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W-Flange Overhead Monorail Beam Analysis Calculator

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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: W10x30

Design Parameters:

Beam Fy = 36 ksi

Beam Simple-Span, L = 8.2000 ft.

Unbraced Length, Lb = 1.0000 ft.

Bending Coef., Cb = 1.00

Overhang Length, Lo = 0.0000 ft. Nomenclature

Unbraced Length, Lbo = 0 ft.

Bending Coef., Cbo = 1.00 W10x30 Member Properties:

Lifted Load, P = 1.350 kips A = 8.84 in.^2 d/Af = 3.53

Trolley Weight, Wt = 0.100 kips d = 10.500 in. Ix = 170.00 in.^4

Hoist Weight, Wh = 0.100 kips tw = 0.300 in. Sx = 32.40 in.^3

Vert. Impact Factor, Vi = 15 % bf = 5.810 in. Iy = 16.70 in.^4

Horz. Load Factor, HLF = 10 % tf = 0.510 in. Sy = 5.75 in.^3

Total No. Wheels, Nw = 4 k= 0.810 in. J = 0.622 in.^4

Wheel Spacing, S = 3.9300 ft. rt = 1.550 in. Cw = 414.0 in.^6

Distance on Flange, a = 3.1500 in.

Support Reactions: (no overhang)

Results: RR(max) = 1.46 = Pv*(L-S/2)/L+w/1000*L/2

RL(min) = 0.54 = Pv*(S/2)/L+w/1000*L/2

Parameters and Coefficients:

Pv = 1.753 kips Pv = P*(1+Vi/100)+Wt+Wh (vertical load)

Pw = 0.438 kips/wheel Pw = Pv/Nw (load per trolley wheel)

Ph = 0.135 kips Ph = HLF*P (horizontal load)

ta = 0.510 in. ta = tf (for W-shape)

� = 1.143 � = 2*a/(bf-tw)

Cxo = 13.435 Cxo = -2.110+1.977*�+0.0076*e^(6.53*�)

Cx1 = -0.487 Cx1 = 10.108-7.408*�-10.108*e^(-1.364*�)

Czo = 4.036 Czo = 0.050-0.580*�+0.148*e^(3.015*�)

Cz1 = 0.526 Cz1 = 2.230-1.490*�+1.390*e^(-18.33*�)

Bending Moments for Simple-Span:

x = 3.117 ft. x = 1/2*(L-S/2) (location of max. moments from left end of simple-span)

Mx = 2.31 ft-kips Mx = (Pv/2)/(2*L)*(L-S/2)^2+w/1000*x/2*(L-x)

My = 0.16 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 = 5.250 in. e = d/2 (assume horiz. load taken at bot. flange)

at = 41.514 at = SQRT(E*Cw/(J*G)) , E=29000 ksi and G=11200 ksi

Mt = 0.10 ft-kips Mt = Ph*e*at/(2*(d-tf))*TANH(L*12/(2*at))/12

X-axis Stresses for Simple-Span:

fbx = 0.86 ksi fbx = Mx/Sx SR = 0.036

Lb/rt = 7.74 Lb/rt = Lb*12/rt

Fbx = 23.76 ksi Fbx = 0.66*Fy fbx <= Fbx, O.K.

(continued)

Y-axis Stresses for Simple-Span:

fby = 0.33 ksi fby = My/Sy

fwns = 0.42 ksi fwns = Mt*12/(Sy/2) (warping normal stress)

fby(total) = 0.76 ksi fby(total) = fby+fwns

Fby = 27.00 ksi Fby = 0.75*Fy fby <= Fby, O.K.

SR = 0.028

Combined Stress Ratio for Simple-

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Span:

S.R. = 0.064 S.R. = fbx/Fbx+fby(total)/Fby S.R. <= 1.0, O.K.

SR = 0.064

Vertical Deflection for Simple-Span:

Pv = 1.550 kips Pv = P+Wh+Wt (without vertical impact)

�(max)

= 0.0051 in. �(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)

�(ratio)

=L/19474 �(ratio) = L*12/�(max)

�(allow)

= 0.2187 in. �(allow) = L*12/450 Defl.(max) <= Defl.(allow), O.K.

SR = 0.023

Bending Moments for Overhang:

Mx = N.A. ft-kips Mx = (Pv/2)*(Lo+(Lo-S))+w/1000*Lo^2/2

My = 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 ksi

Mt = 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/Sx

Lbo/rt = N.A. Lbo/rt = Lbo*12/rt

Fbx = N.A. ksi Fbx = 0.66*Fy

SR =

Y-axis Stresses for Overhang:

fby = N.A ksi fby = My/Sy

fwns = N.A. ksi fwns = Mt*12/(Sy/2) (warping normal stress)

fby(total) = N.A. ksi fby(total) = fby+fwns

Fby = N.A. ksi Fby = 0.75*Fy

SR =

Combined Stress Ratio for Overhang:

S.R. = N.A. S.R. = fbx/Fbx+fby(total)/Fby

SR =

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)

�(max)

= N.A. in. �(max) = Pv*Lo^2*(L+Lo)/(3*E*I)+w/12000*Lo*(4*Lo^2*L-L^3+3*Lo^3)/(24*E*I)

�(ratio)

= N.A. �(ratio) = Lo*12/�(max)

�(allow)

= N.A. in. �(allow) = Lo*12/450

SR =

Bottom Flange Bending (simplified):

be = 6.120 in. Min. of: be = 12*tf or S*12 (effective flange bending length)

am = 2.455 in. am = (bf/2-tw/2)-(k-tf) (where: k-tf = radius of fillet)

Mf = 1.076 in.-kips Mf = Pw*am

Sf = 0.265 in.^3 Sf = be*tf^2/6

fb = 4.05 ksi fb = Mf/Sf

Fb = 27.00 ksi Fb = 0.75*Fy fb <= Fb, O.K.

SR = 0.150

Bottom Flange Bending per CMAA Specification No. 74 (2004):

(Note: torsion is neglected)

Local Flange Bending Stress @ Point 0: (Sign convention: + = tension, - = compression)

�xo = 22.63 ksi �xo = Cxo*Pw/ta^2

�zo = 6.80 ksi �zo = Czo*Pw/ta^2

Local Flange Bending Stress @ Point 1:

�x1 = -0.82 ksi �x1 = Cx1*Pw/ta^2

�z1 = 0.89 ksi �z1 = Cz1*Pw/ta^2

Local Flange Bending Stress @ Point 2:

�x2 = -22.63 ksi �x2 = -�xo

�z2 = -6.80 ksi �z2 = -�zo

Resultant Biaxial Stress @ Point 0:

�z = 6.29 ksi �z = fbx+fby+0.75*�zo

�x = 16.97 ksi �x = 0.75*�xo

�xz = 0.00 ksi �xz = 0 (assumed negligible)

�to = 14.86 ksi �to = SQRT(�x^2+�z^2-�x*�z+3*�xz^2) <= Fb = 0.66*Fy = 23.76 ksi, O.K.

SR = 0.626


�z = 1.86 ksi �z = fbx+fby+0.75*�z1

�x = -0.62 ksi �x = 0.75*�x1



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�t1 = 2.23 ksi �t1 = SQRT(�x^2+�z^2-�x*�z+3*�xz^2) <= Fb = 0.66*Fy = 23.76 ksi, O.K.

SR = 0.094


�z = -3.91 ksi �z = fbx+fby+0.75*�z2

�x = -16.97 ksi �x = 0.75*�x2


�t2 = 15.40 ksi �t2 = SQRT(�x^2+�z^2-�x*�z+3*�xz^2) <= Fb = 0.66*Fy = 23.76 ksi, O.K.

SR = 0.648



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