Bending and torsion on curved monorail
Bending and torsion on curved monorail
(OP)
I am designing a curved monorail and would like anyone's input on the best method to use to calculate bending and shear stress in the beam when the load is applied on a curve between supports.
Thanks.
Thanks.






RE: Bending and torsion on curved monorail
EA W'' = - n
EIxx V'''' = mx + vy
EIyy U'''' = - my + vx
EIww F'''' - GJs F'' = - mw' + t'
where
E: Young Modulus of elasticity
G: shear modulus
A: Cross sectional area
Ixx, Iyy: second moments of area in shear center principal coordinates (x,y)
Iww: warping constant in principal coordinates (in^6)
Js: St. Venant torsional rigidity
W'' = d^2 W/dz^2 where W is the axial deformation
V'''' = d^4 V/dz^4 where V is dislacement in y dir
U'''' = d^4 U/dz^4 where U is dislacement in x dir
F: twist of the section
n: distributed axial force
mx, my: distributed bending moments
vx, vy: distributed lateral loads
mw: distributed warping moment
t': distributed torquwe
Solve these equations with appropriate boundary conditions.
Most of the work is in finding the principal axis and the various cross sectional properties...
RE: Bending and torsion on curved monorail
If that doesn't work, make a composite section of a Rectangular Hollow Section (RHS) above a Wide Flange Beam, with the RHS welded to the Top Flange with a pair of fillet welds. Use the RHS to resist the torsion, and the Beam + RHS to resist the vertical bending.
Russell Keays