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.

PROJECT: -3

MAXIMUM DIFLECTION OF BEAM WITH DIFFERENT C/S RECTANGULAR, CIRCULAR, I-SECTION.

Given Conditions: -

Length of the beam = 1000 mm.

Load acting end of the beam=1000N

Area of the I-cross section = Area of the rectangle.

1)Now we will find the moment of inertia of circle = πD4/64

= πx (50)4/64

=306796.15.

Maximum deflection of circle = FxL3/3xExI

=1000x (1000)3/3x306796.15x210

=0.0051737

From Workbench: -

Maximum deflection of circle

2)we will find the moment of inertia of Rectangle= bxd3/12

=50x (2500)3/12

= 4166666666.6

Maximum deflection of Rectangle = FxL3/3xExI

=1000x (1000)3/3 x 4166666666.6 x 210

=0.000038095

From Workbench: -

Maximum deflection of Rectangle

3)we will find the moment of inertia of I-Cross section.

Area of the I-cross section = Area of the rectangle.

2500/3 = 833.3

We Know that I-Section is divided into 3- rectangles

1. upper section
2. lower section
3. middle section

i) for upper section Area of rectangle = LxB

50xb=833.3

B=16.66

ii)for upper section Area of rectangle = LxB

50xb=833.3

B=16.66

iii) for middle section Area of rectangle = LxB

for every triangle b =16.66

then A=2xlxb (here l = except width of middle i.e.,50-16.66=33.34, if we consider half it is 33.34/2 =16.67.

=2x16.67x16.78

A =559.44

Total area – obtained area

2500-559.44 =1940.56

moment of inertia of I-section = bxd3/12

=50x (1940.56)3/12

=30448786138.86

Maximum deflection of I-section = FxL3/3xExI

=1000x (1000)3/3 x 30448786138.86x 210

=0.000000052

From Workbench: -

Maximum deflection of I-section

Hence from above concept we have done caliculation/model according to their cross sections and we find the difflections for each.

Kindly consider above concept and provide grade accordingly.

Thanks & Regards,

Praveen Kumar reddy.