Section Modulus calculation and optimization

AIM

To find section modulus of hood design that i designed.

What is Section Modulus?

Section modulus is a fundamental concept used in structural engineering and mechanics to quantify a cross-sectional shape's resistance to bending. When a load or force is applied perpendicular to the longitudinal axis of a structural member, like a beam or column, it causes the member to bend.

The section modulus (Z) is a property that describes the shape's ability to resist this bending moment. It is calculated as the moment of inertia (I) of the cross-section divided by the maximum distance from the neutral axis to the outermost fibers (y_max). Mathematically, it can be expressed as:

Z = I / y_max

Where:
Z = Section modulus
I = Moment of inertia of the cross-section about the neutral axis
y_max = Maximum distance from the neutral axis to the outermost fibers

In simpler terms,

Imagine you have a long piece of material, like a beam, and you want to know how well it can resist being bent when you put weight on it.

Section modulus is like a measure of its "bendability resistance." It tells you how strong the material is against bending forces. If the section modulus is large, it means the material is better at handling the bending and can support more weight without breaking. On the other hand, if the section modulus is small, the material is weaker, and it may bend or break more easily under the same weight.

So, section modulus helps engineers design strong and safe structures by choosing the right shape and size of the beam or other components to handle the expected loads and forces.

According to my Design of view

First Section of inertia without any changes

To find section modulus

Formula

S=I/Y

where,

Imax= 2.906183074*10^5mm4

Imin= 8.984431074*10^7mm4

and Y=876.8066mm

At neutral axis Y=D/2 = 876.8066/2 = 438.4099mm

S1 = Imax/Y

= 2.906183074*10^5mm4/438.4099

= 661.982 mm^3

Second inertia when changing its thickness to 0.8mm to optimize hood strength

Imin = 2.962781482*10^5mm4

Moment of inertia (I) = 2.962781482 * 10^5 mm^4 Maximum distance from the neutral axis (y_max) = 438.4099 mm

Now, calculate the section modulus (Z):

S2 = 2.962781482 * 10^5 mm^4 / 438.4099 mm

S2 = 676.736 mm^3

Conclusion

So, here the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design(depth)