1、SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirelyvoluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefro
2、m, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.Copyright 2007 SAE InternationalAll rights reserved. No part of this publication may be
3、reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying,recording, or otherwise, without the prior written permission of SAE.TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada)Tel: 724-776-4970 (outside USA)Fax: 724-
4、776-0790Email: CustomerServicesae.orgSAE WEB ADDRESS: http:/www.sae.orgSURFACEVEHICLEINFORMATIONREPORTJ1078REAF.NOV2007Issued 1974-07Reaffirmed 2007-11Superseding J1078 APR1994A Recommended Method of Analytically Determiningthe Competence of Hydraulic Telescopic Cantilevered Crane Booms1. ScopeThis
5、analysis applies to crane types as covered by Power Crane and Shovel Association StandardNumber Two, Mobile Hydraulic Crane Standards and ANSI B30.15; refer to 5.1.1.1 PurposeThis calculation method has been established to illustrate an analysis to determine thecompetence of hydraulic telescopic can
6、tilevered crane booms.2. References2.1 Applicable PublicationsThe following publications form a part of this specification to the extent specifiedherein.2.1.1 AISC, “Specification for the Design, Fabrication and Erection of Structural Steel for Buildings,“ adoptedFebruary 12, 1969. In addition, Supp
7、lement Nos. 1, 2, 3, and Commentary with additions and revisionswhere applicable.2.1.2 AISI, “Specification for the Design of Cold-Formed Steel Structural Members,“ 1968 edition. In addition,“Commentary on the 1968 Edition,“ by George Winter and Supplementary Information Part II.2.1.3 Column Researc
8、h Council, “Guide to Design Criteria for Metal Compression Members,“ Second Printing,1960.2.1.4 “USS Steel Design Manual,“ by R. L. Brockenbrough and B. G. Johnston, November 1968 printing.2.1.5 ANSI B30.15SAE J1078 Reaffirmed NOV2007-2-2.1.6 NOMENCLATUREa =Clear distance between transverse stiffene
9、rs on side plate; also the ratio of the material yield of the webto the material yield of the compression flangeA =Actual area of sectionAe=Total effective area of section used in calculating Fa(refer to Appendix E for illustration)Af=Area of compression flangeAi=Area based on inside dimensions of s
10、ection (refer to Appendix E for illustration)Am=Area based on mean dimensions of section (refer to Appendix E for illustration)Ao=Area based on outside dimensions of section (refer to Appendix E for illustrationAst=Cross-sectional area of stiffener or pair of stiffenersAw=Area of both websb =Actual
11、width of stiffened and unstiffened compression elements whether flange or web (refer toAppendix F for illustration)be=Effective width of stiffened compression element (refer to Appendix E for illustration)bf=Actual flange width (refer to Appendix E for illustration)bm=Mean width of section or bw- tw
12、(refer to Appendix E for illustration)bw=Overall width of section (refer to Appendix E for illustration)Ct=Distance from neutral axis to extreme tension fiber of box section (refer to Appendix E for illustration)Cc=Distance from neutral axis to compressive fiber of box section (refer to Appendix E f
13、or illustration)Cb=Bending coefficient dependent upon moment gradient; equal to (see Equation 1)(Eq. 1)but not more than 1.3 (refer to Appendix C for illustration)Cc=Column slenderness ratio dividing elastic and inelastic buckling equal to (see Equation 2)(Eq. 2)Cc=Effective column slenderness ratio
14、 dividing elastic and inelastic buckling equal to (see Equation 3)(Eq. 3)Cm=Coefficient applied to bending term in the interaction formula and dependent upon column curvaturecaused by applied moments; use 0.85Cmx=0.85Cmy=0.85Cv=Ratio of “critical“ web stress, according to linear buckling theory, to
15、the shear yield stress of webmateriald =Overall depth of section (refer to Appendix E for illustration)D =Factor depending upon type of transverse stiffenersE =Modulus of elasticity 29 500 ksif =Computed axial and bending compression stress on appropriate flange or webfa=Computed axial stress based
16、on total section areafb=Computed bending stress about the appropriate axisfc=Sum of the computed axial and side bending compressive stressesfbx=Computed bending stress about the x-x axisfby=Computed bending stress about the y-y axisfs=Sum of the computed torsional and vertical shear stressfv=Compute
17、d average web or flange shear stressfvs=Total shear transfer of stiffener(s), kips per inch of lengthFa=Allowable axial stress permitted in the absence of a bending momentFb=Allowable bending stress for the appropriate axisFbx=Allowable bending stress about the x-x axis if this bending moment alone
18、existed1.75 1.05MxminMxmax0.3MxminMxmax2+2EFyrc()2EQsQaFyre()SAE J1078 Reaffirmed NOV2007-3-Fbx=Allowable bending stress in compression flange of box sections as reduced for hybrid sections orbecause of large web depth-to-thickness ratioFby=Allowable bending stress about the y-y axis if this bending
19、 moment alone existedFe=Euler stress divided by factor of safety; equal to (see Equation 4)(Eq. 4)Fex=Same as Feabout the x-x axisFey=Same as Feabout the y-y axisFv=Allowable web shear stressFy=Specified minimum yield stress of material being used, based on “yield stress“ or yield strength,whichever
20、 is applicableg =Wind load, lb/in2, g = 0.004 (mph)2/144G =Shear modulus of elasticity 11 300 ksih =Clear distance between flanges (refer to Appendix E for illustration)hm=Mean height of section d (tc+ tt)/2 (refer to Appendix E for illustrationhv=Vertical height of horizontal stiffenerHo=Height to
21、boom foot pin from groundHp=Height to center of pressure on boomHr=Reference height at which wind velocity is measured (20 ft in U.S.)Ix=Area moment of inertia about the x-x axisIy=Area moment of inertia about the y-y axisIst=Moment of inertia of a pair of intermediate stiffeners, or a single interm
22、ediate stiffener, with reference toan axis in the plane of the webIxe=Effective moment of inertia about the x-x axisIye=Effective moment of inertia about the y-y axisJ =Torsional constant; equal to (refer to Appendix D for other equations) (see Equation 5)(Eq. 5)k =Coefficient relating linear buckli
23、ng strength of a plate to its dimensions and conditions of edge supportK =Effective length factor, for cantilevered section use the value 2 unless a smaller one can be justifiedKt=Torsional length factor for cantilevered sections, use the value 4/3I =Dimensional lengths of boomL =Distance from tip t
24、o section in questionLb=Actual unbraced length of section in the plane of bendingM =Bending moment about the appropriate axisM1=Constant moment load about the x-x axis resulting from eccentric loading on the headM2=Constant moment load about the y-y axis resulting from the side loading on the headMx
25、min=Smaller moment at end of unbraced length of beam-column at tipMxmax=Larger moment at end of unbraced length of beam-column at section in questionMx=Bending moment about the x-x axisMy=Bending moment about the y-y axisN =Number of parts of linep =Wind velocity exponentP =Externally applied load a
26、t the tipPa=Axial load applied to sectionPx=Lateral loading component (side load)Py=Vertical loading componentPz=Axial loading componentQa=Ratio of effective profile area of an axially loaded member to its total profile area of Ae/AQs=Axial stress reduction factor for unstiffened elements of a secti
27、on; refer to Appendix F122E23 Kl r()24bm()2hm()22hmtwbmtcbmtt+SAE J1078 Reaffirmed NOV2007-4-r =Radius of gyration for appropriate axisrb=Radius of gyration about the axis of concurrent bending, computed on the basis of actual cross-sectional areaR =Load radius from centerline of rotation to centerl
28、ine of loadRh=Hoist cylinder reactionRx=Reaction loads in the lateral directionRy=Reaction loads in the vertical directionRz=Reaction loads in the axial directionSx=Strong axis section modulus with c taken to the compressive sideSy=Weak axis section modulus with c taken to the compressive sideSxe=Ef
29、fective strong axis section modulus with c taken to the compressive sideSye=Effective weak axis section modulus with c taken to the compressive sidet =Thickness of flange or web in compression (refer to Appendix E for illustration)tc=Thickness of compression flange (refer to Appendix E for illustrat
30、ion)tt=Thickness of tension flange (refer to Appendix E for illustration)tw=Thickness of web (refer to Appendix E for illustration)T =Torsional momentVp=Wind velocity (mph) at center of pressure height HpVr=Wind velocity (mph) at reference height HrVx=Statical shear load on section in the lateral di
31、rectionVy=Statical shear load on section in the vertical directionw =Component weight, lb/inW =Total component weightx =Subscript relating symbol to strong axis bendingY =Ratio of yield stress of web steel to that of yield stress of stiffener steely =Subscript relating symbol to weak axis bendingz =
32、Subscript relating symbol to axial loading =Boom centerline elevation angle relative to a horizontal plane, or the ratio of web yield stress to flangeyield stress =Angle between a line perpendicular to the boom axis and the hoist cylinder axisrc=Residual compressive stress, equal to 0.5 Fyin lieu of
33、 specific information on steel usedu =Poissons ratioequal to 0.33. CriteriaCalculations shall include the dead weight loads, rated load and a minimum side load of 2% of therated load at the rated load radius. The side load provides for “normal“ conditions of machine operation. Inaddition, the effect
34、 of the wind on the boom should be considered, as is provided for in the calculations.3.1 The factors of safety used herein are the recommended factors of the AISC “Specification for the Design,Fabrication and Erection of Structural Steel for Buildings,“ adopted February 12, 1969.3.2 The boom shall
35、be deemed competent when the solution of the interaction equations provided herein yield avalue equal to or less than one (1.0).4. Loads and Forces4.1 The 2% side load provides for “normal“ conditions of boom motion. No allowances have been made fordynamic loads, duty cycle operation, effects of the
36、 wind on the load lifted or operations other than lifting craneservice.4.2 All forces and loads are expressed in pounds. Dimensions are in inches. Stresses both allowable andcalculated are in units of ksi. Also, the modulus of elasticity is expressed in units of ksi.SAE J1078 Reaffirmed NOV2007-5-5.
37、 Analytical Determination of Stresses and Critical Loads5.1 ApplicabilityThis analysis is applicable to multisectioned “box“ type booms, which are totally enclosed andcantilevered beyond the base section.5.2 Basis for AnalysisThe equations presented in this analysis are based on laterally unsupporte
38、d beamcolumn formulas, the solution of which are combined in interaction equations. In determining the sectionproperties, the effective width of the plates in compression are used. The areas covered in this analysisconsist of axial and torsional loading, bidirectional bending, and panel buckling. Of
39、 primary importance in theanalysis are the compressive stress calculations.The work of this committee is not intended to cover all design concepts, but rather a basic system. However,other design configurations may use alternative calculation methods when substantiated with suitable testdata.5.3 Sum
40、maryWhere strain gage results are available they should be used to supplement the analytical data.6. Load Moment Diagrams and Equations6.1 Assumptions Used on Load Moment Equations6.1.1 Wind force is negligible on head (should include effects if jib used).6.1.2 Torque is created by the side load P o
41、n the head (would also be applicable for a jib).6.1.3 Equations are still applicable if jib used but dimensions, weights, and center of gravity to be adjustedaccordingly.6.1.4 Py= P cos ; Pz= P sin 6.1.5 Winch rope fleet angle and angle relative to boom is negligible.6.1.6 Wind force is uniformly di
42、stributed along the exposed length of the side of the section with its reaction at thecenter (is a valid assumption since each section considered individually).6.1.7 That the dimensions are to the reaction points and that the tips of each section beyond these points are smallin length and will not a
43、ffect the validity of the equations.6.1.8 That the axial stresses produced by the friction forces due to the section reaction ponts from one to the nextare small in comparison to the other stresses, that the section support cylinders carry the axial loads.6.1.9 That equations and formulations appear
44、ing in the foregoing analysis are for the boom in the extendedposition Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7. Partially retracted positions willrequire reformulation of some equations; as an example in Figure 4 when I11is zero or negative the cylinderno longer takes th
45、e axial load at the section being considered. The moment equations would then appear asthose written for reference Figure 3. Similar changes would appear in the axial load, reactions, and shearforce equations.SAE J1078 Reaffirmed NOV2007-6-FIGURE 1LOADING DIAGRAMBOOM ASSEMBLYFIGURE 2LOAD MOMENT DIAG
46、RAMHEAD SECTIONSAE J1078 Reaffirmed NOV2007-7-FIGURE 3LOAD MOMENT DIAGRAMTIP SECTIONFIGURE 4LOAD MOMENT DIAGRAMALTERNATE TIP SECTIONSAE J1078 Reaffirmed NOV2007-8-FIGURE 5LOAD MOMENT DIAGRAMINTERMEDIATE SECTIONFIGURE 6LOAD MOMENT DIAGRAMINTERMEDIATE SECTIONSAE J1078 Reaffirmed NOV2007-9-FIGURE 7LOAD
47、 MOMENT DIAGRAMBASE SECTION6.2 Refer Figure 2Load Moment EquationsReaction of Head Forces on Tip Section (see Equations 6, 7,8, and 9)MOMENT (Equation 6)(Eq. 6)AXIAL LOAD (Equation 7)(Eq. 7)SHEAR LOADS (Equation 8)(Eq. 8)SIDE LOAD (Equation 9)(Eq. 9)M1Py11Pz12PN14W1+ 15 16sin+cosM2Px11TPx12=+=RZ1PN
48、PZ+ W1sin+=VxRx1PxVyRy1W1 Py+cos=Px0.02P=SAE J1078 Reaffirmed NOV2007-10-6.3 Refer Figure 3Load Moment Equations for Tip Section at Section Z1 - Z1 (see Equations 10, 11, 12, 13,14, 15, and 16)MOMENTS (Equation 10)(Eq. 10)AXIAL LOAD ON PIN (Equation 11)(Eq. 11)AXIAL LOAD ON SECTION (Equation 12)(Eq.
49、 12)VERTICAL REACTIONS (Equation 13)(Eq. 13)LATERAL REACTIONS (Equation 14)(Eq. 14)VERTICAL SHEAR FORCES (Equation 15)(Eq. 15)LATERAL SHEAR FORCES (Equation 16)(Eq. 16)NOTE Subscripts r and L refer to right and left of Section Z1- Z16.4 Refer Figure 4Load Moment Equations for Alternate Tip Section at Section Z1- Z1(see Equation 17,Equation 18, Equation 19, Equation 20, Equation 21, Equation 22, Equation 23)MxM1Ry1170.5W217
