Section Modulus calculation and optimization

Section Modulus

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus.

For general design, the elastic section modulus is used, applicable up to the yield point for most metals and other common materials.

The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (M_y) such that M_y = S ⋅ σ_y, where σ_y is the yield strength of the material.

Section modulus of my hood

I calculated the section modulus of my hood by taking the outlines of my outer hood panel and inner hood panel in yz cordinates. Then I joined the outline with the use of points and lines after joining the curves. Then using fill tool I made a surface entrapped in the closed line. Then I meassured the Inertia of the 2D plane using inertia meassuring tool and I got the values of minimum and maximum as 2.447*10^-6 m^4 and 1.732*10^-4 m^-4 respectively and exported it to the file. Then inorder to get the distance from the neutral axis, I used sketch in yz plane by swapping and reversing the cordinates and meassured the distance of it by giving to points at its both extremes and then drawing 2 vertical reference lines from both the points . Thus I got the distance between two extremes. Then I calculated section modulus by myself with the help of the equation S = I / y.

we know that, I = 2.447*10^6 mm^4 (after converting to mm^4 and taking the minimum value of Inertia)

y = 239.7945 mm (after taking half of distance between the two extreme points mentioned above)

therefore, S = (2.447*10^6) / (239.7945) = 10204.5709 mm^3

Now, Inorder to check the variation in the section modulus after offsetting the inner hood panel's outline to some more depth to decrease the gap between inner panel's outline and hemming region in outer panel's outline , I used parallel curve tool to .75 mm. Then again I enclosed the curves using the required tools and do the same process as done in the first condition.

Now I got the meassurement and calculation as:

M1 = 2.581*10^-6 m^4 = 2.581*10^6 mm^4

M2 = 1.815*10^-4 m^4 = 1.815*10^8 mm^4

So we taken Inertia of minimum for calculation . So I=2.581*10^6 mm^4

y will remains the same as 239.7945 mm

therefore, S = (2.581*10^6) / (239.7945) = 10763.3828 mm^3

So, the second case has got the more section modulus implies that it will have more strenth than the first case. Therefore we understood that by reducing the gap between the hemming region of outer panel and Inner panel , we can improve the strength of the hood which will capable of bear more weigth with less affect for the hood body.