Section Modulus calculation and optimization

Aim: To compare and determine the section modulus of the hood and how it can be incresed by making the necessary changes to its cross-section.

Introduction: 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.

To calculate the section modulus, the following formula applies:

S=I/Y

Where, I = moment of inertia, Y = distance from reference line (neutral axis) to the other extreme end.

For symmetrical sections the value of I is the same above or below the centroid

For asymmetrical sections, two values are found: I max and I min

Calculations:

CASE 1: Initial section taken across plane z to find the optimal values:

Fig 1.1 Sketch 1

Fig 1.2 section values of sketch 1

From the fig 1.1 we have the values,

Imax = 4.544454335e+06 mm4 Y = total distance/2

Y = 871.9/2 Y= 435.95mm

Therefore, S = I/Y

S = 4.544454335e+06 / 435.95

S =10424.25 mm3

CASE 2: Now the sketch has been modified to get the desired values as shown in the figure

Fig 2.1 Sketch 2

Fig 2.1 section values of sketch 2

From the fig 2.1 we have the values,

Imax = 4.544744523e+06 mm4 Y = total distance/2

S = 10424.92 mm3

By comparing case1 and case2 we can say that there has not been any significant change in the value of section modulus.

CASE 3 (optimised section): Now the section has been offsetted by 2mm:

Fig 3.1 sketch 3 offseted by 2 mm outward

Fig 3.2 section values of sketch 3

From the fig 3.1 we have the values,

Imax = 4.640962162e+06 mm4 Y = total distance/2

S = 10645.62 mm3

Therefore by from case (2) and case (3) we can conclude that by offsetting the section by 2 mm we have increased the strength of the hood by approximately 2 %

Conclusion: Section modulus is directly proportional to the cross-sectional area, thus if we want to increase the load bearing capacity of the hood we have to implement more embosses and increase the cross- sectional area.