Section Modulus calculation and optimization

Section Modulus calculation and optimization

Aim:

To find the section modulus of the hood and optimization to improve the overall section modulus.

Objective:

Use the section from your Hood design and calculate the section modulus using the formula S= I/y.

Section Modulus:

The section modulus is a cross-sectional geometric property of structural elements such as beams, columns, slabs, etc. and it is used to calculate stresses in Cross-sections. In general, it can be said that the greater the dimensions of a cross-section under a given load, the greater the Section modulus and the smaller the bending stress.

S=I/Y

Where ;

S= Section modulus

I= min area moment of inertia

Y= distance b/w neutral axis & extreme end of the object

1.Rectangular section:

2. I/H section:

3. Circular section:

4. Hollow Circular tube section:

5. Hollow Rectangular tube section:

6. U profile/ C section:

7. T Section:

Procedure :

we are going to calculate the section modulus for the Hood Assembly and can analyze one with more section modulus.

Hood - Outer panel

Hood - Inner Panel

Now we take the intersection curve of the Outer and Inner hood and make a complete single closed curve for the inertia analysis.

Cross section Area

Calculation:

Case 1: Before Optimization

From the above Sectional Analysis the results apperared :

Moment of Inertia (Imin) = 6.905012192 ×10^4 mm^4

Moment of Inertia (Imax) =1.534335296 ×10^7 mm^4

The Distance from neutral fibre to extreme fibre is calculated by making two points to the extreme of section and measuring distance between them and half it.

So the distance from neutral fibre is :(Ymax)

Ymax = 486.9189/2 mm

Ymax = 243.45945mm

Section modulus :

S = I / Ymax

S (Min) = (6.905012192 ×10^4) / 243.45945

S (Min) = 0.00154852 ×10^3 mm^3

S (Max) = (1.534335296 ×10^7) / 243.45945

S (Max) = 0.0069112247×10^3 mm^3.

Case 2: After Optimization

In this case, the inner hood panel is offset to 2mm outside so that the section area will be increased as Sectional Inertia is directly proportional to the sectional modulus the value of sectional modulus will increase. the result as shown below.

From the above Sectional Analysis the results apperared :

Moment of Inertia (Imin) = 8.267497825 ×10^4 mm^4

Moment of Inertia (Imax) =1.532017126 ×10^7 mm^4

So the distance from neutral fibre is : (Ymax)

Ymax = 486.9189/2 mm

Ymax = 243.45945mm

Section modulus :

S = I / Ymax

S (Min) = (8.267497825 ×10^4) / 243.45945

S (Min) = 0.0018540668 ×10^3 mm^3

S (Max) = (1.532017126 ×10^7) / 243.45945

S (Max) = 0.0069007828×10^3 mm^3

Conclusion:

Thus the strength of the hood assembly was sucessfully increased by modifying it. the safety of the vehicle also improved.

We can see that the value of S (Min) increased from (0.00154852 ×10^3 mm^3 to 0.0018540668 ×10^3 mm^3) as the modification of the object & distance b/w the hood inner & outer panel is increased as S is directly proportional to moment of inertia.thus the section is proved that ok. & optimised better section modulus value.