Section Modulus calculation and optimization

Aim: To deterine whether the section modulus/strength increase as increase in the moment of Inertia

Objective: calculate section modulus of a hood panel and optimize the section to improve strength by offsetting the intersecting cruve of outer curve the inner panel.

Introduction:

What is Section modulus?

Section modulus is a geometric property of a cross-section of a beam or column that describes its ability to resist bending or flexure. It is a measure of the strength of a structural member against bending and is defined as the ratio of the moment of inertia of the cross-section about its neutral axis to the distance from the neutral axis to the most distant point on the cross-section.

The moment of inertia, also known as the second moment of area, is a property of a shape that measures its resistance to bending. The distance from the neutral axis to the most distant point on the cross-section is called the extreme fiber distance. The section modulus can be expressed mathematically as:

S = I/y

Where,

S = Section Modulus in mm3

I = Moment of Inertia in mm4

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

I = (1/12)bh^3

y = h/2

Calculation Part

1. without optimization

Take a intersection curve between the inner and outer panel to the suitable plane and apply Section Inertia Analysis

Fig. Intersecion curve for case 1

Fig. Applied inertia analysis

Fig. Distance measure

From above fig,

_{I1 = 1.56537e+07 mm4}

I2 = 1.633e+05 mm4

h = 487.4152 mm

So,

S = I/y

S = I2/y

S = 1.6333e+05/(487.4152/2)

S = 670.083 mm3

2. With optimization:

Take the intersetion curve between the inner and outer panel and offset the outermost curve of the inner panel by 2mm and apply Section Inertia Analysis

Fig. Offset of 2mm

Fig. Intersecion curve for case 2

Fig. Applied inertia analysis

Fig. Distance measure

From above fig,

_{I1 = 1.5651e+07 mm4}

_{I2 = 1.8327e+05 mm4}

h = 487.4152 mm

So,

S = I/y

S = I2/y

S = 1.8327e+05/(487.4152/2)

S = 751.590 mm3

Conclusion,

Intial section modulus S = 670.083 mm3 and

Final section modulus after optimization S = 751.590 mm3

As the cross section increases the section modulus also increases and Thus, increases the strength of the Hood.