Challenge

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.

BBeeraka Srinivasulu2 Oct 2024

FEA

Given data:

Load = P = 1000N

Span length = L =1000mm = 1m

E = 210 Gpa

μ = 0.3

1. Circular cross section (Diameter = 100mm):

-Solving using analytical equation:

δ = PL³/3EI

I_circular = πd⁴/64 = π(100)4/64 = 4910714.28 mm⁴ = 4.910714*10^-6m⁴

δ = PL3/3EI = (1000)*(1)³/(3*210*10⁹*4.91071428*10^-6) = 0.3232mm

-Solving using FEA Ansys:

Analysis selection

Element selection

Material properties

Section definition

Geometry

Meshing

Analysis type

Loading & Boundary conditions

Deflection

Maximum deflection = 0.325mm

2. Rectangular / Square cross section (50mm*50mm):

-Solving using analytical equation:

δ = PL3/3EI

Isquare = a4/12 = (50)4/12 = 520833.33 mm4 = 5.20833*10-7 m4

δ = PL3/3EI = (1000)*(1)3/(3*210*109*5.20833*10-7 ) = 3.047mm

-Solving using FEA Ansys:

Analysis selection

Element selection

Material properties

Section definition

Geometry

Meshing

Analysis type

Loading & Boundary conditions

Deflection

Maximum deflection = 3.047mm

3. I section (similar area as of square-2500mm²):

Dimensions of I section taken to get 2500mm² area of cross section :

Depth = 90mm

Breadth = 50mm

Flange thickness = 20mm

Web thickness = 10mm

-Solving using analytical equation:

δ = PL3/3EI

I = 2620000 mm4

δ = PL3/3EI = 0.605mm