Section Modulus calculation and optimization

Aim

• Use the Section from your Hood design and calculate the Section Modulus using the formula
• S = I/y

S = Section Modulus

I = Moment of Inertia

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

Come up with a new section that has an improved Section Modulus compared to the previous one and mention what changes you made which resulted in the increased strength.

Section Modulus

Section Modulus is the geometric property of the given cross-section of any shaft or beam structures. It is the direct measure of the strength of the shaft section or the beam section. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section modulus is defined as the ratio of polar moment of inertia to the radius of the shaft or the distance from the neutral axis to the outer fibers.

The formula for calculating the section modulus of a cross-section is given below

S = I/y (where I is moment of inertia and y is radius of the shaft or the distance from the neutral axis to the outer fibers.)

There are following sections with the formulas of section modulus (Refer image below).

Use the Section from your Hood design and calculate the Section Modulus using the formula

To calculate the section modulus, we have to make an intersection curve and project that curve to the another plane parallel to that plan and join the cross section at some place and then with the help of section inertia analysis command we can find the moment of inertia of that section and then we have to calculate the y the distance between the neutral axis and the outer fiber/point.

The hood inner and outer section is shown below

Section Inertia Analysis result

So Moment of inertia will be 1.518851603x10^4 (mm^4) and the distance between the neutral axis and the outer fiber/point will be (y=865.4894/2) 432.7447 mm.

Section Modulus = Moment of Inertia/ distance between the neutral axis and the outer fiber/point.

S=1.518851603x10^4 (mm^4)/ 432.7447 mm.

S= 35.098107 in³

Now with a new section that has an improved Section Modulus compared to the previous one and mention what changes you made which resulted in the increased strength.

We offset the inner panel projected section to 1 mm to see the change in Moment of Inertia and the results are shown below

Calculating the section modulus of the new section

S=1.530278853x10^4 (mm^4)/ 432.7447 mm.

S= 35.362166 in³

Conclusion

Hence it is concluded from the above results as per increasing the section area the section modulus of that section increased and the resultant increase in the strength and resistance to bending as there is a proportional relationship between the Section modulus and the Moment of Inertia