SECTION MODULUS CALCULATION

OBJECTIVE:

To calculate the section modulus of the designed hood for analyzing the strength and also optimizing the design of the hood inner panel to check the differences in the bending strength.

SECTION MODULUS:

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. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below.

S = I/Y,

Where

S = Section modulus (mm^3)

I = Moment of Inertia of the section about the bending axis. (mm^4)

Y = Distance between the neutral axis and extreme end of the object (mm)

Area moment of Inertia:

The area moment of inertia of a beams cross sectional area measures the beam ability to resist bending. The larger the moment of inertia less will be the bend.

Where,

M = Bending moment

I = Area moment of Inertia

E = Youngs modulus

R = Radius of gyration

Neutral axis: When beam is subjected to pure bending the top most fibres of the beam are subjected to maximum compression, while the bottom most fibres of the beams are subjected to maximum tension.

CALCULATIONS:

Existing design of hood (case 1)

A intersection line is plotted on hood inner and outer panel in 0,y axis of the hood and section inertia analysis is followed.

Maximum moment of inertia (MOI Max) = 8.223183380*10⁵mm⁴

Minimum moment of inertia (MOI Min) =5.268078403*10³mm⁴

Y = 487.1313/2

= 243.56565

S = I/y

S = 5268.078403/243.56565

=21.6289mm³

Optimised hood design (case 2)

The emboss of the hood inner panel is slightly changed and the section inertia analysis is followed.

Maximum moment of inertia (MOI Max) = 8.202810864*10⁵mm⁴

Minimum moment of inertia (MOI Min) = 5.351099333*10³mm⁴

Y = 487.1313/2

= 243.56565

S = I/y

S = 5351.099333/243.56565

=21.9698mm³

CONCLUSION:

The section modulus of case 2 is slightly higher than case 1, thus by changing the design of embosses the strength of the material can be increased.