Section Modulus calculation and optimization

Section Modulus

Section modulus can be defined as the ratio of moment of inertia(MI) of a section about neutral axis to the distance of outermost layer from neutral axis. It is denoted by Z and its unit is mm^3.

Mathematically

Z=I/Ymax

Where Z= Section modulus

I= Moment of Inertia

Ymax= distance of outermost layer from neutral axis.

Moment of Inertia(MI)

The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or second moment of inertia. The area moment of inertia has dimensions of length to the fourth power.

Neutral Axis

The neutral axis is an axis in the cross section of a a member resisting bending along which there are no longitudinal stresses or strains. As shown in the sketch layers below neutral axis will subject to tensile stress and layers above neutral axis will subject to compressive stress.

Bending Equation

Bending equation of a section can be described as below.

Section Modulus in Bending Equation

The relation between section modulus and other parameters in the bending equation can be derived by re arranging the parameters as shoen below. Ratio of Young's modulus to radius of curvature is not considerd in this part.

From the above relation we can understand that, in order to increase the bending moment of a section, its section modulus has to be optimised. Bending moment (M) is directly proportional to section modulus (Z)

Section Modulus of Hood Section

In order to calculate the section modulus of the completed hood section its moment of inertia as well as the distance from center to its outermost layer has to be calculated.

Section for frontal impact is being considerd.

A section perpendicular to the direction of impact is being taken for the analysis as shown below.

Moment of Inertia of the Section

Withe the help of inertia analysis tool MI of the section has measured. Minimum value from the measurement is taken into consideration for factor of safety.

Distance of outermost layer from neutral axis

Distance of outermost layer from neutral axis can be measured from the assembly as shown below.

Section Modulus of the Hood Section

Z=I/Ymax

I=(1.51x10^4)mm^4

Ymax=438.2mm

Z= (1.51x10^4)/438.2

=34.46 mm^3

Optimization of Section Modulus

Section modulus of the initial section can be optimized for better strength. Since section modulus is directly proportional to moment of inertia and Ymax value is constant in this case. We can optimize the section modulus by increasing moment of inertia with the following ways.

• By increasing the gap between outer and inner panel.
• By increasing the sheet thickness.

Since increasing the sheet thickness will increase the material cost as well as weight of the part we can optimize the section modulus by increasing the gap between panels by 0.5mm as shown below

Moment of Inertia of the Modified Section

Withe the help of inertia analysis tool MI of the modified section can be measured. Minimum value from the measurement is taken into consideration for factor of safety.

Here we can see the minimum MI value of this section has improved from the previous value.

Distance of outermost layer from neutral axis

Distance of outermost layer from neutral axis will not change since we have only modified the thickness of the section.

Section Modulus of the Modified Hood Section

Z=I/Ymax

I=(1.5578x10^4)mm^4

Ymax=438.2mm

Z= (1.5578x10^4)/438.2

=35.53mm^3

As explained in the above example section modulus of the initial hood section has been improved by increasing the gap between outer and inner panels. In case if the desired value for crash requirement is not yet achieved, sheet thickness can also be increased to attain the desired value.

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