Bending stress of a "T" collored tube kind of structure

Hi everyone,

I am a under graduate (B.E-Mechanical) student carrying out project for my curriculam.

In this project I was alloted to study the strength of collered tube kind of product. In this product I have to study the stress at fillet region (Please refer the attached presentation) and suggest the required section improvement.

According to my knowledge, fillet region would undergo two kind of stresses

1. Normal stress (stress due to axial load and bending stress due to moment arm from the fixed end)

Normal stress due to axial load = load / axially resisting area = 40000/(3.14*(9.5^2-7^2)) = 309 MPa

Normal stress due to bending = (M*Y)/I

Max. B.M = 40000*4 = 160000 N-mm
Y= 3/2 = 1.5 mm
I = (b*d^3/12) cutting and opening the section (resulting rectangular c/s), hence I = ((2*3.14*9.5)*3^3)/12 = 44.745 mm^4

Bending stress = 5364 MPa

2. shear sress.

Shear Stress = load/shear area = 40000/2*3.14*9.5*3 = 223 MPa

My guide says, the ways used to calculate the axial stress and shear strear stress are correct but for bending not accepting the pocedure I followed.

He says there is different prcedure to calculate the moment and area moment of inertia for this kind of structure. If anyone knows the procedure, please
help me in this regard.

1. How to find out the area moment of inertia for this kind of structure?

2. How to find the max bending moment for this kind of structure?

3. Ultimately bending stress at the fillet region?

Note: - I reffered PETERSON BOOK too in oder to see whether this kind of structure was handled by him, but i couldn't find this kind of problem over there.

- I reffered strength of materials by timoshenko also for this kind of problem. In this book I found circular plate kind of problems.
Still I couldn't get grip so as to solve this problem.

Answers to the above three queries or else resource path to solve this problem would be greatly appreciated.

Thanks in advance

M Gopalakrishnan