Section Modulus calculation and optimization
OBJECTIVE:
To calculate the section modulus of the hood and to modify the design for better srength of the hood assembly.
THEORY:
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. For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials. The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (My) such that My = S × σy, where σy is the yield strength of the material.
PROCEDURE:
Here, the middle section of the hood is selected by using the intersection tool in catia surface workbench. The outer most portion of the outer panel and inner panel were extracted as shown below.
Then, the discontinuities were joined together using spline tool. Extra portions were splitted. Finally a closed sketch was formed and filled it using 'fill' tool in surface workbench as we need a closed profile to measure inertia.
Then using the 'Measure inertia' tool in Catia, we have to find the minimum & maximum moment of inertias (M1 & M2 respectively). Here M1 denotes the 'I' value in section modulus formula we are going to use.
(y=882.069/2)
The calculations are as given below.
Section modulus, S = I/y
Where,
S - Section modulus
I - Area moment of inertia
y - Distance between neutral axis and extreme end of the fibre
Therefore, I = 1.734 × 10^6 mm^4
y = 882.069/2
= 441.0345 mm
So, Section modulus, S = 1.734 x 10^6 mm^4 / 441.0345 mm
= 3931.665mm^3
Yield moment, My = S × σy
where,
σy - Yield strength of material - Stainless steel AISI 302 - cold - rolled
σy = 520 N/mm^2
So, yield moment, My = 3931.665 × 520
= 2044465.8 N mm
(Note: 302 stainless steel is an Austenitic, non-magnetic, extremely tough and ductile stainless steel alloy. AISI 302 annealed stainless steel is highly corrosion resistant and maintains its strength at high temperatures up to 550°F (288°C). Additionally, 302 stainless steel is non-magnetic in the annealed condition and cannot be further hardened by heat treatment. As an added benefit both the hardness and tensile strength of AISI 302 can be increased by cold working)
MODIFICATIONS TO IMPROVE THE STRENGTH
Now, in order to improve the strength, I tried changing the distance between inner and outer panel of hood assembly. So, I offsetted the outer contour of inner panel by 0.5mm (outwards).
The result is as shown below.
The calculations are as given below.
Section modulus, S = I/y
Where,
S - Section modulus
I - Area moment of inertia
= 1.84 × 10^6 mm^4
y - Distance between neutral axis and extreme end of the fibre, which is same as in previous case
= 441.0345 mm
Section modulus, S = 1.84 x 10^6 mm^4 / 441.0345 mm
=4172mm^3
Yield moment, My = S × σy
where,
σy - Yield strength of material - Stainless steel AISI 302 - cold - rolled
σy = 520 N/mm^2
So, yield moment, My = 4172 × 520
= 2169440 N mm
CONCLUSION
Thus the strength of the hood assembly was successfully increased by modifying it. Thus the safety of the vehicle also improved.