Section Modulus calculation and optimization

Aim:

To calculate the section modulus of the previously designed hood for analysing its strength and optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section Modulus:

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members, it is also referred to as the Polar Modulus or the Torsional Sectional Modulus. 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. There are two types of section moduli, the elastic section modulus, and the plastic section modulus.

S : I/Y(MAX)

I= AREA MOMENT OF INERTIA OR SECOND ORDER MOMENT OF INERTIA.

Y(MAX)= DISTANCE OF EXTREME LAYER FROM NEUTRAL AXIS.

DESIGN 1: Section Modulus of Initial Hood Design:

From the above analysis, following minimum and maximum moment of inertia are obtained

I_max = 4865657.280 mm⁴

I_min = 14190.445 mm⁴

y = 440 mm

S_max = I_max / y = 4865657.280 / 440 = 11,058.31 mm³

S_min = I_min / y = 14190.445/ 440 = 32.25 mm³

DESIGN 2: Section Modulus of Optimized Hood Design:

From the above analysis, following minimum and maximum moment of inertia are obtained

I_max = 9106701.509 mm⁴

I_min = 26971.432 mm⁴

y = 440 mm

S_max = I_max / y = 9106701.509 / 440 = 20697.04 mm³

S_min = I_min / y = 26971.432 / 440 = 61.29 mm³

Conclusion:

So, here the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design(depth).