L = [in] Bridge wheel spacing s = [in] a = [in] Max deflection at center Δ max = Pa (3L 4a ) 4 E I = 1.36 P / I Vertical Deflection Unfactored max ver. wheel load P = 69.0 [kips / per wheel] impact factor NOT included I x = [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = 0.11 [in] 4 E I Rev Page 54 of 11

55 Allowable deflection Δ a = L / B v = 0.47 [in] ratio = Δ max / Δ a = 0.49 OK Code Reference 7 of 7 Lateral Deflection Unfactored max hor. wheel load P = 4.8 [kips / per wheel] I t =367.7 [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = 0.16 [in] 4 E I Allowable deflection Δ a = L / B h = [in] ratio = Δ max / Δ a = 0.5 OK Rev Page 55 of 11

56 Example 03: Top Running 45 Ton Crane + Runway W Shape with Cap Plate Imperial Unit This is a 40 tonne bridge crane with 5 tonne auxiliary hoist. The bridge has 4 wheels at each side. We need to convert the 4- wheel bridge to equivalent -wheel bridge for analysis. Crane Plan Convert the 4-wheel bridge to equivalent -wheel bridge by consolidating -wheel into a single wheel. For an equivalent -wheel bridge Bridge wheel spacing s = = 458 mm = 14.0 ft Max static wheel load = 187 kn x = 374 kn = 84.1 kips Rev Page 56 of 11

57 Crane Elevation Rev Page 57 of 11

58 Crane Runway Beam Connection Runway Beam Size W610x155 + PL457x Rev Page 58 of 11

59 Crane Data Imperial Metric Crane capacity 49.6 US Tons =99. kips 45 Metric Tons = kn Bridge weight kips kg Trolley + hoist weight 8.8 kips 4010 kg Max static wheel load 84.1 kips kn Bridge span S r ft m Left min. hook approach S L 4.6 ft m Right min. hook approach S R 4.6 ft m Bridge wheel spacing s 14.0 ft 4.58 m Crane runway beam span L 1.3 ft m Left runway CL to column CL dist e L.1 ft m Right runway CL to column CL dist e R.1 ft m Crane rail size ASCE 85 ASCE 85 CMAA crane service class Class C Class C Vertical impact factor 5% 5% Crane type Top Running Top Running Crane runway beam size W4x104 + Plate 18" x 3/4" W610x155 + Plate 457x19 W shape F y 50 ksi 345 MPa Plate cap F y 50 ksi 345 MPa Rev Page 59 of 11

60 1 of 6 BRIDGE CRANE LOAD CALCULATION Bridge crane load calc based on Code Abbreviation CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition CISC Crane Guide AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric CMAA Overhead Traveling Cranes Crane Data suggested value Crane rated capacity W rc = 49.6 [US Ton] = 99. [kips] Bridge weight W br =106.9 [kips] 90.7 = [kg] Trolley + hoist weight W th =8.8 [kips] 7.3 = 399 [kg] Bridge wheel spacing s = 14.0 [ ft ] 13.8 Max. static wheel load by vendor P max-v = 84.1 [kips] input 0 if vendor data is unknown Crane bridge span S r = [ ft ] Min. hook approach-left S L = 4.6 [ ft ] 4.6 Min. hook approach-right S R = 4.6 [ ft ] 4.6 Crane runway beam span L = 1.3 [ ft ] Runway CL to col CL dist-left e L =.1 [ ft ].1 Runway CL to col CL dist-right e R =.1 [ ft ].1 Crane column C to C distance S r + e = [ ft ] suggested section Runway beam type = W_Shape_Cap_Plate? Runway beam size = W4x104 size > W1x6 C1x0.7 Top flange cap plate size width b p = [in] thick t p = [in] applicable suggest ASCE 60 U rb = [kip/ft] Crane rail size = ASCE 85 U cr =85 [lbs/yd] = 0.08 [kip/ft] Rail base width B w =5.188 [in] Rail height H t = [in] W section yield strength f wy = 50.0 [ksi] = 345 [MPa] Cap channel or plate yield strength f cy = 50.0 [ksi] = 345 [MPa] CMAA crane service class = Class C? Moderate service Crane type = Top Running? Rev Page 60 of 11

61 Code Reference CISC Crane Guide Vertical load impact factor = 0.5? Table.1 of 6 Crane side thrust load option = Option 1? Table.1 Crane side thrust load can be calculated using one of the following 3 options Option 1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) Option H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) Option 3 H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) 0.4 Lifted Load Conclusion Runway Beam Design Using AISC ASD 9 Overall ratio = 0.7 OK Local buckling OK Bending about X-X Axis ratio = 0.7 OK Bending about Y-Y Axis on Top Flange ratio = 0.15 OK Biaxial Bending on Top Flange ratio = 0.56 OK Shear along Y-Y Axis ratio = 0.59 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.51 OK Runway Beam Lateral Deflection ratio = 0.0 OK Runway Beam Design Using AISC LRFD 13 Overall ratio = 0.71 OK Local buckling OK Biaxial Bending on Top Flange ratio = 0.71 OK Shear along Y-Y Axis ratio = 0.65 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.51 OK Runway Beam Lateral Deflection ratio = 0.0 OK Runway Beam Bottom Flange Local Bending ratio = 0.00 OK Rev Page 61 of 11

62 3 of 6 Crane Load Calculation Code Reference Crane runway + rail selfweight R sw = (U rb + U cr ) x B = 3.8 [kips] Wheel load by bridge selfwei P br = W br / 4 wheel = 6.7 [kip/per wheel] Side Thrust Load Crane side thrust load calculated by = Option 1 CISC Crane Guide H s1 = 0.4 Lifted Load = 39.7 [kips] Table.1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) = 1.6 [kips] H s3 = 0.1 (Lifted Load+ Entire Crane Wt) = 1.5 [kips] H st = side thrust load calc using Option 1 = 5.4 [kip/per wheel] H st1 =H st3 = H st (1 + (B-s) / B) = 7.3 [kips] H st =H st4 = H st s / B = 3.5 [kips] Tractive Load Table.1 H tr = 0. Max wheel load = 16.8 [kip/per wheel] H tr1 =H tr3 = H tr (1 + (B-s) / B) =.6 [kips] H tr =H tr4 = H tr s / B = 11.1 [kips] Vertical Load Case 1 Hook at One Side Min. hook aproach S min = min (S 1, S ) = 4.6 [ ft ] Max wheel load by calc P max-c = [(W rc +W th )x(s r -S min )/ S r ]/ wheel+p br = 78.8 [kip/per wheel] Max. wheel load by vendor P max-v = = 84.1 [kip/per wheel] Max static wheel load P max = max (P max-v, P max-c ) = 84.1 [kip/per wheel] Min wheel load P min = [(W rc +W th )xs min /S r ]/ wheel+p br = 8.6 [kip/per wheel] Rev Page 6 of 11

63 4 of 6 Reaction on runway support R 1 = P max (1 + (B-s) / B) + R sw = [kips] R = P max s / B + R sw = 59.1 [kips] R 3 = P min (1 + (B-s) / B) + R sw = 4. [kips] R 4 = P min s / B + R sw =.6 [kips] Point moment to column center M 1 = R 1 x e R = 45.1 [kip-ft] M = R x e R = 14.1 [kip-ft] M 3 = R 3 x e L = 88.7 [kip-ft] M 4 = R 4 x e L = 47.5 [kip-ft] Case 1 Hook at One Side - Crane Load Summary 7.3 kips 4. kips 88.7 kip-ft 3.5 kips 11.1 kips.6 kips.6 kips 47.5 kip-ft 45.1 kip-ft.6 kips kips 7.3 kips 14.1 kip-ft 59.1 kips 3.5 kips 11.1 kips Note: The crane loads shown above may be reverse if crane hook goes to the other side. When reverse the loads and apply them on building columns, the point moment value may need adjusted if eccentricity e L <> e R Rev Page 63 of 11

64 5 of 6 Case Hook at Center of Bridge Max wheel load P max = P min = (W rc +W br +W th )/4 wheel = 53.7 [kip/per wheel] Reaction on runway support R 1 = R 3 = P max (1 + (B-s) / B) + R sw = 75.9 [kips] R = R 4 = P max s / B + R sw = 39.1 [kips] Point moment to column center M 1 = M 3 = R 1 x max (e L, e R ) = [kip-ft] M = R x max (e L, e R ) = 8. [kip-ft] Case Hook at Center of Bridge - Load Summary 7.3 kips 75.9 kips kip-ft 3.5 kips 11.1 kips.6 kips 39.1 kips 8. kip-ft kip-ft.6 kips 75.9 kips 7.3 kips 8. kip-ft 39.1 kips 3.5 kips 11.1 kips Rev Page 64 of 11

65 Code Reference 6 of 6 Bumper Force at End Frame AISC Design Guide 7 Bumper force to be the greater of 1 Twice the tractive force = 33.6 [kips] % of entire crane weight = 10.7 [kips] Bumper force used for design = 33.6 [kips] Apply longitudinal bumper force to both sides of end frame 33.6 kips 33.6 kips Rev Page 65 of 11

66 1 of 3 CRANE RUNWAY BEAM DESIGN Crane beam design using two codes : AISC LRFD-13 and AISC ASD 9th Edition Code Abbreviation AISC Specification for Structural Steel Buildings AISC LRFD-13 AISC Manual of Steel Construction: Allowable Stress Design 9th Edition ASD 9th Edition CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition CISC Crane Guide AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane Data Crane rated capacity W rc = 49.6 [tonne] = [kips] Bridge weight W br = [kips] = [kg] Trolley + hoist weight W th = 8.8 [kips] = 399 [kg] Bridge wheel spacing s = 14.0 [ ft ] = 4.67 [m] For 4-wheel crane double the vendor provided max static wheel load as input Max static wheel load P max = 84.1 [kips] = [kn] Crane bridge span S r = [ ft ] = [m] Left min. hook approach S 1 = 4.6 [ ft ] = 1.40 [m] Right min. hook approach S = 4.6 [ ft ] = 1.40 [m] Crane runway beam span L = 1.3 [ ft ] = 6.49 [m] Runway CL to column CL dist e =.1 [ ft ] = [m] Runway beam type W_Shape_Cap_Plate Runway beam size W4x104 U rb = 0.15 [kip/ft] =. [kn/m] Crane rail size ASCE 85 U cr = 0.03 [kip/ft] = 0.4 [kn/m] Rev Page 66 of 11

67 Crane Load Calculation CISC Crane Guide Ver. load impact factor α = 1.5 Table.1 Crane side thrust load H s = Option 1 = 1.6 [kips] Option 1 H s = 0. (Lifted Load+ Trolley/Hoist Wt) of 3 Option H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) Option 3 H s = max of 0. (Lifted Load+ Trolley/Hoist Wt) 0.1 (Lifted Load+ Entire Crane Wt) 0.4 Lifted Load Runway beam span L = 1.3 [ ft ] Bridge wheel spacing s = 14.0 [ ft ] M max = P s L L =4.80 P Runway beam + rail selfwei U = U rb + U cr = [kip/ft] Crane Load for Design per AISC ASD 9th Ed Max ver. load /wheel (no impact) P v = = 84.1 [kips / per wheel] Max hor. load /wheel P h = H s / 4 = 5.4 [kips / per wheel] Bending moment x-x axis M x = 4.80 xp v x α (impact) + U x L / 8 = [kip-ft] Bending moment y-y axis M y = 4.80 xp h = 5.9 [kip-ft] Shear along y-y axis V x = P v [ 1+ (L - s) / L ]x α (mpact) + UxL/ = [kips] Crane Load for Design per AISC LRFD-13th Ed Wheel load by bridge selfwei P br = W br / 4 = 6.7 [kips] as dead load Wheel load by lift load + trolley P lt = P max - P br = 57.4 [kips] as live load Max factored ver. load /wheel P v = 1. x P br x P lt = 13.9 [kips] impact not included Max factored hor. load /wheel P h = H x 1.6 / 4 = 8.6 [kips] Factor bending moment x-x axis M x = 4.80 xp v x α(impact)+1.xuxl / 8 = [kip-ft] Factor bending moment y-y axis M y = 4.80 xp h = 41.5 [kip-ft] Factor shear along y-y axis V x = P v [1+ (L - s) /L]xα(mpact)+1.xUxL/ = 10. [kips] Rev Page 67 of 11

68 CRANE RUNWAY BEAM - COMBINED SECTION PROPERTIES CALCULATION 1 of 3 Crane runway beam section W4x104 Top Cap Plate = PL 18 x 0.75 Section Properties W Section d = 4.1 [in] b f = 1.8 [in] t f =0.750 [in] t w = [in] A = 30.6 [in ] h =.6 [in] r x = [in] r y =.91 [in] I x = [in 4 ] S x = 58.0 [in 3 ] Z x =89.0 [in 3 ] I y =59.0 [in 4 ] S y = 40.7 [in 3 ] Z y =6.4 [in 3 ] J = 4.7 [in 4 ] C w = 3500 [in 6 ] Top Cap Plate Top cap plate size width b p = [in] thick t p = [in] Combined Section Overall Top Flange A = 44.1 [in ] d all = 4.9 [in] top y =9.0 [in] bott. y 1 = 15.9 [in] I x = [in 4 ] I y = 66.9 [in 4 ] top S =505.4 [in 3 ] bott. S 1 = 86.8 [in 3 ] S y =69.7 [in 3 ] Z x =364.6 [in 3 ] Z y = 91.5 [in 3 ] r x = [in] r y =3.77 [in] J = 17. [in 4 ] C w =0 [in 6 ] A f =3.1 [in ] d all / A f =1.076 [in -1 ] r T =4.51 [in] r yt =4.63 [in] I t =495.6 [in 4 ] S t =55.1 [in 3 ] Z t = 91.5 [in 3 ] Rev Page 68 of 11

69 of 3 Calculate Plastic Z x and Z y Plastic neutral axis area above neutral axis equals area below neutral axis A 1 = b p x t p = 13.5 [in ] A = b f x t f =9.6 [in ] A 3 = h x t w = 11.3 [in ] h = (h x t w + A 1 ) / ( x t w ) = 4.8 [in] Plastic modulus x-x axis Centroid of top a = -1.1 [in] b = -1.8 [in] c = -1.1 [in] top web area A wt =-1.1 [in ] c t =-1.4 [in] Centroid of bott a = 1.4 [in] b = 5. [in] bott web area A wb = 1.4 [in ] c b =18.0 [in] Total area of bottom part A bott = t w x h + A =.0 [in ] Plastic modulus x-x axis Z x = A bott x ( c b + c t ) = [in 3 ] Plastic modulus y-y axis only top flange & cap plate are considered Z y = ( t f x b f + t p x b p ) / 4 = 91.5 [in 3 ] Calculate Elastic Properties X-X Axis A y b Axy b Axy b in in in 3 in 4 W4x Plate 18 x Sum I 0 in Rev Page 69 of 11

70 y B = Σ Ay b / Σ A = 15.9 [in] y T = d + t p - y B = 9.0 [in] Code Reference 3 of 3 I x = Σ I 0 + Σ Ay b -y B Σ A = [in 4 ] S B = I x / y B = 86.8 [in 3 ] S T = I x / y T = [in 3 ] Calculate Elastic Properties Y-Y Axis Top flange + plate I y1 = ( t f x b 3 f + t p x b 3 p ) / 1 = [in 4 ] Web I y = h x t 3 w / 1 =0. [in 4 ] Bott. flange I y3 = t f x b 3 f / 1 = [in 4 ] Sum I y = = 66.9 [in 4 ] S y = I y / [ 0.5 x max(b f, b p ) ] = 69.7 [in 3 ] Calculate Torsional Properties t ft =1.5 [in] t fb = 0.8 [in] d' = d all - (t ft + t fb ) / = 3.7 [in] J = ( b f x t 3 ft + b f x t 3 fb + d' x t 3 w ) / 3 = 17. [in 4 ] Calculate Top Flange Properties 1/3 compression web depth h cw = [ y - ( t f + t p ) ] / 3 =.5 [in] I tw = ( t f x b 3 f + t p x b 3 p + h cw x t 3 w ) / 1 = [in 4 ] A tw = t f x b f + t p x b p + h cw x t w = 4.3 [in ] r T = sqrt( I tw / A tw ) = 4.5 [in] I t = ( t f x b 3 f + t p x b 3 p ) / 1 = [in 4 ] Z t = ( t f x b f + t p x b p ) / 4 = 91.5 [in 3 ] Rev Page 70 of 11

71 1 of 5 CRANE RUNWAY BEAM DESIGN - ASD 9 Crane runway design based on Code Abbreviation AISC Manual of Steel Construction: Allowable Stress Design 9th Edition ASD 9th Edition AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane runway beam section W4x104 W4x104 and PL 18 x 0.75 Section Properties Combined Section Overall A = [in ] d all = [in] top y =8.996 [in] bott. y 1 = [in] I x = [in 4 ] I y = 66.9 [in 4 ] top S =505.4 [in 3 ] bott. S 1 = 86.8 [in 3 ] S y =69.7 [in 3 ] Z x =364.6 [in 3 ] Z y = 91.5 [in 3 ] r x = [in] r y = [in] J = 17. [in 4 ] C w =0 [in 6 ] W Section d = [in] b f = [in] t w =0.500 [in] t f = [in] h = [in] Top Flange A f =3.100 [in ] d all / A f =1.076 [in -1 ] r T =4.511 [in] r yt = 4.63 [in] I t = [in 4 ] S t =55.06 [in 3 ] Z t = [in 3 ] Top cap plate size width b p = [in] thick t p = [in] W section yield strength F wy = 50.0 [ksi] = 345 [MPa] Compression flange yield strength F cy = 50.0 [ksi] = 345 [MPa] Runway beam unbraced length L b =55.60 [in] Design Forces Bending moment x-x axis M x = [kip-ft] Bending moment y-y axis M y = 5.9 [kip-ft] Shear along y-y axis V x = [kips] Conclusion Overall ratio = 0.7 OK Local buckling OK Bending about X-X Axis ratio = 0.7 OK Bending about Y-Y Axis on Top Flange ratio = 0.15 OK Biaxial Bending on Top Flange ratio = 0.56 OK Shear along Y-Y Axis ratio = 0.59 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.51 OK Runway Beam Lateral Deflection ratio = 0.0 OK Rev Page 71 of 11

72 of 5 Code Reference Design Basis & Assumption AISC Design Guide 7 1. The cap plate and W section top flange resist the hor. load and the combined section resists the 18.1 on page 56 ver. load. This assumption eliminates the need for an analysis of torsional effects on the combined section and simplifies the analysis.. If A36 cap plate is used on A99 W section then lateral torsional buckling and weak axis on page 57 flexure strength must be calculated based on A36 yield stress. Check Local Buckling Flange of W shape ASD 9th Edition Compact limit λ p = 65 / sqrt (F wy ) = 9.19 Table B5.1 Noncompact limit λ r = 95 / sqrt (F wy ) = b f / t f = 8.53 Compact Web of W shape Compact limit λ p = 640 / sqrt (F wy ) = Table B5.1 Noncompact limit λ r = 760 / sqrt ( 0.66F wy ) = d / t w =48.0 h / t w = 43.0 Compact W shape classification Compact Flange Cover Plate Between Lines of Welds AISC LRFD-13 Compact limit λ p = 1.1 sqrt (E / F py ) = 6.97 Table B4.1 Case 1 Noncompact limit λ r = 1.40 sqrt (E / F py ) = 33.7 Cap plate classification b f / t p =17.07 Compact Combined section classification Compact = 0.00 OK Check Bending about X-X Axis Tension Allowable tension stress F bx t = 0.6 x F wy = [ksi] Actual tension stress f bx t = M x / S 1 = 1.54 [ksi] ratio = f bx t / F bx t = 0.7 OK Compression Comb sect top flange yield stress F y = 50.0 [ksi] see assumption Comb sect top flange width b f =1.8 [in] Rev Page 7 of 11

73 Code Reference Critical length L c ASD 9th Edition 4 = = [in] Eq F1-76 xb f x10 min, F d y all / A f xfy 3 of 5 76 b f / sqrt( F y ) = = [in] When L b <= L c For compact sect For non-compact sect This part is NOT applicable Not Applicable F bx = 0.66 x F y = 0.00 [ksi] Eq F1-1 Not Applicable b f / t f = = 8.53 b f F bx = Fy Fy = 0.00 [ksi] Eq F1-3 t f F bx = 0.6 x F y = 0.00 [ksi] Eq F1-5 When L b > L c This part is applicable L b / r T = = Bending coefficient C b = 1.0 to be conservative 510 x10 xc b x = = F y 3 For ( L b / r T ) <= x Applicable Fy L b / r T F bx = Fy 0.6Fy = 8.09 [ksi] Eq F x10 C b For ( L b / r T ) > x Not Applicable 170 x10 Cb F bx = 0.6F y = 0.00 [ksi] Eq F1-7 L / r b T 3 For any value of ( L b / r T ) Applicable 1x10 C F bx = b 0.6Fy = [ksi] Eq F1-8 L xd / A b Allowable compression stress F bx c = = [ksi] Actual compression stress f bx c = M x / S = 1. [ksi] ratio = f bx c / F bx c = 0.41 OK all 3 f Check Bending about Y-Y Axis on Top Flange For compact top flange Applicable F by = 0.75 x F y = [ksi] Eq F Rev Page 73 of 11

74 Code Reference For non-compact top flange Not Applicable ASD 9th Edition F by = 0.60 x F y = 0.00 [ksi] Eq F- Allowable compression stress F by c = = [ksi] Actual compression stress f by c = M y / S t =5.65 [ksi] ratio = f bx c / F bx c = 0.15 OK 4 of 5 Check Biaxial Bending on Top Flange Combined bending stress f bx / F bx + f by / F by = 0.56 OK Eq H1-3 Check Shear along Y-Y Axis Clear dist between trans. stiffeners a = L b = [in] W sect clear dist between flange h = [in] a / h = k v = / (a / h) if a / h <=1 =5.37 F / (a / h) if a / h >1 h / t w =43.0 C v =1.44 For h / t w <= 380 / sqrt ( F y ) Applicable F v = 0.40 x F y = 0.00 [ksi] Eq F4-1 For h / t w > 380 / sqrt ( F y ) Not Applicable F v = ( F y x C v ) /.89 <=0.4 F y = 0.00 [ksi] Eq F4- Allowable shear stress F v = = 0.00 [ksi] Actual shear stress f v = V x / S t = [ksi] ratio = f v / F v = 0.59 OK Check Web Sidesway Buckling AISC Design Guide 7 Use LRFD 13 instead of ASD 9 to increase web sidesway buckling resistance when flexural page 61 stress in the web is less than 0.66F y (h / t w ) / (L b / b f ) =.16 >1.7 AISC LRFD-13 Max actual bending stress f b =1.54 [ksi] When f b < (F y / 1.5) = 0.66 F y Applicable C r = 9.6E+05 [ksi] When f b >= (F y / 1.5) = 0.66 F y Not Applicable C r = 0.0E+00 [ksi] R n = 3 3 C r t w t f h / t w 0.4 h L b / b f = NA [kips] Eq J10-7 R a = R n / Ω = R n / 1.76 =NA [kips] P v-impt = P v x α (impact factor) = [kips] Ratio = P v-impt / R a = 0.00 OK Rev Page 74 of 11

75 5 of 5 Check Runway Beam Deflection Code Reference Crane serviceability criteria based on CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition Table 4.1 item 14,15 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition page 56 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric Cl Overhead Traveling Cranes CMAA crane service class Class C Moderate service Ver deflection limit (no impact, max wheel load) B v = L / 600 Hor deflection limit (no impact, 10% max wheel load) B h = L / 400 Runway beam span L = [in] Bridge wheel spacing s = [in] a = [in] Pa(3L 4a ) Max deflection at center Δ max = = P / I 4 E I Vertical Deflection Unfactored max ver. wheel load P = 84.1 [kips / per wheel] impact factor NOT included I x = [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = 0.19 [in] 4 E I Allowable deflection Δ a = L / B v = 0.46 [in] Ratio = Δ max / Δ a = 0.51 OK Lateral Deflection Unfactored max hor. wheel load P = 5.4 [kips / per wheel] I t =495.6 [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = 0.19 [in] 4 E I Allowable deflection Δ a = L / B h = [in] Ratio = Δ max / Δ a = 0.0 OK Rev Page 75 of 11

76 1 of 7 CRANE RUNWAY BEAM DESIGN - LRFD 13 Crane runway design based on Code Abbreviation AISC Specification for Structural Steel Buildings AISC LRFD-13 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition AISC Design Guide 7 Crane runway beam section W4x104 W4x104 and PL 18 x 0.75 Section Properties Combined Section Overall A = [in ] d all = [in] top y c =8.996 [in] bott. y t = [in] I x = [in 4 ] I y = 66.9 [in 4 ] top S xc =505.4 [in 3 ] bott. S xt = 86.8 [in 3 ] S y =69.7 [in 3 ] Z x =364.6 [in 3 ] Z y = 91.5 [in 3 ] r x = [in] r y = [in] J = 17. [in 4 ] C w =0 [in 6 ] W Section d = [in] b f = [in] t w =0.500 [in] t f = [in] h = [in] h c = ( y c - k ) = [in] h 0 = d - t f =3.350 [in] Top Flange A f =3.10 [in ] d all / A f =1.076 [in -1 ] r t =4.511 [in] r yt = 4.63 [in] I t =495.6 [in 4 ] S t =55.1 [in 3 ] Z t = 91.5 [in 3 ] Top cap plate size width b p = [in] thick t p = [in] W section yield strength F wy = 50.0 [ksi] = 345 [MPa] Compression flange yield strength F cy = 50.0 [ksi] = 345 [MPa] Runway beam unbraced length L b =55.60 [in] Design Forces Bending moment x-x axis M x = [kip-ft] Bending moment y-y axis M y = [kip-ft] Shear along y-y axis V y = [kips] Conclusion Overall ratio = 0.71 OK Local buckling OK Biaxial Bending on Top Flange ratio = 0.71 OK Shear along Y-Y Axis ratio = 0.65 OK Web Sidesway Buckling ratio = 0.00 OK Runway Beam Vertical Deflection ratio = 0.51 OK Runway Beam Lateral Deflection ratio = 0.0 OK Rev Page 76 of 11

77 of 7 Code Reference Design Basis & Assumption AISC Design Guide 7 1. The channel and W section top flange resist the hor. load and the combined section resists the 18.1 on page 56 ver. load. This assumption eliminates the need for an analysis of torsional effects on the combined section and simplifies the analysis.. If A36 channel cap is used on A99 W section then lateral torsional buckling and weak axis on page 57 flexure strength must be calculated based on A36 yield stress. Check Local Buckling Flange of W shape AISC LRFD-13 Compact limit λ p = 0.38 sqrt (E / F wy ) = 9.15 Table B4.1 Case 1 Noncompact limit λ r = 1.0 sqrt (E / F wy ) = 4.08 b f / t f = 8.53 Compact Web of W shape Compact limit λ p = 3.76 sqrt (E / F wy ) = Table B4.1 Case 9 Noncompact limit λ r = 5.7 sqrt (E / F wy ) = h / t w = 43.0 Compact W shape classification Compact Flange Cover Plate Between Lines of Welds Compact limit λ p = 1.1 sqrt (E / F cy ) = 6.97 Table B4.1 Case 1 Noncompact limit λ r = 1.4 sqrt (E / F cy ) = 33.7 Cap plate classification b f / t p =17.07 Compact Combined section classification Compact = 0.00 OK Check Bending about X-X Axis Calculate R pc λ pw =90.55 λ rw = M yc = S xc F y = [kip-ft] M p = min ( Z x F y, 1.6 S xc F y ) = [kip-ft] λ = h c / t w = M p / M yc = = 0.7 For λ <= λ pw Applicable R pc = M p / M yc =0.7 Eq F4-9a Rev Page 77 of 11

78 Code Reference For λ > λ pw Not Applicable AISC LRFD-13 3 of 7 Mp Mp pw Mp R pc = 1 = 0.00 Eq F4-9b M yc M yc rw pw Myc R pc used for design R pc = = 0.7 Calculate R pt M yt = S xt F y = [kip-ft] M p = min ( Z x F y, 1.6 S xt F y ) = [kip-ft] M p / M yt = = 1.7 For λ <= λ pw Applicable R pt = M p / M yc =1.7 Eq F4-15a For λ > λ pw Not Applicable Mp Mp pw Mp R pt = 1 = 0.00 Eq F4-15b M yt M yt rw pw Myt R pt used for design R pt = = 1.7 Calculate F L Sxt / Sxc =0.57 For S xt / S xc >= 0.7 For S xt / S xc < 0.7 Not Applicable F L = 0.7 F y = 0.0 [ksi] Eq F4-6a Applicable F L = max ( F y x (S xt / S xc ), 0.5F y ) = 8.4 [ksi] Eq F4-6b F L used for design F L = = 8.4 [ksi] M n - Compression Flange Yielding M n1 = R pc F y S xc = [kip-ft] Eq F4-1 M n - Lateral Torsional Buckling Runway beam unbraced length L b = = [in] Calculate L p & L r E Lp = 1.1 rt = [in] Eq F4-7 F y E J F L L S xcho r = 1.95 rt Eq F4-8 F S h E J L xc o = [in] Rev Page 78 of 11

79 Code Reference For L b <= L p Not Applicable AISC LRFD-13 M n = = NA [kip-ft] 4 of 7 For L p < L b <= L r Applicable C b = 1.0 to be conservative Lb Lp M n = Cb RpcMyc R pcmyc FL S xc RpcMyc Eq F4- Lr L p For L b > L r Not Applicable = [kip-ft] For I t / I y <= 0.3 J = 0 Not Applicable J = [in 4 ] Cb E J Lb F cr = = 0.0 [ksi] Eq F4-5 L S b xcho rt rt M n = F cr S xc <= R pc F y S xc = NA [kip-ft] Eq F4-3 M n - LTB M n = = [kip-ft] M n - Compression Flange Local Buckling For λ <= λ pf λ =8.53 λ pf =9.15 λ rf = 4.08 Applicable M n3 = = NA [kip-ft] For λ pf < λ <= λ rf Not Applicable M n3 pf = R pcm yc R pcm yc FL S xc rf pf = NA [kip-ft] Eq F4-1 M n3 = = NA [kip-ft] M n - Tension Flange Yielding M n4 = R pt F y S xt = [kip-ft] Eq F4-14 M nx = min( M n1, M n, M n3, M n4 ) = [kip-ft] Rev Page 79 of 11

80 Check Bending about Y-Y Axis Check top flange compactness, for W check W flange only, for W+Cap Plate check both W and Cap Plate Code Reference 5 of 7 Top flange compactness = Compact AISC LRFD-13 For compact top flange M ny = F y Z t = [kip-ft] Eq F6-1 For noncompact top flange M ny = F y S t = 9.4 [kip-ft] M ny = = [kip-ft] Check Biaxial Bending on Top Flange Combined bending M x / (Φ M nx ) + M y / (Φ M ny ) = 0.71 OK Eq H1-1b Check Shear along Y-Y Axis Clear dist between trans. stiffeners a = L b = [in] W sect clear dist between flange h = [in] a / h = h / t w =43.0 k v = 5 if h / t w < 60 =5.00 G.1 (b) 5 if a / h > 3.0 or a / h >[60/(h / t w )] / (a / h) T = sqrt(k v E / F y ) = 53.9 For h / t w <= 1.10 T Applicable C v = 1.0 Eq G-3 For 1.10 T < h / t w <= 1.37 T Not Applicable C v = 1.10 x sqrt(k v E / F y ) / (h / t w ) =NA Eq G-4 For h / t w > 1.37 T Not Applicable C v = 1.51 E k v / [ (h / t w ) F y ] =NA Eq G-5 C v used for design C v = = 1.0 ΦV n = 0.9 x 0.6 F y (d t w ) C v = 35.4 [kips] Eq G-1 ratio = V y / ΦV n = 0.65 OK Rev Page 80 of 11

81 Check Web Sidesway Buckling (h / t w ) / (L b / b f ) =.16 >1.7 Code Reference AISC LRFD-13 6 of 7 When M u < M y Applicable C r = 9.6E+05 [ksi] When M u >= M y Not Applicable C r = 0.0E+00 [ksi] 3 3 R n = C r t w t f h / t w 0.4 = NA [kips] Eq J10-7 h L b / b f Φ = = 0.85 P v-impt = P v x α (impact factor) = [kips] ratio = P v-impt / ΦR n = 0.00 OK Check Runway Beam Deflection Crane serviceability criteria based on CISC Guide for the Design of Crane-Supporting Steel Structures nd Edition Table 4.1 item 14,15 AISC Design Guide 7: Industrial Buildings-Roofs to Anchor Rods nd Edition page 56 CMAA Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric Cl Overhead Traveling Cranes CMAA crane service class Class C Moderate service Ver deflection limit (no impact, max wheel load) B v = L / 600 Hor deflection limit (no impact, 10% max wheel load) B h = L / 400 Runway beam span L = [in] Bridge wheel spacing s = [in] a = [in] Max deflection at center Δ max = Pa (3L 4a ) 4 E I = P / I Vertical Deflection Unfactored max ver. wheel load P = 84.1 [kips / per wheel] impact factor NOT included I x = [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = 0.19 [in] 4 E I Rev Page 81 of 11

82 Allowable deflection Δ a = L / B v = 0.46 [in] ratio = Δ max / Δ a = 0.51 OK Code Reference 7 of 7 Lateral Deflection Unfactored max hor. wheel load P = 5.4 [kips / per wheel] I t =495.6 [in 4 ] Pa(3L 4a ) Max deflection at center Δ max = = 0.19 [in] 4 E I Allowable deflection Δ a = L / B h = [in] ratio = Δ max / Δ a = 0.0 OK Rev Page 8 of 11

83 Example 04: Underhung 7.5 Ton Crane + Runway W Shape Metric Unit 6660 (OVERALL) (SPAN) S.W.L. 7½-TONNE U/S BRIDGE 91 HIGH HOOK (6m AVAILABLE ON HOIST) (O/O) (WHEELBASE) DOWN POWER SHOP FEED 496 PLAN VIEW T/O RUNWAY THIS SPACE NOT TO BE ENCROACHED FLOOR ELEVATION VIEW Rev Page 83 of 11

84 7.5 Tonne Underhung Crane Runway Beam Plan Rev Page 84 of 11