MONORAIL BEAM ANALYSIS

For Sshaped
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 = 1.096+1.095*l+0.192*e^(6.0*l)




Cx1 =



Cx1 = 3.9654.835*l3.965*e^(2.675*l)




Czo =



Czo = 0.9811.479*l+1.120*e^(1.322*l)




Cz1 =



Cz1 = 1.8101.150*l+1.060*e^(7.70*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







Lb/rt =









Fbx =


ksi












SR =












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.





tf2 =


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 =
























































































































































































SBeam Configurations 















