Monorail (1)

"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 approaches. This program is a workbook consisting of three (3) worksheets, described as follows:

Worksheet Name

Description

Doc S-shaped Monorail Beam W-shaped Monorail Beam

This documentation sheet Monorail beam analysis for S-shaped beams Monorail 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/2 b. Dupont Standard DB1X: Lbo = 3*Lo c. ANSI Standard MH27.1: Lbo = 2*Lo d. 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" Program Version 1.3

MONORAIL BEAM ANALYSIS For S-shaped Underhung Monorails Analyzed as Simple-Spans with / without Overhang Per AISC 9th Edition ASD Manual and CMAA Specification No. 74 (2004) Job Name: Subject: Job Number: Originator: Checker: Input: RL(min)=0.29

Monorail Size: Select: S8x23 Design Parameters: Beam Fy = 36 ksi Beam Simple-Span, L = 4.5000 ft. Unbraced Length, Lb = 10.0000 ft. Bending Coef., Cb = 1.00 Overhang Length, Lo = 0.0000 ft. Unbraced Length, Lbo = 0.0000 ft. Bending Coef., Cbo = 1.00 Lifted Load, P = 3.300 kips Trolley Weight, Wt = 0.400 kips Hoist Weight, Wh = 0.100 kips Vert. Impact Factor, Vi = 20 % Horz. Load Factor, HLF = 10 % Total No. Wheels, Nw = 4 Wheel Spacing, S = 0.4900 ft. Distance on Flange, a = 0.7900 in. Results: Parameters and Coefficients: Pv = 4.460 kips Pw = 1.115 kips/wheel Ph = 0.330 kips ta = 0.383 in.  = 0.424 Cxo = -0.617 Cx1 = 0.640 Czo = 0.353 Cz1 = 1.363

RR(max)=4.27 Lo=0

L=4.5 x=2.128 S=0.49

S8x23 Pv=4.46

Nomenclature

A= d= tw = bf = tf = k= rt =

S8x23 Member Properties: 6.76 d/Af = 4.51 in.^2 8.000 in. Ix = 64.70 0.441 in. Sx = 16.20 4.170 in. Iy = 4.27 0.425 in. Sy = 2.05 1.000 in. J = 0.550 0.950 in. Cw = 61.3

Support Reactions: (no overhang) RR(max) = 4.27 = Pv*(L-S/2)/L+w/1000*L/2 RL(min) = 0.29 = Pv*(S/2)/L+w/1000*L/2 Pv = P*(1+Vi/100)+Wt+Wh (vertical load) Pw = Pv/Nw (load per trolley wheel) Ph = HLF*P (horizontal load) ta = tf-bf/24+a/6 (for S-shape)  = 2*a/(bf-tw) Cxo = -1.096+1.095*+0.192*e^(-6.0*) Cx1 = 3.965-4.835*-3.965*e^(-2.675*) Czo = -0.981-1.479*+1.120*e^(1.322*) Cz1 = 1.810-1.150*+1.060*e^(-7.70*)

### ### ### ### ta = = Cxo = Cx1 = Czo = Cz1 = Section Ratio bf/(2*tf) = d/tw = Qs =

For Lo = 0 (n in.^4 in.^3 in.^4 in.^3 in.^4 in.^6

x= Mx = My =

Lateral Flang e= at = Mt =

X-axis Stress fbx = Lc = Lu = Lb/rt = fa/Fy = Is Lb<=Lc? Is d/tw<=allow? Bending Moments for Simple-Span: Is b/t<=65/SQRT(Fy)? x = 2.128 ft. x = 1/2*(L-S/2) (location of max. moments from left end ofIssimple-span) b/t>95/SQRT(Fy)? Mx = 4.49 Mx = (Pv/2)/(2*L)*(L-S/2)^2+w/1000*x/2*(L-x) Fbx = ft-kips My = 0.33 My = (Ph/2)/(2*L)*(L-S/2)^2 Fbx = ft-kips Fbx = Lateral Flange Bending Moment from Torsion for Simple-Span: (per USS Steel Design Manual, 1981)Fbx = e = 4.000 in. e = d/2 (assume horiz. load taken at bot. flange) Fbx = at = 16.988 at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksi Fbx = Mt = 0.11 Mt = Ph*e*at/(2*(d-tf))*TANH(L*12/(2*at))/12 Fbx = ft-kips Use: Fbx = X-axis Stresses for Simple-Span: Y-axis Stress fbx = 3.32 fbx = Mx/Sx fby = ksi Lb/rt = 126.32 Lb/rt = Lb*12/rt fwns =

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"MONORAIL.xls" Program Version 1.3 Fbx =

21.60

ksi

Fbx = 12000*Cb/(Lb*12/(d/Af)) <= 0.60*Fy

fbx <= Fbx, O.K. (continued)

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"MONORAIL.xls" Program Version 1.3

Y-axis Stresses for Simple-Span: fby = 1.94 ksi fwns = 1.33 ksi fby(total) = 3.27 ksi Fby = 27.00 ksi

S.R. = fby = My/Sy fwns = Mt*12/(Sy/2) (warping normal stress) fby(total) = fby+fwns Fby = 0.75*Fy

Combined Stress Ratio for Simple-Span: S.R. = 0.275 S.R. = fbx/Fbx+fby(total)/Fby

Pv = (max) = fby <= Fby, O.K. (allow) = S.R. <= 1.0, O.K. My =

Vertical Deflection for Simple-Span: Pv = 3.800 kips Pv = P+Wh+Wt (without vertical impact) e= (max) = 0.0066 in. (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) at = (ratio) = L/8129 (ratio) = L*12/(max) Mt = (allow) = 0.1200 in. (allow) = L*12/450 Defl.(max) <= Defl.(allow), O.K. fbx = Bending Moments for Overhang: Lc = Mx = N.A. Mx = (Pv/2)*(Lo+(Lo-S))+w/1000*Lo^2/2 Lu = ft-kips My = N.A. My = (Ph/2)*(Lo+(Lo-S)) Lbo/rt = ft-kips fa/Fy = Lateral Flange Bending Moment from Torsion for Overhang: (per USS Steel Design Manual,Is1981) Lbo<=Lc? e= N.A. e = d/2 (assume horiz. load taken at bot. flange) Is d/tw<=allow? in. at = N.A. at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksi Is b/t<=65/SQRT(Fy)? Mt = N.A. Mt = Ph*e*at/(d-tf)*TANH(Lo*12/at)/12 Is b/t>95/SQRT(Fy)? ft-kips Fbx = X-axis Stresses for Overhang: Fbx = fbx = N.A. fbx = Mx/Sx Fbx = ksi Lbo/rt = N.A. Lbo/rt = Lbo*12/rt Fbx = Fbx = N.A. Fbx = 0.66*Fy Fbx = ksi Fbx = Y-axis Stresses for Overhang: Fbx = fby = N.A fby = My/Sy Use: Fbx = ksi fwns = N.A. fwns = Mt*12/(Sy/2) (warping normal stress) ksi fby(total) = N.A. fby(total) = fby+fwns fby = ksi Fby = N.A. Fby = 0.75*Fy fwns = ksi fby(total) = Combined Stress Ratio for Overhang: Fby = S.R. = N.A. S.R. = fbx/Fbx+fby(total)/Fby S.R. = Vertical Deflection for Overhang: (assuming full design load, Pv without impact, at end of overhang) Pv = N.A. Pv = P+Wh+Wt (without vertical impact) Pv = kips (max) = (max) = Pv*Lo^2*(L+Lo)/(3*E*I)+w/12000*Lo*(4*Lo^2*L-L^3+3*Lo^3)/(24*E*I) (max) = N.A. in. (ratio) = (ratio) = Lo*12/(max) (ratio) = N.A. (allow) = (allow) = Lo*12/450 N.A. in.

Lateral Flang

Y-axis Stress

Combined St

Vertical Defle

Bottom Flange Bending (simplified): be = 5.100 in. Min. of: be = 12*tf or S*12 (effective flange bending length) be = tf2 = 0.580 in. tf2 = tf+(bf/2-tw/2)/2*(1/6) (flange thk. at web based on 1:6 slope of flange) tf2 = am = 1.445 in. am = (bf/2-tw/2)-(k-tf2) (where: k-tf2 = radius of fillet) am = Mf = 1.611 Mf = Pw*am Mf = in.-kips Sf = 0.154 in.^3 Sf = be*tf^2/6 Sf = fb = 10.49 ksi fb = Mf/Sf fb = Fb = 27.00 ksi Fb = 0.75*Fy fb <= Fb, O.K.

Bottom Flang

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"MONORAIL.xls" Program Version 1.3 (continued)

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"MONORAIL.xls" Program Version 1.3

Bottom Flange Bending per CMAA Specification No. 74 (2004): Local Flange Bending Stress @ Point 0: xo = xo = Cxo*Pw/ta^2 -4.69 ksi zo = zo = Czo*Pw/ta^2 2.69 ksi

xo = zo =

(Note: torsion is neglected)

(Sign convention: + = tension, - = compression) z1 = S-shape

Local Flange Bending Stress @ Point 1: x1 = x1 = Cx1*Pw/ta^2 4.87 ksi z1 = 10.37 ksi z1 = Cz1*Pw/ta^2

Trolley Wheel

Local Flange Bending Stress @ Point 2: x2 = x2 = -xo 4.69 ksi z2 = z2 = -zo -2.69 ksi

Pw

Resultant Biaxial Stress @ Point 0: z = 7.28 ksi x = -3.52 ksi xz = 0.00 ksi to = 9.54 ksi

z = fbx+fby+0.75*zo x = 0.75*xo xz = 0 (assumed negligible) to = SQRT(x^2+z^2-x*z+3*xz^2)

Resultant Biaxial Stress @ Point 1: z = 13.04 ksi x = 3.65 ksi xz = 0.00 ksi t1 = 11.65 ksi

y = fbx+fby+0.75*z1 x = 0.75*x1 xz = 0 (assumed negligible) t1 = SQRT(x^2+z^2-x*z+3*xz^2)

Resultant Biaxial Stress @ Point 2: z = 3.25 ksi x = 3.52 ksi xz = 0.00 ksi t2 = 3.39 ksi

z = fbx+fby+0.75*z2 x = 0.75*x2 xz = 0 (assumed negligible) t2 = SQRT(x^2+z^2-x*z+3*xz^2)

Pw

x2 = z2 = z = x = xz = to = z = x = xz = t1 =

<= Fb = 0.66*Fy = 23.76 ksi, O.K. x = xz = t2 =

<= Fb = 0.66*Fy = 23.76 ksi, O.K.

<= Fb = 0.66*Fy = 23.76 ksi, O.K.

Y

tw X Pw

Pw

Z

tf

Point 2 Point 0

Point 1

ta

bf/4

tw/2

bf

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"MONORAIL.xls" Program Version 1.3

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"MONORAIL.xls" Program Version 1.3

MONORAIL BEAM ANALYSIS For W-shaped Underhung Monorails Analyzed as Simple-Spans with / without Overhang Per AISC 9th Edition ASD Manual and CMAA Specification No. 74 (2004) Job Name: Subject: Job Number: Originator: Checker: Input: RL(min)=-0.73

Monorail Size: Select: Design Parameters: Beam Fy = Beam Simple-Span, L = Unbraced Length, Lb = Bending Coef., Cb = Overhang Length, Lo = Unbraced Length, Lbo = Bending Coef., Cbo = Lifted Load, P = Trolley Weight, Wt = Hoist Weight, Wh = Vert. Impact Factor, Vi = Horz. Load Factor, HLF = Total No. Wheels, Nw = Wheel Spacing, S = Distance on Flange, a =

RR(max)=9.13 Lo=3

L=17

W12x50

x=8.313 S=0.75

36 ksi 17.0000 ft. 17.0000 ft. 1.00 3.0000 ft. 11.5000 ft. 1.00 6.000 kips 0.400 kips 0.100 kips 15 % 10 % 4 0.7500 ft. 0.3750 in.

W12x50 Pv=7.4

Nomenclature

A= d= tw = bf = tf = k= rt =

W12x50 Member Properties: 14.60 in.^2 d/Af = 2.36 12.200 in. Ix = 391.00 0.370 in. Sx = 64.20 8.080 in. Iy = 56.30 0.640 in. Sy = 13.90 1.140 in. J = 1.710 2.170 in. Cw = 1880.0

### ### ### ### ta = = Cxo = Cx1 = Czo = Cz1 = Section Ratio bf/(2*tf) = d/tw = Qs =

For Lo = 0 (n in.^4 in.^3 in.^4 in.^3 in.^4 in.^6

x= Support Reactions: (with overhang) Mx = RR(max) = Results: 9.13 = Pv*(L+(Lo-S/2))/L+w/1000/(2*L)*(L+Lo)^2My = RL(min) = -0.73 Lateral Flang = -Pv*(Lo-S/2)/L+w/1000/(2*L)*(L^2-Lo^2) Parameters and Coefficients: e= Pv = 7.400 kips Pv = P*(1+Vi/100)+Wt+Wh (vertical load) at = Pw = 1.850 kips/wheel Pw = Pv/Nw (load per trolley wheel) Mt = Ph = 0.600 kips Ph = HLF*P (horizontal load) X-axis Stress ta = 0.640 in. ta = tf (for W-shape) fbx =  = 0.097  = 2*a/(bf-tw) Lc = Cxo = -2.110+1.977*+0.0076*e^(6.53*) Cxo = -1.903 Lu = Cx1 = 10.108-7.408*-10.108*e^(-1.364*) Cx1 = 0.535 Lb/rt = Czo = 0.050-0.580*+0.148*e^(3.015*) Czo = 0.192 fa/Fy = Cz1 = 2.230-1.490*+1.390*e^(-18.33*) Cz1 = 2.319 Is Lb<=Lc? Is d/tw<=allow? Bending Moments for Simple-Span: Is b/t<=65/SQRT(Fy)? x = 8.313 ft. x = 1/2*(L-S/2) (location of max. moments from left end ofIssimple-span) b/t>95/SQRT(Fy)? Mx = 30.08 ft-kips Mx = (Pv/2)/(2*L)*(L-S/2)^2+w/1000*x/2*(L-x) Fbx = My = 2.44 My = (Ph/2)/(2*L)*(L-S/2)^2 Fbx = ft-kips Fbx = Lateral Flange Bending Moment from Torsion for Simple-Span: (per USS Steel Design Manual, 1981)Fbx = e = 6.100 in. e = d/2 (assume horiz. load taken at bot. flange) Fbx = at = 53.354 at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksi Fbx = Mt = 0.67 Mt = Ph*e*at/(2*(d-tf))*TANH(L*12/(2*at))/12 Fbx = ft-kips Use: Fbx = X-axis Stresses for Simple-Span: Y-axis Stress fbx = 5.62 fbx = Mx/Sx fby = ksi Lb/rt = 94.01 Lb/rt = Lb*12/rt fwns =

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"MONORAIL.xls" Program Version 1.3 Fbx =

21.60

ksi

Fbx = 12000*Cb/(Lb*12/(d/Af)) <= 0.60*Fy

fbx <= Fbx, O.K. (continued)

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"MONORAIL.xls" Program Version 1.3

Combined St Y-axis Stresses for Simple-Span: fby = 2.11 ksi fwns = 1.16 ksi fby(total) = 3.27 ksi Fby = 27.00 ksi

S.R. = fby = My/Sy fwns = Mt*12/(Sy/2) (warping normal stress) fby(total) = fby+fwns Fby = 0.75*Fy

Combined Stress Ratio for Simple-Span: S.R. = 0.381 S.R. = fbx/Fbx+fby(total)/Fby

Vertical Defle Pv = (max) = fby <= Fby, O.K. (allow) =

Bending Mom S.R. <= 1.0, O.K. My =

Vertical Deflection for Simple-Span: Pv = 6.500 kips Pv = P+Wh+Wt (without vertical impact) e= (max) = 0.1094 in. (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) at = (ratio) = L/1865 (ratio) = L*12/(max) Mt = (allow) = 0.4533 in. (allow) = L*12/450 Defl.(max) <= Defl.(allow), O.K. fbx = Bending Moments for Overhang: Lc = Mx = 19.65 ft-kips Mx = (Pv/2)*(Lo+(Lo-S))+w/1000*Lo^2/2 Lu = My = 1.58 My = (Ph/2)*(Lo+(Lo-S)) Lbo/rt = ft-kips fa/Fy = Lateral Flange Bending Moment from Torsion for Overhang: (per USS Steel Design Manual,Is1981) Lbo<=Lc? e = 6.100 in. e = d/2 (assume horiz. load taken at bot. flange) Is d/tw<=allow? at = 53.354 at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksi Is b/t<=65/SQRT(Fy)? Mt = 1.41 Mt = Ph*e*at/(d-tf)*TANH(Lo*12/at)/12 Is b/t>95/SQRT(Fy)? ft-kips Fbx = X-axis Stresses for Overhang: Fbx = fbx = 3.67 fbx = Mx/Sx Fbx = ksi Lbo/rt = 63.59 Lbo/rt = Lbo*12/rt Fbx = Fbx = 21.60 ksi Fbx = 12000*Cbo/(Lbo*12/(d/Af)) <= 0.60*Fy fbx <= Fbx, O.K. Fbx = Fbx = Y-axis Stresses for Overhang: Fbx = fby = 1.36 fby = My/Sy Use: Fbx = ksi fwns = 2.43 fwns = Mt*12/(Sy/2) (warping normal stress) ksi fby(total) = 3.79 fby(total) = fby+fwns fby = ksi Fby = 27.00 ksi Fby = 0.75*Fy fby <= Fby, O.K. fwns = fby(total) = Combined Stress Ratio for Overhang: Fby = S.R. = 0.310 S.R. = fbx/Fbx+fby(total)/Fby S.R. <= 1.0, O.K. S.R. = Vertical Deflection for Overhang: (assuming full design load, Pv without impact, at end of overhang) Pv = 6.500 kips Pv = P+Wh+Wt (without vertical impact) Pv = (max) = 0.0554 in. (max) = Pv*Lo^2*(L+Lo)/(3*E*I)+w/12000*Lo*(4*Lo^2*L-L^3+3*Lo^3)/(24*E*I) (max) = (ratio) = L/650 (ratio) = Lo*12/(max) (ratio) = (allow) = 0.0800 in. (allow) = Lo*12/450 Defl.(max) <= Defl.(allow), O.K.

Lateral Flang

Y-axis Stress

Combined St

Vertical Defle

Bottom Flange Bending (simplified): Bottom Flang be = 7.680 in. Min. of: be = 12*tf or S*12 (effective flange bending length) be = am = 3.355 in. am = (bf/2-tw/2)-(k-tf) (where: k-tf = radius of fillet) tf2 = Mf = 6.207 in.-kips Mf = Pw*am am = Sf = 0.524 in.^3 Sf = be*tf^2/6 Mf = fb = 11.84 fb = Mf/Sf Sf = ksi Fb = 27.00 ksi Fb = 0.75*Fy fb <= Fb, O.K. Fb = Bottom Flang

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"MONORAIL.xls" Program Version 1.3 (continued)

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"MONORAIL.xls" Program Version 1.3

Bottom Flange Bending per CMAA Specification No. 74 (2004):

(Note: torsion is neglected)

xo = zo =

Local Flange Local Flange Bending Stress @ Point 0: xo = xo = Cxo*Pw/ta^2 -8.60 ksi zo = zo = Czo*Pw/ta^2 0.87 ksi

(Sign convention: + = tension, - = compression) z1 = x2 = z2 =

Local Flange Bending Stress @ Point 1: x1 = x1 = Cx1*Pw/ta^2 2.42 ksi z1 = 10.47 ksi z1 = Cz1*Pw/ta^2

z = x = xz = to =

Local Flange Bending Stress @ Point 2: x2 = x2 = -xo 8.60 ksi z2 = z2 = -zo -0.87 ksi Resultant Biaxial Stress @ Point 0: z = 8.38 ksi x = -6.45 ksi xz = 0.00 ksi to = 12.88 ksi

z = fbx+fby+0.75*zo x = 0.75*xo xz = 0 (assumed negligible) to = SQRT(x^2+z^2-x*z+3*xz^2)

Resultant Biaxial Stress @ Point 1: z = 15.58 ksi x = 1.81 ksi xz = 0.00 ksi t1 = 14.76 ksi

y = fbx+fby+0.75*z1 x = 0.75*x1 xz = 0 (assumed negligible) t1 = SQRT(x^2+z^2-x*z+3*xz^2)

z = x = xz = t1 =

Local Flange

Resultant Bia

Resultant Bia

Resultant Bia <= Fb = 0.66*Fy = 23.76 ksi, O.K. x = xz = t2 = W24x370 W24x335

<= Fb = 0.66*Fy = 23.76 ksi, O.K. W24x279

Resultant Biaxial Stress @ Point 2: z = 7.08 ksi x = 6.45 ksi xz = 0.00 ksi t2 = 6.78 ksi

z = fbx+fby+0.75*z2 x = 0.75*x2 xz = 0 (assumed negligible) t2 = SQRT(x^2+z^2-x*z+3*xz^2)

W24x250 W24x229 W24x207 W24x192

<= Fb = 0.66*Fy = 23.76 ksi, O.K. W24x162 W24x146

Y

W24x131 W24x117 W24x104 W24x103 W24x94 W24x84 W24x76 W24x68

tw X

Pw

W24x62

Pw

W24x55

Z

W21x402 W21x364

Point 2

W21x333 W21x300 W21x275 W21x248

tf

Point 0

W21x223 W21x201

Point 1

W21x182 W21x166

bf

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"MONORAIL.xls" Program Version 1.3 W21x147

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