Section Modulus calculation and optimization

Aim:

Section of the Car hood.

Objective :

To obtain the section modulus of the designed Car hood and further obtain the new improvised section that has a better section modulus than the earlier one.

Theory :

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. 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. Section modulus is calculated using the formula

`S=I/y`

Where,

S = Section Modulus

I = Moment of Inertia

Y = distance between the neutral axis and the extreme end of the object

The section modulus is the ratio of bending moment to bending stress for steel.

or

The ratio of the total moment resisted by the section to the stress in the extreme fiber.

It means much the load a given structure can take.

According to the bending moment equation:

`S=I/y``M/I=E/R=sigma/y`

Now,

`M/I=sigma/y`

Therefore,

`M/sigma=I/y`

`M/I=S (I/y=section modulus )`

For Ex:- 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.

We need to divide the maximum bending moment by the section modulus to get the bending stress and then compare the bending stress to the allowable tensile stress to see if the steel can take that much moment.

Section modulus is inversely proportional to the bending stress. That means sections having a high section modulus will have lower bending stresses.

Procedure for finding the section modulus :

Section 1 :

• Use the intersect to intersect the center and bow rail with the XY plane. The output will be the boundary lines for both rails.

• Now use the multi-extract to extract the outer boundary of the center rail and the inner boundary of the bow roof rail.

• Draw a line and join them to form closed lines.

• Use the fill option to create the surface for the closed lines.

• Now, use the measure inertia for 2d to measure the inertia of the surface. The minimum value of M will be the moment of inertia for the given surface.

• For the y i.e distance between the neutral axis and extreme end, go the sketch draw a line connecting the mid of the opposite edges. And then draw a straight vertical line from these two points to measure the distance as 2*y.

here,

`M1=6.748e^-007 m^4`

`M2=1.465e^-004 m^4`

Taking the minimum of the two values and converting the m4 to mm4

`I=M1=6.748X10^5 mm^4`

And,

`y=483.274/2`

y=241.637 mm

Now, the section modulus for hood section 1 is

`S=I/y`

`S=(6.74X10^5)/241.637`

`S=2792.61 mm^3`

Improved section 2:

For the improved section, we are going to increased the section area for the given hood by offsetting the inner panel lines by 0.6mm and then again splitting and joining the lines to form a closed section.

• The below picture shows section 1 and the improved section.

• Then, the closed lines are filled to form a surface section and the inertia is measured.

here,

`M1=7.168e^-007 m^4`

`M2=1.524e^-004 m^4`

Taking the minimum of the two values and converting the m4 to mm4

`I=M1=7.168X10^5 mm^4`

And,

`y=483.274/2`

y=241.637 mm

Now, the section modulus for hood section 1 is

`S=I/y`

`S=(7.168X10^5)/241.637`

`S=2966.51 mm^3`

Conclusion :

The above calculation shows that section 2 has a greater section modulus than section 1.

All these calculations are essential while designing to know the strength and load-carrying capacity of the given component.

It is quite evident that increasing the distance between the inner and outer panel has a significant impact on increasing the section modulus which in turn it's strength also. But it also depends on the designer to choose the best option from the calculation that gives satisfactory results.