Section Modulus calculation and optimization

AIM

To calculate the Section modulus of the original hood design and optimize it by changing design so as to increase the moment of inertia of the designed part.

INTRODUCTION

• Section Modulus

Section Modulus also known as Polar modulus or the Torsional Section Modulus, can be defined as a geometric property of the given cross-section of the shaft or beam structure. It is the measure of the strength of the shaft or beam section. Higher the Section Modulus of structure more it has the resistive power to the bending.

It can also be defined as the ratio of the second area moment of inertia to the distance from the Neutral axis to the Extreme fiber.

Thus,

Here,

Z = Section Modulus (mm³)

I = Area Moment of Inertia (mm⁴)

Y= Distance from Neutral Axis to the extreme fiber. (mm)

CALCULATIONS

The BIW Hood Panel is taken into consideration and section Modulus is calculated on 2 Input conditions. Since the hood panel is not symmetric therefore maximum and minimum moments are generated.

• Input Condition -1

This is taken as the original deigned section of the hood panel and its analysis for the moments is done.

The analysis report states

MOI (max)= 4.814638579 e+06 mm⁴

MOI (min)= 1.523504016 e+04 mm⁴

Section Area= 74.012417228 mm²

Calculating Y (distance from neutral axis to extreme fiber)

Since Y is the distance from the neutral axis to the extreme fiber therefore

Y= 876.434/2

y=438.217 mm

Hence,

Section Modulus, Z(max) = MOI (max)/Y

= 4.814638579 e+05/438.217

= 34.0701 e+02 mm³

Section Modulus, Z(min) = MOI (min)/Y

= 1.523504016 e+04 /438.217

= 10.9695 e+03 mm³

• Input Condition-2

In this condition optimization is performed on the inner panel by increasing the distance between outer and inner panel further by 1mm. Also, the analysis for the inertia is performed.

The analysis report states

MOI (max)=4.806523750 e+06 mm⁴

MOI (min)= 1.493009994 e+04 mm⁴

Section Area= 73.610837540 mm²

y=438.217 mm

Hence,

Section Modulus, Z(max) = MOI (max)/Y

=4.806523750 e+06 / 438.217

=35.7659 e+02 mm³

Section Modulus, Z(min) = MOI (min)/Y

= 1.493009994 e+04 /438.217

= 10.9868 e+03 mm³

RESULTS

	INPUT CONDITION-1 (I1)	INPUT CONDITION-2 (I2)	DIFFERENCE (I2-I1)
Zmax	34.0701 e+02 mm3	35.7659 e+02 mm3	1.6958 mm3
Zmin	10.9695 e+03 mm3	10.9868 e+03 mm3	0.0173mm3
Area	74.012417228mm2	73.610837540mm2	0.40157968mm2

It can be noted from the above results that in condition 2 the area of the section increases and the minimum and maximum section modulus also increases thus increasing the bending resistivity of the panel. Hence by increasing the distance between the inner and outer panel will lead to increase in the moment of inertia of the section thus leading to overall increase in the bending strength of the panel.

CONCLUSION

The section modulus analysis carried out on the BIW hood panel gives the perception about the bending stresses, forces and the load bearing capacity of the BIW panel.