Section Modulus calculation and optimization

Hi colleagues,

As requested in challenge first I should report what the Section modulus is - in short Section Modulus is the geometric property of the given cross-section geometrical structures.It is the direct measure of the strength of the geometrical section.As higher the section modulus of a structure,the more the resistive is to bending.Section modulus is defined as the ratio of Moment of inertia and the distance from the neutral axis to the outer fibres.

Now about how I got Data for calculating Moment of Inertia and Section Modulus.

As requested,I should make a section of Hood assembly that I have already made in previous challenge.Therefore I have opened Hood assembly.

Then I have made sections with Edit Section as shown and got intersection curves.

As it can be seen,intersection curves are with outer and inner surfaces and they have interruptions,that means,I should have only outer curves and without interruptions to get a closed curve.On such closed curve it is possible to conduct a Moment Inertia analysis of a section.

So,I have extracted outer curves

and added splines to form a closed curve.

Then with a command Section Inertia Analysis I got values for a Moment of Inertia as follows.

Now about result analysis.

First moment of inertia is not always zero but only if you take the moment about the centroid.The reason why it is zero lies in the definition of the centroid.The first moment of area is area multiplied by the distance,and the definition of the centroid is that point which is at the centre or around which all the area is equally distributed. Now if the area will be equally distributed then in that case the area in +r distance from centroid will be equal to the area in -r distance.So,every positive value and negative value of the area and distance multiplication cancel each other out and the first moment of area become zero.But if you take the first moment around any other point in distance from centroid it will not be zero.

In the image shown above it can be seen,those values are almost in centroid and less than values shown in exercise -

Max (0.000191029; 0.999999989;0.000000000)

Min (0.999999989; 0.000191029; 0.000000000).

On that basis the values Max (-0.000000071; 1.000000000;0.000000000)

Min (1.000000000; 0.000000071; 0.000000000) are little bit better defined.

I have got firts Moment of Inertia and on the basis of formula S = I/y I am able to calculate S - Section modulus (Second moment of Inertia).

My Section modulus is S=5175636.157 / 750.011659185 = 6,900.740933313095 (mm3).

Section modulus in exercise is S=4508704.556 / 737.267614478 = 6,115.424667326872 (mm3).

As result shows,the first Section modulus has higher value,that means it is able to withstand higher forces and on that basis it is better to have a Hood assembly with that value.With added embosses,regarding section,it is possible to get a higher Section modulus value.

Thank you on consideration and time for reading this article.

Best regards,

Ivan Tole