Hood design modification and calculations for section modulus

Section modulus:

Section modulus is defined as a geometric property of a given cross-section used in designing the flexural structures. It is purely dependent only on the cross-section of the member.

We use this parameter to measure the strength of the given member or beam by determining its resistance towards bending. For symmetric sections, the section modulus is considered to be same for both the values whereas for asymmetric sections, the max value is given as S_max and min value as S_min.

There are two different types of section modulus ; Plastic section modulus (Z) and Elastic section modulus (S). In this case, we are considering only elastic section modulus (S) which is governed by the following equation:

Section modulus, (S) = I / Y ………. (1)

Where, I = moment of inertia of the member

Y = yield strength of the member

As discussed above, section modulus is a measure of resistance towards bending of the flexural member. The bending equation is governed by the equation as follows:

E/R = M/I = σ/Y ………. (2)

Considering only related terms with respect to moment of inertia (I) and yield strength (Y),

M/I = σ/Y ………. (3)

Where, M = bending moment about the neutral axis

σ = bending stress of the member

From equations (1) and (3),

σ = M/S …… (4)

Therefore, from the equation (4), we can say that bending stress is inversely proportional to the section modulus. It implies that as the section modulus becomes larger, the resistance towards bending also increases.

#1 Initial hood design and its cross-section analysis

The section inertia analysis is performed on the hood design using NX CAD tool. The intersection curve is selected across the YZ-plane and analyzed. It is made sure that the curve is fully closed for accurate results.

From the above figure, following results have been noted:

I_max = 809805.515 mm⁴

I_min = 382766.110 mm⁴

Material of the hood design is AISI 1018 Low Carbon Steel and its Yield Strength, Y = 370 MPa

Therefore,

S_max = I_max / Y = 809805.515/370 = 218.866 mm³

S_min = I_min / Y = 382766.110/370 = 103.450 mm³

#2 Modifications in the hood design and analysis

Here, the main aim is to improve the section modulus of the hood by varying its design parameters. Firstly, I checked for tangential nature of the curve i.e. by smoothening the curve. The results obtained is as below figure:

As we can see from the above figure, the I_max and I_min values are increased by 2%. Therefore, we can predict that the cross-sectional curve of the member should have smooth edges i.e. less no. of sections and more tangential in nature which impacts for positive section modulus. In the hood design, the radius of the sections can be improved for greater stability and thus improve bending resistance.

In addition, we know that section modulus is directly proportional to the sectional area. Therefore, section modulus can be improved by simply increasing the cross-section area of the member. In order to increase the cross-section area, the outer panel is offset at a distance of 2mm and joined with the inner panel. The results are as follows:

From the above figures,

I_max = 8470035.389 mm⁴

I_min = 458643.341 mm⁴

S_max = I_max / Y = 8470035.389/370 = 228.919 mm³

S_min = I_min / Y = 458643.341/370 = 123.957 mm³

When we compare the obtained results with the initial hood design analysis, the section modulus has been increased by 5%.

Conclusion

From the overall study, it can be noted that moment of inertia of the member plays a major role in the determining the strength of the member. The report illustrates that the tangential nature of the curve helps to slightly improve the section modulus. Also, the sectional area can be increased by offsetting the outer panel to certain distance which helps to improve the section modulus and bending resistance. Furthermore, study can be performed by adding more flanges in the section and analyze for section inertia analysis.