Section Modulus calculation and optimization

Section Modulus Calculation and Optimization:

Section Modulus:

• Section Modulus is the geometric property to measure the ability of the cross section area of the component to withstand against the load without failure.
• Several other geometrical properties are also used to measure and to enhance the strength of the component while designing like (Area, Radius of Gyration, Moment of Inertia, Polar Moment of Inertia for Tension & Shear, Compression and Stiffness respectively)
• There are two types of Section Modulus are there,
  • Elastic Section Modulus - It is applying up to the yield point of the most common materials. It can be measured by using the following formula,
    • S = I/Y where, S is the Section Modulus, I is the Area Moment of Inertia and Y is the distance between the neutral axis and the extreme end of the component.
    • Area Moment of Inertia - It is the property of 2D shape which it defines that the deflection of that shape under loading.
  • Plastic Section Modulus - It is applied to the material which has the acceptable limit of the plastic behaviour and elastic yielding. It can be measured by using the following formula,
    • Z(P) = A(1)*Y(1) + A(2)*Y(2), where, Z(P) is the Plastic section modulus, A(1) area of the cross section side1, Y(1) is the Distance from the local centroid(side1) to the Neutral axis, A(2) area of the cross section side2 and Y(2) is the Distance from the local centroid(side2) to the Neutral axis.

Here I taken my Hood design to calculate the Section Modulus by proceeding with the Elasic Section Modulus formula,

Elastic Section Modulus, S = I/Y

Steps followed in the calculation and optimization of section modulus in hood design:

• Hood assembly with inner panel and outer panel has been sectioned along with the 0-Y direction.
• The outer edge of the outer panel and Outer edge of the inner panel are projected as the curve and making those curve as smooth by using the composite curve command.
• To calculate the section modulus, area moment of inertia has to be measured by using the section inertia analysis tool. For that Closed curve is required to measure. That's why the outer panel curve and the inner panel curve is connected by using the trim and line commands.
• By using the section inertia analysis tool, the we'ill get the maximum area moment of inertia and minimum area moment of inertia.
• Also we require the distance between the neutal axis and the extreme end of the component. So that the total distance between the extreme ends has been calculated and the that value is divided by 2 to obtain the Y value.

By using seimens NX, the following datas are measured from my hood design to calculate the section modulus,

Case:01

Area Moment of Inertia,

MOI_(max) = 8.2947x10⁵

MOI_(min) = 6.0527x10³

Distance Between the extreme ends of the component, D = 486.9mm

So, that Distance between the neutral axis and the extreme end of the component Y = D/2

Y=486.9/2

Y=243.45mm

Section Modulus with Maximum Strength:

S_(max) = MOI_(max) /Y

S_(max) = 8.2947x10⁵/243.45

S_(max) = 3.4071x10³

Section Modulus with Minimum Strength:

S_(min) = MOI_(min) /Y

S_(min) = 6.0527x10³/243.45

S_(min) = 0.0247x10³

According to this value, the section modulus of the hood has varies from 0.0247x10³mm³ to 3.4071x10³mm³

Case:02

To examine the section modulus of the hood more, small changes has been made in the inner panel curve of the hood. The inner panel curve has offsetted to 0.2mm to downwards of the hood to increase the cross section area. Then the measured datas and results are,

Area Moment of Inertia,

MOI_(max) = 8.2861x10⁵

MOI_(min) = 6.1252x10³

Distance Between the extreme ends of the component same as, D = 486.9mm

So, that Distance between the neutral axis and the extreme end of the component Y = D/2

Y=486.9/2

Y=243.45mm

Section Modulus with Maximum Strength:

S_(max) = MOI_(max) /Y

S_(max) = 8.2861x10⁵/243.45

S_(max) = 3.4036x10³

Section Modulus with Minimum Strength:

S_(min) = MOI_(min) /Y

S_(min) = 6.1252x10³/243.45

S_(min) = 0.0251x10³

According to this value, the section modulus of the hood has varies from 0.0251x10³mm³ to 3.4036x10³mm³

Results:

• Before changing the curve, the section modulus of the hood varies from 0.0247x10³mm³ to 3.4071x10³mm³
• After changing the curve, the section modulus of the hood varies from 0.0251x10³mm³ to 3.4036x10³mm³

Conclusion:

• Here, concluding the section modulus calculation and optimization of the hood design by considering the obtained results before and after the curve changes done.
• So that the minimum strength has increased from 0.0247x10³mm³ to 0.0251x10³mm³ and the maximum strength has decreased from 3.4071x10³mm³ to 3.4036x10³mm³ with respect to this Section Modulus Calculation. So that, increasing the cross section area which result the increase in strength of the hood.
• To be mention, the strength of the component has depends on various factor, not only depends on section modulus calculation. But this is also one of the factor to improve the strengthening of the component. That is what, here been done.