Section Modulus calculation and optimization
Use the Section from your Hood design and calculate the section modulus using the formula S = I/y
S = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object
Come up with a new section that has improved the section modulus of the previous section and mention what change you made that has increased the strength.
ANS
SECTION MODULUS OF THE HOOD
Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such.
- Section modulus is one of the ways to calculate the strength and the moment of inertia to improve the strength of the object about an its reference axis.
- We can also improve the strength by calculating the MOI and compare with the parent car.
- This strength can measured directly from section modulus formula and defined by given formula.
- Section modulus represented with a symbol of
Formula s=i/y
S = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object
What is Moment of Inertia?
Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis. The moment of Inertia is also known as the angular mass or rotational inertia.
The SI unit of moment of inertia is kg m2.
Moment of inertia is usually specified concerning a chosen axis of rotation. It mainly depends on the distribution of mass around an axis of rotation. MOI varies depending on the axis that is chosen.
Case 1
By using the same skitch to calculate the moment of inertia of the hood panel.
Here the moment of inertia is calculated by using NX- cad software obtained values are
Imax: 4.853527950e+06[mm^4]
Imin: 1.391309596e+04[mm^4]
Total length of ‘y’ is 969.4136 mm
Neutral axis of ‘y’ is half of the value in orginal length of y
y/2=969.4136/2= 484.7068
- Section modulus(S):I/y=13913.09596mm^4/484.7068mm
= 28.70416625 as Imin
Case 2
in case we have offset the outer panel to words down now, we can see how the moment of inertia varies,
offset distance of 5mm
Here the moment of inertia is calculated by using NX- cad software obtained values are
Imax: 4.875518637e+06[mm^4]
Imin: 1.771044034e+04[mm^4]
Total length of ‘y’ is 969.4136 mm
The neutral axis of ‘y’ is half of the value in the original length of y
y/2=969.4136/2= 484.7068
- Section modulus(S):I/y=17710.44034mm^4/484.7068mm
= 36.5384606529 as Imin
Case 3
In this case, 3 distances of the inner panel and outer panel are the same bet extra emboss are added to the 2D skitch to see the change in moment of inertia.
Here the moment of inertia is calculated by using NX- cad software obtained values are
Imax: 6.63737382089e+06[mm^4]
Imin: 2.667017827e+04[mm^4]
Total length of ‘y’ is 969.4136 mm
Neutral axis of ‘y’ is half of the value in orginal length of y
y/2=969.4136/2= 484.7068
- Section modulus(S):I/y=26670.17827mm^4/484.7068mm
= 55.023321872109 as Imin
Final result:
Thus the stiffness of the car hood has been increased by increasing its area moment of inertia.
Conclusion:
Section modulus is directly dependent on the area moment of inertia and the distance from the neutral axis. Hence, to improve the geometry of the carry more bending load, the section modulus can be improved by increasing the area MOI of a given section. We can increase the section modulus just increasing the gap between the outer & inner panel.