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 improved the section modulus of the previous section and mention what change you made that has increased the strength.

Solution :

First we will define a few basic terms :

Moment of Inertia : 

Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis. Moment of Inertia is also known as the angular mass or rotational inertia. The SI unit of moment of inertia is kg m².

Now we will calculate the section modulus of the hood as shown below :

We have created a plane in the middle as shown above and we will extract the middle section as shown below :

Now we will find out the section modulus of it as shown below :

Hence we get the following :

Now we will apply the section modulus formula as shown below :

Moment of Inertia (Max ) : 8.20 * 10^5 mm^4

Moment of Inertia (Min ) : 5.05 * 10^3 mm^4

Y = 485.759 /2 = 242.8

S = I /Y =  5.05 * 10^3 mm^4 / 242.8 = 20.79 MM^3

We can optimize the hood by increasing the thickness by 0.5 or more as shown below :

As you can see the minimum moment of inertia increases therefore this is the best way to increase the section modulus.