MONORAIL BEAM ANALYSIS

For Wshaped
Underhung Monorails Analyzed as SimpleSpans 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 SimpleSpan, L
=


ft.







Unbraced Length, Lb
=


ft.







Bending Coef., Cb =









Overhang Length, Lo
=


ft.


Unbraced Length, Lbo
=


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) =







RL(min) =



Parameters
and Coefficients:









Pv =


kips


Pw =


kips/wheel


Ph =


kips


ta =


in.


l =



l = 2*a/(bftw)

Cxo =



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

Cx1 =



Cx1 = 10.1087.408*l10.108*e^(1.364*l)

Czo =



Czo = 0.0500.580*l+0.148*e^(3.015*l)

Cz1 =



Cz1 = 2.2301.490*l+1.390*e^(18.33*l)











Bending
Moments for SimpleSpan:








x =


ft.


Mx =


ftkips


My =


ftkips












Lateral
Flange Bending Moment from Torsion for SimpleSpan:


(per USS Steel Design
Manual, 1981)

e =


in.


at =




Mt =


ftkips












Xaxis
Stresses for SimpleSpan:








fbx =


ksi



SR =




Lb/rt =







Fbx =


ksi




















(continued)


Yaxis
Stresses for SimpleSpan:








fby =


ksi






fwns =


ksi





fby(total) =


ksi





Fby =


ksi



















SR =



Combined
Stress Ratio for SimpleSpan:








S.R. =













SR =



Vertical
Deflection for SimpleSpan:








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 =


ftkips




My =


ftkips














Lateral
Flange Bending Moment from Torsion for Overhang:


(per USS Steel Design
Manual, 1981)

e =


in.



at =





Mt =


ftkips













Xaxis
Stresses for Overhang:








fbx =


ksi





Lbo/rt =







Fbx =


ksi




















SR =



Yaxis
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^2sx*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^2sx*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^2sx*sz+3*txz^2)


















SR =












