Section Modulus calculation and optimization

Objective

Calculate the section modulus of Hood design and Explain the changes made to improved section modulus which resulted in increased strength.

Section Modulus

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. It is the ratio of the total moment resisted by the section to the distance from the neutral axis to the extreme end. In other words, section modulus is a direct measure of strength of any sectional area of an object about neutral axis. It gives idea of how much the material is resistant to bend. As the moment of inertia increases the section modulus increases and hence there is more restitant to the bend.

Section modulus is calculated by below formula

`S=I/y`
Where,
S- Section modulus `(mm^3)`
I- Moment of inertia `(mm^4)`
y- Distance between neutral axis and extreme end of the object (mm`

Section Modulus of some common shapes is as below

Certain shapes are better than others at resisting bending and also the orientation of the shape affects bending as shown in below figure. Therefore moment of inertia is measure of efficiency of a shape to resist bending caused by loading.

Section Modulus of Hood
Case 1

1. Moment of inertia is found in NX cad using Section Inertia Analysis. This command calculates principal moment of inertia, curcumference, area and center of gravity of sections.
2. First using intersection curve command, cross section of hood assembly is created. It is joined if there is any gap and using Section inertia analysis.
3. Next, distance between neutral axis and extreme end calculated from the sketch.
4. Using both the values section modulus is calculated.

Calculation

`text(Imax)=8.304e+05 mm^4` y=`478.3/2=`239.15mm Smax=`text(Imax)/y=`3472.5`mm^3`

`text(Imin)=5.969e+03mm^4` y=239.15mm Smin=`text(Imin)/y=`24.96`mm^3`

Case 2 (Improved Section of modulus)

1. To improve section of modulus of hood, increased the distance between inner and outer panel.
2. So gap between both panels is increased by 0.75mm so there is change in cross sectional area.

Calculation

`text(Imax)=8.319e+05 mm^4` y=239.15mm Smax=`text(Imax)/y`3478.57`mm^3`

`text(Imin)=6.532e+03mm^4` y=239.15mm Smin=`text(Imin)/y=`27.31`mm^3`

Conclusion

From the above 2 cases it can be seen that, when gap between inner and oute panel is increased, the minimum and maximum moment of inertia is also increased. Since, case 2 has better range of section modulus than case 1, we can say that it will be stronger and capable of supporting greater loads than case 1. Hence, Section modulus of the cross-sectional shape is a direct measure of the strength.