Section Modulus calculation and optimization

Section Modulus:

The Section Modulus(S) is geometric property of the cross section used for designing beams and flexural members.

It is a way of quantifying a cross-section of a given geometry. It is directly proportional to the area moment of inertia of the cross-section. Higher the section modulus, the more the moment of inertia, more stiffness and thus more resistance to deformation and bending. Section modulus can be improved by varying the geometry of the cross-section. In other words, stiffness can be improved by just improving the geometry without the need for adding extra material.

S= I / Y

S - Section Modulus. (mm^3)

I - Moment of Inertia. (mm^4)

y - Distance from neutral axis to the end of the object. (mm)

Below is the list of Section Modulus fror different cross sections:

Cross-sectional Shape	Figure	Equation	Comment
Rectangle			Solid arrow represents neutrsal axis
Double symmetri I-section (Major axis)			NA indicates neutral axis
Double symmetri I-section (Minor axis)			NA indicates neutral axis
Circle			Solid arrow represents neutral axis
Circular hollow section			Solid arrow represents neutral axis
Rectangular hollow section			NA indicates neutral axis
Diamond			NA indicates neutral axis
C-Channel			NA indicates neutral axis

Calculation:

Case 1:

I am taking the Hood model from the previous challenge.

The value we get after section analysis

Moment of inertia(max) = 8.105030505×10^5 mm^4

Moment of inertia(min) = 5.903204719×10^3 mm^4

Distance (Y) = 485.2405/2=242.620 mm

S(max)=I/Y

S=8.105030505×10^5/242.620

Section Modulus(max)= 3340.62 mm^3

S(min)=I/Y

S=5.903204719×10^3/242.620

Section Modulus(min)= 24.33 mm^3

Case 2:

After offset of inner panel by 0.5mm.

Moment of inertia(max) = 8.093506348×10^5 mm^4

Moment of inertia(min) = 6.129158280×10^3 mm^4

Distance (Y) = 485.2405/2=242.620 mm

S(max)=I/Y

S=8.093506348×10^5/242.620

Section Modulus(max)= 3335.87 mm^3

S(min)=I/Y

S=6.129158280×10^3/242.620

Section Modulus(min)= 25.26 mm^3

Conclusion

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. As we increase the section area, the moment of inertia & section modulus increases which means strength and load material also increase.