Section Modulus calculation and optimization

Section Modulus:

The section modulus is a geometric property of a cross-section used in the design of beams or other structural members. It measures the strength of the section and is defined as the ratio of the moment of inertia (a measure of an object's resistance to bending) to the distance from the neutral axis to the outermost fiber of the section.

There are two types of section modulus:

1. Elastic Section Modulus(S):

S=I/C

where,

I is the moment of inertia of the section about the neutral axis, and

c is the distance from the neutral axis to the furthest point of the section.

2. Plastic Section Modulus(Z):

Z= b*h^2/4

where,

b is the width and

h is the height of the section.

As per the below shared screenshot of two different calculations done with 2 different I value.

1. In 1st case the value of I is taken as 2.968135847e+05, therefore, I=2.968135847e+05 mm^4

Lets assume S=S1 in this condition,

Hence, S=I/Y

Y is the distance between the neutral axis and the extreme ends of the section, therefore Y=438.72mm

As per Calculations,

S1=2.968135847e+05/438.72

S1=676.544 mm^4

2. In 2nd case in-order to increase the Min. MOI we have the width of the inner hood panel by 0.5mm, hence the value of I varies as the length of the emboss is increase by +0.5mm,i.e. 0.75+0.5=1.25 we get I=3.00561061e+05 mm^4

Lets assume S=S2 in this condition,

As the distance between the neutral axis and the section extreme end remain same

Hence, Y=438.72mm

As per Calculations,

S2=3.00561061e+05/438.72

S2= 685.086 mm^4

Conclusion:

From the above calculation done it is clearly observed that,

^{S1 < S2}

After comparing both the data, we found that as we increase the emboss width it also increases the Min. MOI which further increases the total strength.

NOTE:NOTE: Attached cat part file for your reference.