Description

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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