"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 DescriptionDoc This documentation sheet

S-shaped Monorail Beam Monorail beam analysis for S-shaped beams

W-shaped Monorail Beam 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)

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

British Steel Code B.S. 449: Lbo = 3*Lo (for top flange of monorail beam unrestrained at support)

the contents of that particular "comment box".)

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MONORAIL BEAM ANALYSISFor 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)=-0.73 RR(max)=9.13 ta =

Monorail Size: L=17 Lo=3Select: S12x50 x=8.313 Cxo =

Design Parameters: S=0.75 Cx1 =Beam Fy = 36 ksi Czo =

Beam Simple-Span, L = 17.0000 ft. S12x50 Cz1 =Unbraced Length, Lb = 17.0000 ft. Section Ratios and Parameters:

Bending Coef., Cb = 1.00 Pv=7.4 bf/(2*tf) =Overhang Length, Lo = 3.0000 ft. Nomenclature d/tw =

Unbraced Length, Lbo = 11.5000 ft. Qs =Bending Coef., Cbo = 1.00 S12x50 Member Properties:

Lifted Load, P = 6.000 kips A = 14.60 in.^2 d/Af = 3.32 For Lo = 0 (no overhang):Trolley Weight, Wt = 0.400 kips d = 12.000 in. Ix = 303.00 in.^4

Hoist Weight, Wh = 0.100 kips tw = 0.687 in. Sx = 50.60 in.^3

Vert. Impact Factor, Vi = 15 % bf = 5.480 in. Iy = 15.60 in.^4

Horz. Load Factor, HLF = 10 % tf = 0.659 in. Sy = 5.69 in.^3

Total No. Wheels, Nw = 4 k= 1.438 in. J = 2.770 in.^4

Wheel Spacing, S = 0.7500 ft. rt = 1.250 in. Cw = 502.0 in.^6

Distance on Flange, a = 0.3750 in. x =Support Reactions: (with overhang) Mx =

Results: 9.13 = Pv*(L+(Lo-S/2))/L+w/1000/(2*L)*(L+Lo)^2My =-0.73 = -Pv*(Lo-S/2)/L+w/1000/(2*L)*(L^2-Lo^2) Lateral Flange Bending Moment from Torsion for Simple-Span:

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 Stresses for Simple-Span:ta = 0.493 in. ta = tf-bf/24+a/6 (for S-shape) fbx =

0.156 Lc =Cxo = -0.850 Lu =Cx1 = 0.600 Lb/rt =Czo = 0.165 fa/Fy =Cz1 = 1.948 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 of simple-span)Is 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 ft-kips My = (Ph/2)/(2*L)*(L-S/2)^2 Fbx =

Fbx =Lateral Flange Bending Moment from Torsion for Simple-Span: (per USS Steel Design Manual, 1981)Fbx =

e = 6.000 in. e = d/2 (assume horiz. load taken at bot. flange) Fbx =at = 21.662 at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksi Fbx =Mt = 0.29 ft-kips Mt = Ph*e*at/(2*(d-tf))*TANH(L*12/(2*at))/12 Fbx =

Use: Fbx =X-axis Stresses for Simple-Span: Y-axis Stresses for Simple-Span:

fbx = 7.13 ksi fbx = Mx/Sx fby =Lb/rt = 163.20 Lb/rt = Lb*12/rt fwns =

l =

RR(max) =RL(min) =

l = l = 2*a/(bf-tw)Cxo = -1.096+1.095*l+0.192*e^(-6.0*l)Cx1 = 3.965-4.835*l-3.965*e^(-2.675*l)Czo = -0.981-1.479*l+1.120*e^(1.322*l)Cz1 = 1.810-1.150*l+1.060*e^(-7.70*l)

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Fbx = 17.72 ksi Fbx = 12000*Cb/(Lb*12/(d/Af)) <= 0.60*Fy fbx <= Fbx, O.K. (continued)

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Y-axis Stresses for Simple-Span: S.R. =fby = 5.14 ksi fby = My/Sy

fwns = 1.21 ksi fwns = Mt*12/(Sy/2) (warping normal stress) Pv =fby(total) = 6.35 ksi fby(total) = fby+fwns

Fby = 27.00 ksi Fby = 0.75*Fy fby <= Fby, O.K.

Combined Stress Ratio for Simple-Span:S.R. = 0.638 S.R. = fbx/Fbx+fby(total)/Fby S.R. <= 1.0, O.K.

My =Vertical Deflection for Simple-Span: Lateral Flange Bending Moment from Torsion for Overhang:

Pv = 6.500 kips Pv = P+Wh+Wt (without vertical impact) e =0.1412 in. 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 =L/1445 Mt =0.4533 in. 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 ft-kips My = (Ph/2)*(Lo+(Lo-S)) Lbo/rt =

fa/Fy =Lateral Flange Bending Moment from Torsion for Overhang: (per USS Steel Design Manual, 1981)Is Lbo<=Lc?

e = 6.000 in. e = d/2 (assume horiz. load taken at bot. flange) Is d/tw<=allow?at = 21.662 at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksiIs b/t<=65/SQRT(Fy)?Mt = 0.57 ft-kips Mt = Ph*e*at/(d-tf)*TANH(Lo*12/at)/12 Is b/t>95/SQRT(Fy)?

Fbx =X-axis Stresses for Overhang: Fbx =

fbx = 4.66 ksi fbx = Mx/Sx Fbx =Lbo/rt = 110.40 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 = 3.32 ksi fby = My/Sy Use: Fbx =

fwns = 2.42 ksi fwns = Mt*12/(Sy/2) (warping normal stress) Y-axis Stresses for Overhang:fby(total) = 5.74 ksi fby(total) = fby+fwns fby =

Fby = 27.00 ksi Fby = 0.75*Fy fby <= Fby, O.K.fwns =fby(total) =

Combined Stress Ratio for Overhang: Fby =S.R. = 0.428 S.R. = fbx/Fbx+fby(total)/Fby S.R. <= 1.0, O.K. Combined Stress Ratio for Overhang:

S.R. =Vertical Deflection for Overhang: (assuming full design load, Pv without impact, at end of overhang) Vertical Deflection for Overhang:

Pv = 6.500 kips Pv = P+Wh+Wt (without vertical impact) Pv =0.0715 in. Pv*Lo^2*(L+Lo)/(3*E*I)+w/12000*Lo*(4*Lo^2*L-L^3+3*Lo^3)/(24*E*I)

L/5030.0800 in. Defl.(max) <= Defl.(allow), O.K.

Bottom Flange Bending (simplified):be = 7.908 in. Min. of: be = 12*tf or S*12 (effective flange bending length) be =tf2 = 0.859 in. tf2 = tf+(bf/2-tw/2)/2*(1/6) (flange thk. at web based on 1:6 slope of flange)tf2 =

am = 1.818 in. am = (bf/2-tw/2)-(k-tf2) (where: k-tf2 = radius of fillet) am =Mf = 3.363 in.-kips Mf = Pw*am Mf =Sf = 0.572 in.^3 Sf = be*tf^2/6 Sf =fb = 5.88 ksi fb = Mf/Sf fb =

Fb = 27.00 ksi Fb = 0.75*Fy fb <= Fb, O.K. Bottom Flange Bending per CMAA Specification No. 74 (2004):

D(max) =

D(allow) =

D(max) = D(max) =D(ratio) = D(ratio) = L*12/D(max)D(allow) = D(allow) = L*12/450

D(max) = D(max) = D(max) =D(ratio) = D(ratio) = Lo*12/D(max) D(ratio) =D(allow) = D(allow) = Lo*12/450

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Bottom Flange Bending per CMAA Specification No. 74 (2004): (Note: torsion is neglected)

Local Flange Bending Stress @ Point 0: (Sign convention: + = tension, - = compression)-6.46 ksi

1.25 ksi

Local Flange Bending Stress @ Point 1:4.56 ksi

14.82 ksi

Local Flange Bending Stress @ Point 2:6.46 ksi

-1.25 ksi

Resultant Biaxial Stress @ Point 0:13.22 ksi

-4.85 ksi

0.00 ksi

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

Resultant Biaxial Stress @ Point 1:23.39 ksi

3.42 ksi

0.00 ksi

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

Resultant Biaxial Stress @ Point 2:11.34 ksi

4.85 ksi

0.00 ksi

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

sxo =szo =

sxo = sxo = Cxo*Pw/ta^2 sz1 =szo = szo = Czo*Pw/ta^2

sx2 =sz2 =

sx1 = sx1 = Cx1*Pw/ta^2sz1 = sz1 = Cz1*Pw/ta^2 sz =

sx =txz =

sx2 = sx2 = -sxo sto =sz2 = sz2 = -szo

sz =sx =

sz = sz = fbx+fby+0.75*szo txz =sx = sx = 0.75*sxo st1 =txz = txz = 0 (assumed negligible)sto = sto = SQRT(sx^2+sz^2-sx*sz+3*txz^2)

sx =txz =

sz = sy = fbx+fby+0.75*sz1 st2 =sx = sx = 0.75*sx1txz = txz = 0 (assumed negligible)st1 = st1 = SQRT(sx^2+sz^2-sx*sz+3*txz^2)

sz = sz = fbx+fby+0.75*sz2sx = sx = 0.75*sx2txz = txz = 0 (assumed negligible)st2 = st2 = SQRT(sx^2+sz^2-sx*sz+3*txz^2)

bf

ta

tw

bf/4

tf

X

Z

Y

tw/2

PwPw

Pw Pw

Trolley Wheel

S-shape

Point 2

Point 0

Point 1

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"MONORAIL.xls" ProgramVersion 1.3

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MONORAIL BEAM ANALYSISFor 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 RR(max)=9.13 ta =

Monorail Size: L=17 Lo=3Select: W12x50 x=8.313 Cxo =

Design Parameters: S=0.75 Cx1 =Beam Fy = 36 ksi Czo =

Beam Simple-Span, L = 17.0000 ft. W12x50 Cz1 =Unbraced Length, Lb = 17.0000 ft. Section Ratios and Parameters:

Bending Coef., Cb = 1.00 Pv=7.4 bf/(2*tf) =Overhang Length, Lo = 3.0000 ft. Nomenclature d/tw =

Unbraced Length, Lbo = 11.5000 ft. Qs =Bending Coef., Cbo = 1.00 W12x50 Member Properties:

Lifted Load, P = 6.000 kips A = 14.60 in.^2 d/Af = 2.36 For Lo = 0 (no overhang):Trolley Weight, Wt = 0.400 kips d = 12.200 in. Ix = 391.00 in.^4

Hoist Weight, Wh = 0.100 kips tw = 0.370 in. Sx = 64.20 in.^3

Vert. Impact Factor, Vi = 15 % bf = 8.080 in. Iy = 56.30 in.^4

Horz. Load Factor, HLF = 10 % tf = 0.640 in. Sy = 13.90 in.^3

Total No. Wheels, Nw = 4 k= 1.140 in. J = 1.710 in.^4

Wheel Spacing, S = 0.7500 ft. rt = 2.170 in. Cw = 1880.0 in.^6

Distance on Flange, a = 0.3750 in. x =Support Reactions: (with overhang) Mx =

Results: 9.13 = Pv*(L+(Lo-S/2))/L+w/1000/(2*L)*(L+Lo)^2My =-0.73 = -Pv*(Lo-S/2)/L+w/1000/(2*L)*(L^2-Lo^2) Lateral Flange Bending Moment from Torsion for Simple-Span:

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 Stresses for Simple-Span:ta = 0.640 in. ta = tf (for W-shape) fbx =

0.097 Lc =Cxo = -1.903 Lu =Cx1 = 0.535 Lb/rt =Czo = 0.192 fa/Fy =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 of simple-span)Is 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 ft-kips My = (Ph/2)/(2*L)*(L-S/2)^2 Fbx =

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 ft-kips Mt = Ph*e*at/(2*(d-tf))*TANH(L*12/(2*at))/12 Fbx =

Use: Fbx =X-axis Stresses for Simple-Span: Y-axis Stresses for Simple-Span:

fbx = 5.62 ksi fbx = Mx/Sx fby =Lb/rt = 94.01 Lb/rt = Lb*12/rt fwns =

l =

RR(max) =RL(min) =

l = l = 2*a/(bf-tw)Cxo = -2.110+1.977*l+0.0076*e^(6.53*l)Cx1 = 10.108-7.408*l-10.108*e^(-1.364*l)Czo = 0.050-0.580*l+0.148*e^(3.015*l)Cz1 = 2.230-1.490*l+1.390*e^(-18.33*l)

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Fbx = 21.60 ksi Fbx = 12000*Cb/(Lb*12/(d/Af)) <= 0.60*Fy fbx <= Fbx, O.K. (continued)

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Combined Stress Ratio for Simple-Span:Y-axis Stresses for Simple-Span: S.R. =

fby = 2.11 ksi fby = My/Sy Vertical Deflection for Simple-Span:fwns = 1.16 ksi fwns = Mt*12/(Sy/2) (warping normal stress) Pv =

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: Bending Moments for Overhang:S.R. = 0.381 S.R. = fbx/Fbx+fby(total)/Fby S.R. <= 1.0, O.K.

My =Vertical Deflection for Simple-Span: Lateral Flange Bending Moment from Torsion for Overhang:

Pv = 6.500 kips Pv = P+Wh+Wt (without vertical impact) e =0.1094 in. 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 =L/1865 Mt =0.4533 in. 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 ft-kips My = (Ph/2)*(Lo+(Lo-S)) Lbo/rt =

fa/Fy =Lateral Flange Bending Moment from Torsion for Overhang: (per USS Steel Design Manual, 1981)Is 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 ksiIs b/t<=65/SQRT(Fy)?Mt = 1.41 ft-kips Mt = Ph*e*at/(d-tf)*TANH(Lo*12/at)/12 Is b/t>95/SQRT(Fy)?

Fbx =X-axis Stresses for Overhang: Fbx =

fbx = 3.67 ksi fbx = Mx/Sx Fbx =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 ksi fby = My/Sy Use: Fbx =

fwns = 2.43 ksi fwns = Mt*12/(Sy/2) (warping normal stress) Y-axis Stresses for Overhang:fby(total) = 3.79 ksi fby(total) = fby+fwns fby =

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. Combined Stress Ratio for Overhang:

S.R. =Vertical Deflection for Overhang: (assuming full design load, Pv without impact, at end of overhang) Vertical Deflection for Overhang:

Pv = 6.500 kips Pv = P+Wh+Wt (without vertical impact) Pv =0.0554 in. Pv*Lo^2*(L+Lo)/(3*E*I)+w/12000*Lo*(4*Lo^2*L-L^3+3*Lo^3)/(24*E*I)

L/6500.0800 in. Defl.(max) <= Defl.(allow), O.K.

Bottom Flange Bending (simplified): Bottom Flange Local Bending (simplified):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 ksi fb = Mf/Sf Sf =

Fb = 27.00 ksi Fb = 0.75*Fy fb <= Fb, O.K. Fb =

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

D(max) =

D(allow) =

D(max) = D(max) =D(ratio) = D(ratio) = L*12/D(max)D(allow) = D(allow) = L*12/450

D(max) = D(max) = D(max) =D(ratio) = D(ratio) = Lo*12/D(max) D(ratio) =D(allow) = D(allow) = Lo*12/450

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Bottom Flange Bending per CMAA Specification No. 74 (2004): (Note: torsion is neglected)Local Flange Bending Stress @ Point 1:

Local Flange Bending Stress @ Point 0: (Sign convention: + = tension, - = compression)-8.60 ksi

0.87 ksi Local Flange Bending Stress @ Point 2:

Local Flange Bending Stress @ Point 1:2.42 ksi Resultant Biaxial Stress @ Point 0:

10.47 ksi

Local Flange Bending Stress @ Point 2:8.60 ksi

-0.87 ksi Resultant Biaxial Stress @ Point 1:

Resultant Biaxial Stress @ Point 0:8.38 ksi

-6.45 ksi

0.00 ksi Resultant Biaxial Stress @ Point 2:12.88 ksi <= Fb = 0.66*Fy = 23.76 ksi, O.K.

Resultant Biaxial Stress @ Point 1:15.58 ksi

1.81 ksi W24x370

0.00 ksi W24x335

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

Resultant Biaxial Stress @ Point 2: W24x250

7.08 ksi W24x229

6.45 ksi W24x207

0.00 ksi W24x192

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

W24x146

W24x131

W24x117

W24x104

W24x103

W24x94

W24x84

W24x76

W24x68

W24x62

W24x55

W21x402

W21x364

W21x333

W21x300

W21x275

W21x248

W21x223

W21x201

W21x182

W21x166

sxo =szo =

sxo = sxo = Cxo*Pw/ta^2 sz1 =szo = szo = Czo*Pw/ta^2

sx2 =sz2 =

sx1 = sx1 = Cx1*Pw/ta^2sz1 = sz1 = Cz1*Pw/ta^2 sz =

sx =txz =

sx2 = sx2 = -sxo sto =sz2 = sz2 = -szo

sz =sx =

sz = sz = fbx+fby+0.75*szo txz =sx = sx = 0.75*sxo st1 =txz = txz = 0 (assumed negligible)sto = sto = SQRT(sx^2+sz^2-sx*sz+3*txz^2)

sx =txz =

sz = sy = fbx+fby+0.75*sz1 st2 =sx = sx = 0.75*sx1txz = txz = 0 (assumed negligible)st1 = st1 = SQRT(sx^2+sz^2-sx*sz+3*txz^2)

sz = sz = fbx+fby+0.75*sz2sx = sx = 0.75*sx2txz = txz = 0 (assumed negligible)st2 = st2 = SQRT(sx^2+sz^2-sx*sz+3*txz^2)

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"MONORAIL.xls" ProgramVersion 1.3

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