Section Modulus calculation and optimization

Section Modulus Calculation and Optimization

Aim: calculate the section modulus for different parameter and compare the strength of the section

Section Modulus: Section modulus is a geometric property for given cross-section used in the design of member. Geometric properties used in design include Area for tension, Radius of Gyration for Compression and Moment of Inertia for stiffness. Any of the above properties is highly dependent on the shape of the section.

For our modulus the section modulus is calculated using formula

Where,

S = Section modulus

I = Moment of Inertia

y = distance between the neutral axis and extreme end of the object

Moment of Inertia: The moment of Inertia of an object is a determined measurement for a rigid body rotating around a fixed axis. The axis might be internal or external and can be fixed or not. However, the MOI is always described in relation to that of axis. The MOI depends on the distribution of the mas around its axis of rotation. MOI varies depend upon the position of the axis that is chosen. Other names of MOI are Angular Mass or Rotational Inertia and its SI unit is Kg.m^2.

Lets calculate section modulus for our section.

Case 1:

As we can see in the picture, we had calculated Section Inertia Analysis in NX and get the following result where,

Max MOI = 825.07 mm^4

L = 482.8/2 = 241.4mm

Section modulus of case 1

S = 825.07/241.4

S = 3.417 mm^3

Case 2: lets change the section height and then again calculate

From above figure after reducing the height of the section we get the new values for MOI,

Max MOI = 810.00 mm^4

L=241.4mm

Section modulus of case 2

S = 810/241.4

S = 3.355 mm^3

Result:

As we can see the section modulus is highly depended on the shape of the section when we reduce the height of the section we see a drop in section modulus from 3.417mm^3 to 3.355 mm^3, so for our study the case 1 gives better section of modulus.