Section Modulus calculation and optimization

Study & Optimization of Hood- Section Modulus

Aim:

To calculate the section modulus using the formula S = I/Y. Come up with a new section that has improved the section modulus of the previous section and mention the change that has increased the strength by using the Section from Hood design.

Used Software: CATIA V5

THEORY OF SIMPLE BENDING:

When a Beam is Loaded it is bent and subjected to Bending Moments. Consequently, longitudinal or bending moments. In Order to determine the partial utility of any beam, it is very necessary to establish a relation between the radius of curvature to which the beam bends, the bending moment, the bending stress and its cross-sectional dimensions. The equation which connects these quantities is known as Bending Equation

Where

M = Moment of resistance,

I = Moment of inertia of the section about neutral axis (N.A.),

E= Youngs Modulus of Elasticity

= Bending Stress and

R= Radius of Curvature of (N.A.)

SECTION MODULUS:

From Bending Equation

Where Z is the Section Modulus

Section Modulus is a geometry property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area of tension, radius of gyration for compression, and moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape of the question. Equations for the section moduli, the elastic section modulus (S) and the plastic section modulus (Z).

For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.

The elastic section modulus is defined as S= I/Y, where I is the second moment of Inertia and y is the distance from the neutral axis to any given fiber. It is often reported using y=c, where c is the distance from the neutral axis to the extreme fiber, it is also used to determine the yield moment (M­­_y) Such that M­­_y = S x σ_y, where σ_y is yield strength of the material.

The Section Modulus is usually quoted for all Standard Sections and practically is of greater use than the second moment of area (i.e., MOI). The strength of the beam section depends mainly on the section modulus.

Calculations of Section Modulus:

Case 01: Section Modulus

I = 6.145x10⁵ mm4

Y= 482.004 = 482.004/2 = 241mm

S= I/ Y = 6.145x10⁵ / 241 = 2550mm³

Case 02 : Section Modulus

I = 6.486x10⁵ mm4

Y= 482.004 = 482.004/2 = 241mm

S= I/ Y = 6.486x10⁵ / 241 = 2691mm³

Conclusion:

By Considering the 2 cases Section modulus of the hood is increased by slightly modifying the design of the initial design of the hood and the strength of the hood also increased.

References:

1. Engineering Mechanics by Timoshenko, DH Young, JV RAO
2. Engineering Mechanics by Rajasekharan, Sankara Subramanyian
3. Strength of Materials by RK Rajput
4. https://www.engineersedge.com/material_science/section_modulus_12893.htm