W-Flange Overhead Monorail Beam Analysis Calculator

Beam Deflection and Stress Formula and Calculators

Description and References for This Calculator

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)
Input:
Monorail Size:
Select:
Design Parameters:
Beam Fy =
ksi
Beam Simple-Span, L = ft.
Unbraced Length, Lb = ft.
Bending Coef., Cb =
From AISC 9th Edition ASD Manual, page 5-47:
Cb = 1.75+1.05*(M1/M2)+0.3*(M1/M2) <= 2.3
where: M1/M2 = ratio of smaller to larger bending moment at ends
of the unbraced length, 'Lb'.
Overhang Length, Lo = ft.
Unbraced Length, Lbo =
The unbraced length for the overhang (cantilever) portion, 'Lbo', is often debated.
Here are some recommendations from different sources:
1. Per Fluor Enterprises Guideline 000.215.1257 - "Hoisting Facilities"
Lbo = Lo+L/2
2. Per Dupont Standard DB1X - "Design and Installation of Monorail Beams"
Lbo = 3*Lo
3. Per ANSI MH27.1 - "Underhung Cranes and Monorail Systems"
Lbo = 2*Lo
4. Per British Steel Code B.S. 449, pages 42-44 (1959)
Lbo = 2*Lo (for top flange of monorail beam restrained at support)
Lbo = 3*Lo (for top flange of monorail beam unrestrained at support)
5. Per AISC Journal article by N. Stephen Tanner - "Allowable Bending Stresses
for Overhanging Monorails" (3rd Quarter, 1985)
Lbo = Lo+L (used with a computed value of 'Cbo' from article)
ft.
Bending Coef., Cbo =
Lifted Load, P = kips A = in.^2 d/Af =
Trolley Weight, Wt = kips d = in. Ix = in.^4
Hoist Weight, Wh = kips tw = in. Sx = in.^3
Vert. Impact Factor, Vi = % bf = in. Iy = in.^4
Horz. Load Factor, HLF = % tf = in. Sy = in.^3
Total No. Wheels, Nw =
k= in. J = in.^4
Wheel Spacing, S = ft. rt = in. Cw = in.^6
Distance on Flange, a = in.
Support Reactions:
Results:
RR(max) =
For a monorail consisting of a simple-span with no overhang, 'RR(max)' and 'RL(min)' are determined by positioning the trolley at the right support.

For a monorail consisting of a simple-span with an overhang, 'RR(max)' and 'RL(min)' are determined by positioning the trolley at the end of the overhang.

The self-weight of the monorail beam is also included.
RL(min) =
For a monorail consisting of a simple-span with no overhang, 'RR(max)' and 'RL(min)' are determined by positioning the trolley at the right support.

For a monorail consisting of a simple-span with an overhang, 'RR(max)' and 'RL(min)' are determined by positioning the trolley at the end of the overhang.

The self-weight of the monorail beam is also included.
Parameters and Coefficients:
Pv = kips
Pw = kips/wheel
Ph = kips
ta = in.
l =
l = 2*a/(bf-tw)
Cxo =
Cxo = -2.110+1.977*l+0.0076*e^(6.53*l)
Cx1 =
Cx1 = 10.108-7.408*l-10.108*e^(-1.364*l)
Czo =
Czo = 0.050-0.580*l+0.148*e^(3.015*l)
Cz1 =
Cz1 = 2.230-1.490*l+1.390*e^(-18.33*l)
Bending Moments for Simple-Span:
x = ft.
Mx = ft-kips
My = ft-kips
Lateral Flange Bending Moment from Torsion for Simple-Span:
(per USS Steel Design Manual, 1981)
e = in.
at =
Mt = ft-kips
X-axis Stresses for Simple-Span:
fbx = ksi
SR =
Lb/rt =
Fbx = ksi
(continued)
Y-axis Stresses for Simple-Span:
fby = ksi
fwns = ksi
fby(total) = ksi
Fby = ksi
SR =
Combined Stress Ratio for Simple-Span:
S.R. =
SR =
Vertical Deflection for Simple-Span:
Pv = kips
D(max) = in. D(max) =
D(ratio) =
D(ratio) = L*12/D(max)
D(allow) = in. D(allow) = L*12/450
SR =
Bending Moments for Overhang:
Mx = ft-kips
My = ft-kips
Lateral Flange Bending Moment from Torsion for Overhang:
(per USS Steel Design Manual, 1981)
e = in.
at =
Mt = ft-kips
X-axis Stresses for Overhang:
fbx = ksi
Lbo/rt =
Fbx = ksi
SR =
Y-axis Stresses for Overhang:
fby = ksi
fwns = ksi
fby(total) = ksi
Fby = ksi
SR =
Combined Stress Ratio for Overhang:
S.R. =
SR =
Vertical Deflection for Overhang:
Pv = kips
D(max) = in. D(max) =
D(ratio) =
D(ratio) = Lo*12/D(max)
D(allow) = in. D(allow) = Lo*12/450
SR =
Bottom Flange Bending (simplified):
be = in.
am = in.
Mf = in.-kips
Sf = in.^3
fb = ksi
Fb = ksi
SR =
Bottom Flange Bending per CMAA Specification No. 74 (2004):
(Note: torsion is neglected)
Local Flange Bending Stress @ Point 0:
(Sign convention: + = tension, - = compression)
sxo = ksi sxo = Cxo*Pw/ta^2
szo = ksi szo = Czo*Pw/ta^2
Local Flange Bending Stress @ Point 1:
sx1 = ksi sx1 = Cx1*Pw/ta^2
sz1 = ksi sz1 = Cz1*Pw/ta^2
Local Flange Bending Stress @ Point 2:
sx2 = ksi sx2 = -sxo
sz2 = ksi sz2 = -szo
Resultant Biaxial Stress @ Point 0:
sz = ksi sz = fbx+fby+0.75*szo
sx = ksi sx = 0.75*sxo
txz = ksi txz = 0 (assumed negligible)
sto = ksi sto = SQRT(sx^2+sz^2-sx*sz+3*txz^2)
SR =
Resultant Biaxial Stress @ Point 1:
sz = ksi sz = fbx+fby+0.75*sz1
sx = ksi sx = 0.75*sx1
txz = ksi txz = 0 (assumed negligible)
st1 = ksi st1 = SQRT(sx^2+sz^2-sx*sz+3*txz^2)
SR =
Resultant Biaxial Stress @ Point 2:
sz = ksi sz = fbx+fby+0.75*sz2
sx = ksi sx = 0.75*sx2
txz = ksi txz = 0 (assumed negligible)
st2 = ksi st2 = SQRT(sx^2+sz^2-sx*sz+3*txz^2)
SR =

Contributed by:

Harsh Murugesen
Pune, Maharasha India

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