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MONORAIL.xls

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MONORAIL --- MONORAIL BEAM ANALYSIS Program Description: MONORAIL is a spreadsheet program written in MS-Excel for the purpose of analysis of either S-shape or W-shape underhung monorail beams analyzed as simple-spans with or without overhangs (cantilevers). Specifically, the x-axis and y-axis bending moments as well as any torsion effects are calculated. The actual and allowable stresses are determined, and the effect of lower flange bending is also addressed by two different approach
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  MONORAIL --- MONORAIL BEAM ANALYSIS Program Description: MONORAIL is a spreadsheet program written in MS-Excel for the purpose of analysis of either S-shape or W-shape underhung monorail beams analyzed as simple-spans with or without overhangs (cantilevers). Specifically, the x-axis and y-axis bending moments as well as any torsion effects are calculated. The actual and allowable stresses are determined, and the effect of lower flange bending is also addressed by two differentapproaches.This program is a workbook consisting of three (3) worksheets, described as follows: Worksheet NameDescription DocThis documentation sheetS-shaped Monorail BeamMonorail beam analysis for S-shaped beamsW-shaped Monorail BeamMonorail beam analysis for W-shaped beams Program Assumptions and Limitations: 1. The following references were used in the development of this program:a.Fluor Enterprises, Inc. - Guideline 000.215.1257 - Hoisting Facilities (August 22, 2005)b.Dupont Engineering Design Standard: DB1X - Design and Installation of Monorail Beams (May 2000)c.American National Standards Institute (ANSI): MH27.1 - Underhung Cranes and Monorail Syatems d.American Institute of Steel Construction (AISC) 9th Edition Allowable Stress Design (ASD) Manual (1989)e. Allowable Bending Stresses for Overhanging Monorails - by N. Stephen Tanner -  AISC Engineering Journal (3rd Quarter, 1985)f.Crane Manufacturers Association of America, Inc. (CMAA) - Publication No. 74 - Specifications for Top Running & Under Running Single Girder Electric Traveling Cranes Utilizing Under Running Trolley Hoist (2004)g. Design of Monorail Systems - by Thomas H. Orihuela Jr., PE (www.pdhengineer.com)h.British Steel Code B.S. 449, pages 42-44 (1959)i.USS Steel Design Manual - Chapter 7 Torsion - by R. L. Brockenbrough and B.G. Johnston (1981) j.AISC Steel Design Guide Series No. 9 - Torsional Analysis of Structural Steel Members - by Paul A. Seaburg, PhD, PE and Charlie J. Carter, PE (1997)k. Technical Note: Torsion Analysis of Steel Sections - by William E. Moore II and Keith M. Mueller -  AISC Engineering Journal (4th Quarter, 2002)2. The unbraced length for the overhang (cantilever) portion, 'Lbo', of an underhung monorail beam is often debated. The following are some recommendations from the references cited above:a.Fluor Guideline 000.215.1257: Lbo = Lo+L/2b.Dupont Standard DB1X: Lbo = 3*Loc.ANSI Standard MH27.1: Lbo = 2*Lod.British Steel Code B.S. 449: Lbo = 2*Lo (for top flange of monorail beam restrained at support)British Steel Code B.S. 449: Lbo = 3*Lo (for top flange of monorail beam unrestrained at support)e.AISC Eng. Journal Article by Tanner: Lbo = Lo+L (used with a computed value of 'Cbo' from article)3. This program also determines the calculated value of the bending coefficient, 'Cbo', for the overhang (cantilever) portion of the monorail beam from reference e in note #1 above. This is located off of the main calculation page. Note: if this computed value of 'Cbo' is used and input, then per this reference the total value of Lo+L should be used for the unbraced length, 'Lbo', for the overhang portion of the monorail beam.4. This program ignores effects of axial compressive stress produced by any longitudinal (traction) force which is usually considered minimal for underhung, hand-operated monorail systems. 5. This program contains “comment boxes” which contain a wide variety of information including explanations of input or output items, equations used, data tables, etc. (Note: presence of a “comment box” is denoted by a “red triangle” in the upper right-hand corner of a cell. Merely move the mouse pointer to the desired cell to view the contents of that particular comment box .)  MONORAIL.xls ProgramVersion 1.3 MONORAIL BEAM ANALYSIS For S-shaped Underhung Monorails Analyzed as Simple-Spans with / without OverhangPer AISC 9th Edition ASD Manual and CMAA Specification No. 74 (2004) Job Name:Subject:Job Number:Originator:Checker: Input: RL(min)=0.29RR(max)=4.27 Monorail Size:  L=4.5 Lo=0 Select:S8x23  x=2.128 Design Parameters:  S=0.49 Beam Fy =36 ksi Beam Simple-Span, L =4.5000 ft. S8x23 Unbraced Length, Lb =10.0000 ft. Bending Coef., Cb =1.00  Pv=4.46 Overhang Length, Lo =0.0000 ft. Nomenclature Unbraced Length, Lbo =0.0000 ft. Bending Coef., Cbo =1.00 S8x23 Member Properties: Lifted Load, P =3.300 kips  A =6.76 in.^2 d/Af =4.51Trolley Weight, Wt =0.400 kips d =8.000 in. Ix =64.70 in.^4 Hoist Weight, Wh =0.100 kips tw =0.441 in. Sx =16.20 in.^3 Vert. Impact Factor, Vi =20%bf =4.170 in. Iy =4.27 in.^4 Horz. Load Factor, HLF =10%tf =0.425 in. Sy =2.05 in.^3 Total No. Wheels, Nw =4k=1.000 in. J =0.550 in.^4 Wheel Spacing, S =0.4900 ft. rt =0.950 in. Cw =61.3 in.^6 Distance on Flange, a =0.7900 in. Support Reactions: (no overhang) Results: R R(max)  =4.27 = Pv*(L-S/2)/L+w/1000*L/2 R L(min)  =0.29 = Pv*(S/2)/L+w/1000*L/2 Parameters and Coefficients: Pv =4.460 kips Pv = P*(1+Vi/100)+Wt+Wh (vertical load)Pw =1.115 kips/wheel Pw = Pv/Nw (load per trolley wheel)Ph =0.330 kips Ph = HLF*P (horizontal load)ta =0.383 in. ta = tf-bf/24+a/6 (for S-shape) l  =0.424  l  = 2*a/(bf-tw)Cxo =-0.617Cxo = -1.096+1.095* l +0.192*e^(-6.0* l )Cx1 =0.640Cx1 = 3.965-4.835* l -3.965*e^(-2.675* l )Czo =0.353Czo = -0.981-1.479* l +1.120*e^(1.322* l )Cz1 =1.363Cz1 = 1.810-1.150* l +1.060*e^(-7.70* l ) Bending Moments for Simple-Span: x =2.128 ft. x = 1/2*(L-S/2) (location of max. moments from left end of simple-span)Mx =4.49 ft-kips Mx = (Pv/2)/(2*L)*(L-S/2)^2+w/1000*x/2*(L-x)My =0.33 ft-kips My = (Ph/2)/(2*L)*(L-S/2)^2 Lateral Flange Bending Moment from Torsion for Simple-Span: (per USS Steel Design Manual, 1981)e =4.000 in. e = d/2 (assume horiz. load taken at bot. flange)at =16.988at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksiMt =0.11 ft-kips Mt = Ph*e*at/(2*(d-tf))*TANH(L*12/(2*at))/12 X-axis Stresses for Simple-Span: fbx =3.32 ksi fbx = Mx/SxLb/rt =126.32Lb/rt = Lb*12/rtFbx =21.60 ksi Fbx = 12000*Cb/(Lb*12/(d/Af)) <= 0.60*Fy fbx <= Fbx, O.K. (continued) 2 of 710/23/2014 11:16 AM  MONORAIL.xls ProgramVersion 1.3  Y-axis Stresses for Simple-Span: fby =1.94 ksi fby = My/Syfwns =1.33 ksi fwns = Mt*12/(Sy/2) (warping normal stress)fby(total) =3.27 ksi fby(total) = fby+fwnsFby =27.00 ksi Fby = 0.75*Fy fby <= Fby, O.K. Combined Stress Ratio for Simple-Span: S.R. =0.275S.R. = fbx/Fbx+fby(total)/Fby S.R. <= 1.0, O.K. Vertical Deflection for Simple-Span: Pv =3.800 kips Pv = P+Wh+Wt (without vertical impact) D (max) =0.0066 in.  D (max) = Pv/2*(L-S)/2/(24*E*I)*(3*L^2-4*((L-S)/2)^2)+5*w/12000*L^4/(384*E*I) D (ratio) =L/8129  D (ratio) = L*12/ D (max) D (allow) =0.1200 in.  D (allow) = L*12/450 Defl.(max) <= Defl.(allow), O.K. Bending Moments for Overhang: Mx =N.A. ft-kips Mx = (Pv/2)*(Lo+(Lo-S))+w/1000*Lo^2/2My =N.A. ft-kips My = (Ph/2)*(Lo+(Lo-S)) Lateral Flange Bending Moment from Torsion for Overhang: (per USS Steel Design Manual, 1981)e =N.A. in. e = d/2 (assume horiz. load taken at bot. flange)at =N.A.at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksiMt =N.A. ft-kips Mt = Ph*e*at/(d-tf)*TANH(Lo*12/at)/12 X-axis Stresses for Overhang: fbx =N.A. ksi fbx = Mx/SxLbo/rt =N.A.Lbo/rt = Lbo*12/rtFbx =N.A. ksi Fbx = 0.66*Fy  Y-axis Stresses for Overhang: fby =N.A ksi fby = My/Syfwns =N.A. ksi fwns = Mt*12/(Sy/2) (warping normal stress)fby(total) =N.A. ksi fby(total) = fby+fwnsFby =N.A. ksi Fby = 0.75*Fy Combined Stress Ratio for Overhang: S.R. =N.A.S.R. = fbx/Fbx+fby(total)/Fby Vertical Deflection for Overhang: (assuming full design load, Pv without impact, at end of overhang)Pv =N.A. kips Pv = P+Wh+Wt (without vertical impact) D (max) =N.A. in.  D (max) = Pv*Lo^2*(L+Lo)/(3*E*I)+w/12000*Lo*(4*Lo^2*L-L^3+3*Lo^3)/(24*E*I) D (ratio) =N.A.  D (ratio) = Lo*12/ D (max) D (allow) =N.A. in.  D (allow) = Lo*12/450 Bottom Flange Bending (simplified): be =5.100 in. Min. of: be = 12*tf or S*12 (effective flange bending length)tf2 =0.580 in. tf2 = tf+(bf/2-tw/2)/2*(1/6) (flange thk. at web based on 1:6 slope of flange)am =1.445 in. am = (bf/2-tw/2)-(k-tf2) (where: k-tf2 = radius of fillet)Mf =1.611 in.-kips Mf = Pw*amSf =0.154 in.^3 Sf = be*tf^2/6fb =10.49 ksi fb = Mf/Sf Fb =27.00 ksi Fb = 0.75*Fy fb <= Fb, O.K. (continued) 3 of 710/23/2014 11:16 AM  MONORAIL.xls ProgramVersion 1.3 Bottom Flange Bending per CMAA Specification No. 74 (2004): (Note: torsion is neglected) Local Flange Bending Stress @ Point 0: (Sign convention: + = tension, - = compression) s xo =-4.69 ksi  s xo = Cxo*Pw/ta^2 s zo =2.69 ksi  s zo = Czo*Pw/ta^2 Local Flange Bending Stress @ Point 1: s x1 =4.87 ksi  s x1 = Cx1*Pw/ta^2 s z1 =10.37 ksi  s z1 = Cz1*Pw/ta^2 Local Flange Bending Stress @ Point 2: s x2 =4.69 ksi  s x2 = - s xo s z2 =-2.69 ksi  s z2 = - s zo Resultant Biaxial Stress @ Point 0: s z =7.28 ksi  s z = fbx+fby+0.75* s zo s x =-3.52 ksi  s x = 0.75* s xo t xz =0.00 ksi  t xz = 0 (assumed negligible) s to =9.54 ksi  s to = SQRT( s x^2+ s z^2- s x* s z+3* t xz^2) <= Fb = 0.66*Fy = 23.76 ksi, O.K.Resultant Biaxial Stress @ Point 1: s z =13.04 ksi  s y = fbx+fby+0.75* s z1 s x =3.65 ksi  s x = 0.75* s x1 t xz =0.00 ksi  t xz = 0 (assumed negligible) s t1 =11.65 ksi  s t1 = SQRT( s x^2+ s z^2- s x* s z+3* t xz^2) <= Fb = 0.66*Fy = 23.76 ksi, O.K.Resultant Biaxial Stress @ Point 2: s z =3.25 ksi  s z = fbx+fby+0.75* s z2 s x =3.52 ksi  s x = 0.75* s x2 t xz =0.00 ksi  t xz = 0 (assumed negligible) s t2 =3.39 ksi  s t2 = SQRT( s x^2+ s z^2- s x* s z+3* t xz^2) <= Fb = 0.66*Fy = 23.76 ksi, O.K.   bf ta tw bf/4 tf X Z  Y tw/2 Pw Pw Pw Pw Trolley Wheel S-shape Point 2 Point 0 Point 1 4 of 710/23/2014 11:16 AM
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