5/20/2018 Monorail 13

1/7

"MONORAIL13" --- MONORAIL BEAM ANALYSIS

Program Description:

"MONORAIL13" 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 andallowable 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 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) 13th Edition Allowable Stress Design (ASD) Manual (2005)

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".)

5/20/2018 Monorail 13

2/7

"MONORAIL13.xls" Program

Created By: Joel Berg, P.E

Based on a Spreadsheet By: Alex Tomanovich, P.E

Version 1.2

MONORAIL BEAM ANALYSISFor S-shaped Underhung Monorails Analyzed as Simple-Spans with / without Overhang

Per AISC 13th Edition ASD Manual and CMAA Specification No. 74 (2004)

Project Name: Client:

Project No.: Prep. By: Date:

Input:

RL(min)=-0.73 kips RR(max)=9.13 kips

Monorail Size: L=17 ft. Lo=3 ft.

Select: S12x50 x=8.313ft.

Design Parameters: S=9 in.

Beam Fy = 36 ksi

Beam Simple-Span, L = 17.0000 ft. S12x50

Unbraced Length, Lb = 17.0000 ft.

Bending Coef., Cb = 1.00 Pv=7.4 kips

Overhang Length, Lo = 3.0000 ft. Nomenclature

Unbraced Length, Lbo = 11.5000 ft.

Bending Coef., Cbo = 1.00 S12x50 Member Properties:

Lifted Load, P = 6.000 kips A = 14.60 in.^2 Zx = 60.90 in.^3

Trolley Weight, Wt = 0.400 kips d = 12.000 in. Iy = 15.60 in.^4

Hoist Weight, Wh = 0.100 kips tw = 0.687 in. Sy = 5.69 in.^3

Vert. Impact Factor, Vi = 15 % bf = 5.480 in. ry = 1.030 in.

Horz. Load Factor, HLF = 10 % tf = 0.659 in. Zy = 10.30 in.^3

Total No. Wheels, Nw = 4 k= 1.440 in. J = 2.770 in.^4

Wheel Spacing, S = 9.0000 in. Ix = 303.00 in.^4 Cw = 501.0 in.^6

Distance on Flange, a = 0.3750 in. Sx = 50.60 in.^3 wt / ft. = 50.0 plf

Support Reactions: (with overhang)

Results: RR(max)= 9.13 = Pv*(L+(Lo-(S/12)/2))/L+w/1000/(2*L)*(L+Lo)^2

RL(min)= -0.73 = -Pv*(Lo-(S/12)/2)/L+w/1000/(2*L)*(L 2-Lo^2)

Parameters and Coefficients:

Pv = 7.400 kips Pv = P*(1+Vi/100)+Wt+Wh (vertical load)

Pw = 1.850 kips/wheel Pw = Pv/Nw (load per trolley wheel)

Ph = 0.600 kips Ph = HLF*P (horizontal load)

ta = 0.493 in. ta = tf-bf/24+a/6 (for S-shape)l= 0.156 l= 2*a/(bf-tw)

Cxo = -0.850 Cxo = -1.096+1.095*l+0.192*e^(-6.0*l)

Cx1 = 0.600 Cx1 = 3.965-4.835*l-3.965*e^(-2.675*l)

Czo = 0.165 Czo = -0.981-1.479*l+1.120*e^(1.322*l)

Cz1 = 1.948 Cz1 = 1.810-1.150*l+1.060*e^(-7.70*l)

Bending Moments for Simple-Span:

x = 8.313 ft. x = 1/2*(L-(S/12)/2) (location of max. moments from left end of simple-span)

Mx = 31.88 ft-kips Mx = (Pv/2)/(2*L)*(L-(S/12)/2)^2+w/1000*x/2*(L-x)

My = 2.44 ft-kips My = (Ph/2)/(2*L)*(L-(S/12)/2) 2

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

e = 6.000 in. e = d/2 (assume horiz. load taken at bot. flange)

at = 21.641 at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksi

Mt = 0.29 ft-kips Mt = Ph*e*at/(2*(d-tf))*TANH(L*12/(2*at))/12

X-axis Stresses for Simple-Span:

fbx = 7.56 ksi fbx = Mx/Sx

Lr = 24.91 ft. (Eqn. F2-6, max. value of Lb for inelastic LTB)

Fbx = 19.25 ksi Eqn. F2-2 Controls fbx

5/20/2018 Monorail 13

3/7

"MONORAIL13.xls" Program

Created By: Joel Berg, P.E.

Based on a Spreadsheet By: Alex Tomanovich, P.E.

Version 1.2

Y-axis Stresses for Simple-Span:

fby = 5.14 ksi fby = My/Sy

fwns = 1.21 ksi fwns = Mt*12/(Sy/2) (warping normal stress)

fby(total) = 6.35 ksi fby(total) = fby+fwns

Fby = 34.49 ksi Eqn. F6-1 Controls fby

5/20/2018 Monorail 13

4/7

"MONORAIL13.xls" Program

Created By: Joel Berg, P.E.

Based on a Spreadsheet By: Alex Tomanovich, P.E.

Version 1.2

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

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

sxo = -6.46 ksi sxo = Cxo*Pw/ta^2

szo = 1.25 ksi szo = Czo*Pw/ta^2

Local Flange Bending Stress @ Point 1:

sx1 = 4.56 ksi sx1 = Cx1*Pw/ta^2

sz1 = 14.82 ksi sz1 = Cz1*Pw/ta^2

Local Flange Bending Stress @ Point 2:

sx2 = 6.46 ksi sx2 = -sxo

sz2 = -1.25 ksi sz2 = -szo

Resultant Biaxial Stress @ Point 0:

fbxo = 7.56 ksi fbxo = Mx*(d/2)/Ix = Mx/Sx

fbyo = 0.64 ksi fbyo = My*(tw/2)/Iy

sz = 9.15 ksi sz = fbxo+fbyo+0.75*szo

sx = -4.85 ksi sx = 0.75*sxo

txz = 0.00 ksi txz = 0 (assumed negligible)sto = 12.31 ksi sto = SQRT(sx^2+sz^2-sx*sz+3*txz^2)

5/20/2018 Monorail 13

5/7

"MONORAIL13.xls" Program

Created By: Joel Berg, P.E

Based on a Spreadsheet By: Alex Tomanovich, P.E

Version 1.2

MONORAIL BEAM ANALYSISFor W-shaped Underhung Monorails Analyzed as Simple-Spans with / without Overhang

Per AISC 13th Edition ASD Manual and CMAA Specification No. 74 (2004)

Project Name: Client:

Project No.: Prep. By: Date:

Input:

RL(min)=-0.73 kips RR(max)=9.13 kips

Monorail Size: L=17 ft. Lo=3 ft.

Select: W12x50 x=8.313 ft

Design Parameters: S=9 in.

Beam Fy = 36 ksi

Beam Simple-Span, L = 17.0000 ft. W12x50

Unbraced Length, Lb = 17.0000 ft.

Bending Coef., Cb = 1.00 Pv=7.4 kips

Overhang Length, Lo = 3.0000 ft. Nomenclature

Unbraced Length, Lbo = 11.5000 ft.

Bending Coef., Cbo = 1.00 W12x50 Member Properties:

Lifted Load, P = 6.000 kips A = 14.60 in.^2 Zx = 71.90 in.^3

Trolley Weight, Wt = 0.400kips

d = 12.200in.

Iy = 56.30in.^4

Hoist Weight, Wh = 0.100 kips tw = 0.370 in. Sy = 13.90 in.^3

Vert. Impact Factor, Vi = 15 % bf = 8.080 in. ry = 1.960 in.

Horz. Load Factor, HLF = 10 % tf = 0.640 in. Zy = 21.30 in.^3

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

Wheel Spacing, S = 9.0000 in. Ix = 391.00 in.^4 Cw = 1880.0 in.^6

Distance on Flange, a = 0.3750 in. Sx = 64.20 in.^3 wt / ft. = 50.0 plf

Support Reactions: (with overhang)

Results: RR(max)= 9.13 = Pv*(L+(Lo-(S/12)/2))/L+w/1000/(2*L)*(L+Lo)^2

RL(min)= -0.73 = -Pv*(Lo-(S/12)/2)/L+w/1000/(2*L)*(L^2-Lo^2)

Parameters and Coefficients:

Pv = 7.400 kips Pv = P*(1+Vi/100)+Wt+Wh (vertical load)

Pw = 1.850 kips/wheel Pw = Pv/Nw (load per trolley wheel)

Ph = 0.600 kips Ph = HLF*P (horizontal load)

ta = 0.640 in. ta = tf (for W-shape)l= 0.097 l= 2*a/(bf-tw)

Cxo = -1.903 Cxo = -2.110+1.977*l+0.0076*e^(6.53*l)

Cx1 = 0.535 Cx1 = 10.108-7.408*l-10.108*e^(-1.364*l)

Czo = 0.192 Czo = 0.050-0.580*l+0.148*e^(3.015*l)

Cz1 = 2.319 Cz1 = 2.230-1.490*l+1.390*e^(-18.33*l)

Bending Moments for Simple-Span:

x = 8.313 ft. x = 1/2*(L-(S/12)/2) (location of max. moments from left end of simple-span)

Mx = 31.88 ft-kips Mx = (Pv/2)/(2*L)*(L-(S/12)/2)^2+w/1000*x/2*(L-x)

My = 2.44 ft-kips My = (Ph/2)/(2*L)*(L-(S/12)/2) 2

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

e = 6.100 in. e = d/2 (assume horiz. load taken at bot. flange)

at = 53.354 at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksi

Mt = 0.67 ft-kips Mt = Ph*e*at/(2*(d-tf))*TANH(L*12/(2*at))/12

X-axis Stresses for Simple-Span:

fbx = 5.96 ksi fbx = Mx/Sx

Lr = 31.31 ft. (Eqn. F2-6, max. value of Lb for inelastic LTB)

Fbx = 20.69 ksi Eqn. F2-2 Controls fbx

5/20/2018 Monorail 13

6/7

"MONORAIL13.xls" Program

Created By: Joel Berg, P.E

Based on a Spreadsheet By: Alex Tomanovich, P.E

Version 1.2

Y-axis Stresses for Simple-Span:

fby = 2.11 ksi fby = My/Sy

fwns = 1.16 ksi fwns = Mt*12/(Sy/2) (warping normal stress)

fby(total) = 3.27 ksi fby(total) = fby+fwns

Fby = 33.03 ksi Eqn. F6-1 Controls fby

5/20/2018 Monorail 13

7/7

"MONORAIL13.xls" Program

Created By: Joel Berg, P.E.

Based on a Spreadsheet By: Alex Tomanovich, P.E.

Version 1.2

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

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

sxo = -8.60 ksi sxo = Cxo*Pw/ta^2

szo = 0.87 ksi szo = Czo*Pw/ta^2

Local Flange Bending Stress @ Point 1:

sx1 = 2.42 ksi sx1 = Cx1*Pw/ta^2

sz1 = 10.47 ksi sz1 = Cz1*Pw/ta^2

Local Flange Bending Stress @ Point 2:

sx2 = 8.60 ksi sx2 = -sxo

sz2 = -0.87 ksi sz2 = -szo

Resultant Biaxial Stress @ Point 0:

fbxo = 5.96 ksi fbxo = Mx*(d/2)/Ix = Mx/Sx

fbyo = 0.10 ksi fbyo = My*(tw/2)/Iy

sz = 6.71 ksi sz = fbxo+fbyo+0.75*szo

sx = -6.45 ksi sx = 0.75*sxo

txz = 0.00 ksi txz = 0 (assumed negligible)sto = 11.39 ksi sto = SQRT(sx^2+sz^2-sx*sz+3*txz^2)