Section Modulus calculation and optimization

CALCULATION AND OPTIMIZATION OF SECTION MODULUS FOR HOOD DESIGN

Introduction :

Section Modulus gives a overview of the strength across any Cross section in a particular part or assembly. Section modulus is a direct measure of the strength of the Part. A design that has a larger section modulus than another will be stronger and capable of supporting greater loads.

It includes the idea that most of the work in bending is being done by the extreme fibres of the beam/part , ie the top and bottom or extreme fibres of the section. The distance of the fibres from top to bottom or between two extreme edges is therefore built into the calculation.

Section Modulus is given by the formula, Z = I / Y.

Where I = Moment of Inertia , Y = distance from the neutral fibre to the extreme edge.

Calculation and Optimization :

Initally we will find the section modulus for the hood design we have made without making any changes to the cross section.

Let's choose a cross section along the width of our hood by cutting exactly in the middle of the hood assembly.

SECTION 1 :

Using the section from our hood design we make a sketch in such a way that we have a closed profile including the outer panel and Inner panel so that we can utilise the Section Inertia option to calculate the Moment of Inertia (Min & Max)

The observed values are as below,

We will choose the minimum MOI and calculate Section modulus.

Minimum moment of Inertia helps us understand the minimum threshold/value as this signifies the minimum load that will be required to bend or distort our cross section.

MOI (MIN) / I = 1.5417 x 10^4 mm4

Distance of extreme edge from neutral fibre / Y = 881.1 mm (Common for all the cross section we consider)

The section modulus for the first section is , Z1 = I / Y = 1.5417 X 10^4 / 881.1

Z1 = 17.49 mm3

SECTION 2 :

Now we make some changes to the existing cross section as shown below in order to check whether we can improve our section modulus ,

By changing the emboss away from the hood outer panel, we can see that the minimum moment of Inertia is improved from the previous design.

Let us now calculate the section modulus using the observed values,

MOI (MIN) / I = 1.5962 x 10^4 mm4

Distance of extreme edge from neutral fibre / Y = 881.1 mm

The section modulus for the second section is , Z2 = I / Y = 1.5962 X 10^4 / 881.1

Z2 = 18.11 mm3

We can see that the section modulus is greater than the previous section which means this design can help us improve our hood section to have a better load bearing capacity.

SECTION 3 :

Now we make some changes to the section 2 as shown below in order to check whether we can further improve our section modulus ,

This change has been made by moving the inner panel much closer to the outer panel. And we can see the difference in area under the cross section.

Let us now calculate the section modulus using the observed values,

MOI (MIN) / I = 1.4608 x 10^4 mm4

Distance of extreme edge from neutral fibre / Y = 881.1 mm

The section modulus for the third section is , Z3 = I / Y = 1.5962 X 10^4 / 881.1

Z3 = 16.57 mm3

Among the other two sections we notice that here we have a very low value of section modulus which means this design will be comparitively weaker than the others.

Conclusion :

From the observed three values for section 1 ,2 & 3 we notice that the section 2 with Section modulus of 18.11 mm3 seems to be a better option to improve the stregth of our hood cross sectional area.