| MONORAIL BEAM ANALYSIS |
| For S-shaped Underhung Monorails Analyzed as Simple-Spans with / without Overhang |
| Per AISC 9th Edition ASD Manual and CMAA Specification No. 74 (2004) |
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| Input: |
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| Monorail Size: |
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| Select: |
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| Design Parameters: |
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Beam Fy = |
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ksi |
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| Beam Simple-Span, L = |
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ft. |
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| Unbraced Length, Lb = |
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ft. |
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| Bending Coef., Cb = |
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| Overhang Length, Lo = |
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ft. |
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| Unbraced Length, Lbo = |
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ft. |
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| Bending Coef., Cbo = |
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| Lifted Load, P = |
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kips |
A = |
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in.^2 |
d/Af = |
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| Trolley Weight, Wt = |
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kips |
d = |
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in. |
Ix = |
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in.^4 |
| Hoist Weight, Wh = |
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kips |
tw = |
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in. |
Sx = |
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in.^3 |
| Vert. Impact Factor, Vi = |
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% |
bf = |
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in. |
Iy = |
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in.^4 |
| Horz. Load Factor, HLF = |
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% |
tf = |
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in. |
Sy = |
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in.^3 |
| Total No. Wheels, Nw = |
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k= |
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in. |
J = |
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in.^4 |
| Wheel Spacing, S = |
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ft. |
rt = |
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in. |
Cw = |
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in.^6 |
| Distance on Flange, a = |
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in. |
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Support Reactions: |
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| Results: |
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RR(max) = |
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RL(min) = |
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| Parameters and Coefficients: |
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| Pv = |
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kips |
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| Pw = |
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kips/wheel |
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| Ph = |
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kips |
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| ta = |
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in. |
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| l = |
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l = 2*a/(bf-tw) |
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| Cxo = |
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Cxo = -1.096+1.095*l+0.192*e^(-6.0*l) |
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| Cx1 = |
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Cx1 = 3.965-4.835*l-3.965*e^(-2.675*l) |
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| Czo = |
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Czo = -0.981-1.479*l+1.120*e^(1.322*l) |
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| Cz1 = |
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Cz1 = 1.810-1.150*l+1.060*e^(-7.70*l) |
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| Bending Moments for Simple-Span: |
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| x = |
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ft. |
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| Mx = |
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ft-kips |
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| My = |
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ft-kips |
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| Lateral Flange Bending Moment from Torsion for Simple-Span: |
(per USS Steel Design Manual, 1981) |
| e = |
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in. |
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| at = |
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| Mt = |
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ft-kips |
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| X-axis Stresses for Simple-Span: |
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| fbx = |
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ksi |
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| Lb/rt = |
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| Fbx = |
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ksi |
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SR = |
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| Y-axis Stresses for Simple-Span: |
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| fby = |
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ksi |
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| fwns = |
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ksi |
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| fby(total) = |
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ksi |
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| Fby = |
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ksi |
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SR = |
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| Combined Stress Ratio for Simple-Span: |
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| S.R. = |
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SR = |
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| Vertical Deflection for Simple-Span: |
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| Pv = |
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kips |
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| D(max) = |
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in. |
D(max) = |
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| D(ratio) = |
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D(ratio) = L*12/D(max) |
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| D(allow) = |
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in. |
D(allow) = L*12/450 |
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SR = |
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| Bending Moments for Overhang: |
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| Mx = |
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ft-kips |
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| My = |
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ft-kips |
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| Lateral Flange Bending Moment from Torsion for Overhang: |
(per USS Steel Design Manual, 1981) |
| e = |
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in. |
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| at = |
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| Mt = |
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ft-kips |
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| X-axis Stresses for Overhang: |
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| fbx = |
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ksi |
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| Lbo/rt = |
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| Fbx = |
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ksi |
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SR = |
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| Y-axis Stresses for Overhang: |
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| fby = |
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ksi |
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| fwns = |
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ksi |
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| fby(total) = |
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ksi |
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| Fby = |
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ksi |
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SR = |
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| Combined Stress Ratio for Overhang: |
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| S.R. = |
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SR = |
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| Vertical Deflection for Overhang: |
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| Pv = |
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kips |
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| D(max) = |
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in. |
D(max) = |
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| D(ratio) = |
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D(ratio) = Lo*12/D(max) |
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| D(allow) = |
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in. |
D(allow) = Lo*12/450 |
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SR = |
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| Bottom Flange Bending (simplified): |
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| be = |
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in. |
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| tf2 = |
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in. |
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| am = |
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in. |
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| Mf = |
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in.-kips |
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| Sf = |
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in.^3 |
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| fb = |
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ksi |
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| Fb = |
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ksi |
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SR = |
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| Bottom Flange Bending per CMAA Specification No. 74 (2004): |
(Note: torsion is neglected) |
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| Local Flange Bending Stress @ Point 0: |
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(Sign convention: + = tension, - = compression) |
| sxo = |
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ksi |
sxo = Cxo*Pw/ta^2 |
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| szo = |
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ksi |
szo = Czo*Pw/ta^2 |
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| Local Flange Bending Stress @ Point 1: |
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| sx1 = |
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ksi |
sx1 = Cx1*Pw/ta^2 |
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| sz1 = |
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ksi |
sz1 = Cz1*Pw/ta^2 |
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| Local Flange Bending Stress @ Point 2: |
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| sx2 = |
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ksi |
sx2 = -sxo |
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| sz2 = |
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ksi |
sz2 = -szo |
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| Resultant Biaxial Stress @ Point 0: |
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| sz = |
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ksi |
sz = fbx+fby+0.75*szo |
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| sx = |
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ksi |
sx = 0.75*sxo |
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| txz = |
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ksi |
txz = 0?? (assumed negligible) |
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| sto = |
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ksi |
sto = SQRT(sx^2+sz^2-sx*sz+3*txz^2) |
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SR = |
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| Resultant Biaxial Stress @ Point 1: |
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| sz = |
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ksi |
sz = fbx+fby+0.75*sz1 |
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| sx = |
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ksi |
sx = 0.75*sx1 |
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| txz = |
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ksi |
txz = 0?? (assumed negligible) |
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| st1 = |
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ksi |
st1 = SQRT(sx^2+sz^2-sx*sz+3*txz^2) |
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SR = |
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| Resultant Biaxial Stress @ Point 2: |
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| sz = |
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ksi |
sz = fbx+fby+0.75*sz2 |
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| sx = |
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ksi |
sx = 0.75*sx2 |
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| txz = |
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ksi |
txz = 0?? (assumed negligible) |
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| st2 = |
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ksi |
st2 = SQRT(sx^2+sz^2-sx*sz+3*txz^2) |
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SR = |
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S-Beam Configurations |
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