Project 3- Study of cantilever beam with different cross-sections like circular, rectangular and I section and to find out the effect of cross-section on the deflection of the beam using FEA technique using Ansys Workbench and results has to be verified using strength of material deflection equations.
for a given problem,
workbench setup as below,
1. drag the static structural into work space.
2. go to enginnering data, insert new material add young's modulus-210GPA and and poison's ratio-0.3.
3. double click on model and generate 3D model as per problem statement.
4. go to model, assign material,
5. geneate mesh, ansys will create default mesh, that is enough for our probelm
6. assign boundary condition that one end is fixed and other end is force of 1000N.
7. Go to solution, select total defomation.
8. solve
Case-1: Round bar of radius 50 mm and length 1000 mm
ansys result
Total maximum deflection is 0.00032409 m.
Analytical result
Total deflectionof cantilever beam, y=Wl^3/(3EI)
where E=210 GPa
I=πd^4/64=3.14 x .1^4 /64 =4.908 x 10^-6 m^4.
Then, y= (1000 x 1^3)/(3 x 210 x 10^9 x 4.908 x 10^-6 )
y=0.000323 m.
Therefore, analytical and ansys solved deflection is very close.
Case-2: Rectangular cross section 50 x 50 mm and length 1000 mm
ansys result
Total maximum deflection is 0.0030392 m.
Analytical result
Total deflection of cantilever beam, y=Wl^3/(3EI)
where E=210 GPa
I=bh^3/12=0.05 x 0.05^3 / 12 = 5.208 x 10^-7 m^4.
Then, y= (1000 x 1^3)/(3 x 210 x 10^9 x 5.208 x 10^-7 )
y=0.00304 m.
Therefore, analytical and ansys solved deflection is very close.
Case-3: I section of length 1000 mm, cross section area is equal to preveously calculated rectangular bar = 2500 mm^2.
ansys result
Total maximum deflection is 0.0002198 m.
Analytical result
Total deflection of cantilever beam, y=Wl^3/(3EI)
where E=210 GPa
I=(H^3 x b /12)+2 ((h^3 x B /12) + hB(H+h)^2/4)=7.72 x 10^-6 m^4.
Then, y= (1000 x 1^3)/(3 x 210 x 10^9 x 7.72 x 10^-6 )
y=0.000206 m.
Therefore, analytical and ansys solved deflection is very close.