Section Modulus calculation and optimization

Section Modulus calculation and optimization

Aim: Calculation and Optimization of Section Modulus for Hood (i.e to increase strength of hood)

Section Modulus:

The section modulus of the cross-sectional shape is of significant importance in designing beams or flexural members. It is a geometric property which is of direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger (i.e more resistive to bending) and capable of supporting greater loads.

The elastic section modulus (S) is defined as the ratio of the overall second moment of area (I) (or area moment of inertia) to the most extreme fiber distance (y) from the overall bending neutral axis of a part or beam system.

`S = I/y`

Its unit is `mm^3`

Section Modulus is also referred to as the Polar Modulus (J) or the Torsional Sectional Modulus for circular sections.

Image below shows section modulus of commonly used cross-sections.

Section Modulus calculation of Hood:

Image below shows the design of hood taken for the study.

Image below shows middle section of hood taken for consideration.

Case 1 : Intial hood design study

• Section of the hood design is studied.
• Section inertia analysis tool is used to find area moment of inertia for the section considered.

• Minimum area moment of inertia (I) `= 1.415xx10^4 mm^4`
• y `= 878.538/2 = 439.269mm`
• Section Modulus (S) `= I/y= (1.415xx10^4)/439.269=32.212mm^3`
• Minimum strength = `32.212mm^3`

Case 2: Optimized Hood design study

• The motive here is to increase the strenth of the hood (i.e Section Modulus) that can be achieved by various means like changing the geometry, increasing the thickness etc.
• Here the depth of the inner panel is increased by `0.5mm`

• Minimum area moment of inertia (I) `= 1.4394xx10^4 mm^4`
• y `= 878.538/2 = 439.269mm`
• Section Modulus (S) `= I/y= (1.4394xx10^4)/439.269=32.768mm^3`
• Minimum strength = `32.768mm^3`

Conclusion:

• From above observations, it can be infered that strength of the hood is directly propotional to the Area moment of Inertia(I). When I increases hoods strength increases.
• Thus the strength of the hood was successfully increased by modifying its design thereby improving safety of vehicle.