Section Modulus calculation and optimization

Section modulus is the ratio of the area moment of inertia about a neutral axis and the distance of extreme end from the neutral axis.

S=I/y

where S= Section Modulus

          I= Moment of Inertia

          y= distance between the neutral axis and the extreme end of the object.

Now section modulus gives us an idea of the resistance offered to bend when impacted upon collision.

For a section, there is a minimum moment of inertia and a maximum moment of inertia. For safety requirements, we always have to prepare the design based on the minimum value. From a pre-existing design, we can imply changes so that the resistance value increases and hence call for a design improvement 

Let us proceed to the calculation of section modulus based on the submitted project.

From the Bending Moment Equation,

         

M= (σ*I)/y or M= σ * (I/y)

       (I/y)=S

therefore, M= σ * S , 

which states that the Bending moment is maximum when the section modulus is maximum and section modulus is maximum when the moment of inertia is maximum.

Therefore in order to obtain maximum resistance to bending, our area moment of inertia should be maximum.

The section in the analysis will always be perpendicular to the impact direction. 

On the basis of the current project I have obtained moment of inertias as follows:

and for case 2 I have offset the inner hood profile for about 0.75 mm and have obtained the following:

now the y in both instances equals 439.83mm

For case 1, Z1= I1/y = 617.991mm3

For case 2, Z2 = I2/y = 639.419mm3

here, Z2 > Z1

From the results, we can see that the resistance offered increased as we varied the cross-section profile.

Attached with this is the part cross-section of the modified profile.