Section Modulus calculation and optimization

SECTION MODULAS CALCULATION AND OPTIMIZTION:

Aim:

• Calculate the Moment of Inertia
• Calculate the Section Modulus(Z).

Introduction

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. It includes the idea that most of the work in bending is being done by the extreme fibres of the beam, i.e. the top and bottom fibers of the section. The distance of the fibers from top to bottom is therefore built into the calculation.

The section modulus of the cross-sectional shape is of significant importance in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.

According to bending equation-

Where,

Z = Section modulus of the section

M= Moment of resistance

σ = Bending stress

y = the distance to the extreme fiber from the centroid

Section Modulus Calculations of hood:

The section modulus of the cross-sectional shape is of significant importance in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads. It includes the idea that most of the work in bending is being done by the extreme fibres of the beam, ie the top and bottom fibres of the section. The distance of the fibres from top to bottom is therefore built into the calculation. The elastic modulus is denoted by Z. To calculate Z, the distance (y) to the extreme fibres from the centroid (or neutral axis) must be found as that is where the maximum stress could cause failure.

Case:1

No Modifications in the Hood Assembly.

From The above design section,

Minimum Moment of Inertia (I) = 1.336309 × 10⁴ mm⁴

And the Y = 439.85mm

For section modulus,

Case:2

• Increased the offset distance of hem flange of the outer panel by 0.5 mm.

From the above design section,

Minimum Moment of Inertia (I) = 1.342376 x 10⁴ mm⁴

Y = 439.8 mm

For section modulus,

Conclusion

Thus the Section Modulus of the Hood is calculated and section modulus values are improved by 0.137mm³ after changing the design of Hood.