Cantilever Beam -- comparison of MoM and Finite Element Analysis (FEA)

1D beam model (using Unigraphics)

1D beam mesh

TrueGrid

deflection

maximum stress

 

load variables

Load Value Description
tension 100 lb load parallel to beam
compression 100 lb load parallel to beam
flexure 100 lb load perpendicular to beam
torsion 100 in-lb moment around beam axis
moment 100 in-lb moment perpendicular to beam axis
length 10 in distance from support to load

 

material properties

Material E
(106 psi)		 v Material E
(106 psi)		 v
aluminum 10.4378 0.33 nylon 0.57988 0.40
brass 14.9899 0.35 polypropylene 0.28994 0.40
copper 18.9911 0.35 steel - rolled 29.8638 0.30

 

cross-sectional properties

Cross-section Dimensions
(in)		 Iz
(in4)		 Iy
(in4)		 Jo
(in4)

b = 1
h = 0.5

 0.010417 0.41667 0.052084
r = 1 0.78540 0.78540 1.57080
b = 0.5
h = 1
t = 0.1		 0.015 0.04225 0.5725
r = 1
t = 0.1		 0.07854 0.07854 0.15708
b = 1
h = 0.5
t = tw = 0.1		 0.0286583 0.00215833 0.0308167

 

results comparison

Cross-section Loading Material

Maximum
Stress (psi)

Maximum
Deflection (in)
MOM 1D FEA MOM 1D FEA
rectangle flexure aluminum 24000 24000 0.30657 0.3071
brass 0.21347 0.2138
copper 0.16849 0.1688
nylon 5.5182 5.528
polypro. 11.036 11.06
steel 0.10715 0.1073
rectangle tension steel 200 200 6.697E-5 6.697E-5
compression -200 -200 -6.697E-5 -6.697E-5
flexure 24000 24000 0.10715 0.1073
torsion 63.66   6.429E-4 3.043E-3
moment 2400 2400 0.16072 0.1607
rectangle flexure steel 24000 24000 0.107150 0.1073
circle 1273 1273 0.001421 0.001449
rectangular tube 20000 20000 0.074412 0.07470
circular tube 12732 3702 0.014212 0.004278
I-beam 19192 17650 0.038948 0.03628