Section Modulus calculation and optimization

                                 SECTION MODULUS CALCULATION & OPTIMIZATION

Objective – Main objective of this experiment is to find a hood which has appropriate strength for an      automobile with respect to pedestrians and also for passenger safety. (Or we can say we find a optimize section modulus value by which we strengthen my hood as much as needed not so rigid or not week)

What exactly Section Modulus is?

The section modulus value gives us the strength of the component. Strength basically means that whatever load we apply the resistance provided by the component opposite to the deformation of the component.

Bending a steel section that has a larger section modulus than another will be stronger and harder to bend.

In simple terms the section modulus is the ratio of bending moment to bending stress for steel, if your steel has a high section modulus it will be harder to bend and can withstand a high moment without having high bending stress.

Bending formula – (Deflection of beam)

Why we take (I) minimum?

Because we know when Z is minimum, we get maximum bending stress & We want bending stress at minimum moment of inertia point, where my section is weakest at that point when we calculate maximum bending moment so my rest of the component is safe for me.

According to equation (4 and 5), it can be seen that more the section modulus of the section of a beam less will we the maximum bending stress produce in the beam (as max bending stress is inversely proportional to the section modulus)

                                                           Section modulus study

Use the section from your hood design and calculate the section modulus from using the formula –

Z = I/Y

Z – section modulus

I – moment of inertia

Y – distance between the neutral axis and the extreme end of the object.

For section modulus we always need a closed model.

First, we create intersection curve (intersection curve is a 3d curve),

At the inner panel in intersection curve, we see some small - small gap because when we create inner panel there are some cutouts, we create so for filling these small-small gap we convert intersection curve in to the 2d curve.

After creating 2d curve hide the intersection curve because we don’t need further, fill all the gap in 2d sketch by using line, studio spline, profile, any of the method and create closed loop, we take outermost area of the outer panel and the lowermost area of the inner panel, Ignore the thickness and joint it and complete as a one section.

calculate the value of Y for find out section modulus. (Y = 440.8mm)

Go to search bar and search section inertia then select section inertia analysis, select existing sketch, (in dialog box) and select your sketch and click ok then get the information, we get maximum and minimum moment of inertia Vale.

Then calculate value of Z and search how to strengthen the component further and optimize the component by adopting few of the methods,

How are you very your depth between outer panel and inner panel for better section modulus?

For increasing section modulus value so definitely increase the area of cross section.

A – Offset the inner panel section.

B – And also increase the height of embosses.                                                                        

C – We also create embosses in outer panel.

And there are so many ways for increases the section modulus value. 

Case 1 – At zero mm offset or we can say not any changes.

 MOI (MAX) – 4.935048229 e^7(mm^4)

 MOI (MIN) – 1.454102352 e^5(mm^4)

 Z = I/Y

 Z = (1.454102352 e^5)/440.8

 Z = 329.84 mm^3

Case 2 – At 0.5mm Inner Panel Offset (Increase the area between inner panel or outer panel)

MOI (MAX) – 4.925989576 e^7(mm^4)

MOI (MIN) – 1.47315508 e^5(mm^4)

Z = I/Y

Z = (1.47315508 e^5)/440.8

Z = 334.16 mm^3

Case 3 – At 0.8mm Inner Panel Offset (Increase the area between inner panel or outer panel).

MOI (MAX) – 4.920613934 e^7(mm^4)

MOI (MIN) – 1.485050388 e^5(mm^4)

Z = I/Y

Z = (1.485050388 e^5)/440.8

Z = 336.86 mm^3

Case 4 – At 0.5mm Inner Panel Offset (Decrease the area between inner panel or outer panel)

MOI (MAX) – 4.944041721 e^7(mm^4)

MOI (MIN) – 1.436075780 e^5(mm^4)

Z = I/Y

Z = (1.436075780 e^5)/440.8

Z = 325.75 mm^3

Case 5 – At 0.8mm Inner Panel Offset (Decrease the area between inner panel or outer panel).

MOI (MAX) – 4.949449208 e^7(mm^4)

MOI (MIN) – 1.425775835 e^5(mm^4)

Z = I/Y

Z = (1.425775835 e^5)/440.8

Z = 323.41 mm^3

                                                      Conclusion

S.NO	OFFSET DISTANCE	SECTIONAL MODULUS VALUE (Z)
1	0.0mm	329.84 mm^3
2	+0.5mm	334.16 mm^3
3	+0.8mm	336.86 mm^3
4	-0.5mm	325.75 mm^3
5	-0.8mm	323.41 mm^3

when comparing Cases, the section modulus value of case 3 is higher than then other cases,

So, when we increased the depth of emboss, offset the inner panel, create emboss in outer panel, we get more moment of inertia and also increased the section modulus, therefore if we increase the section modulus, we get more strength of the hood and can resist the better than previous design.

In this challenge we compare the values of section modulus, it is not about calculating the change, in this challenge you are supposed to understand how exactly you are going to influence the section modulus values.

Neeraj Singh