Section Modulus calculation and optimization

Aim:

To know briefly about section modulus and the calculation of it for the hood design.

Section modulus is a geometric property used to calculate the bending stresses in a structural member. Other geometric properties used in the design include an area for tension and shear, the radius of gyration for compression, and the 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. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such.

Types of section modulus:

There are two types of section modulus:

• Elastic Section Modulus
• Plastic Section Modulus

Elastic section modulus:

Elastic section modulus is calculated when we are to use the material behavior till the yield point.

For general design purposes, we use elastic section modulus.

Generally, elastic section modulus is denoted by S.

So,

S = I/ymax

Where,

I = Moment of inertia

ymax = Distance from Neutral Axis to extreme layer.

Plastic Section Modulus:

The plastic section modulus is used for materials where the elastic yield is acceptable and the plastic behavior is considered to be an acceptable range.

It depends on the location of the plastic neutral axis. The Plastic neutral axis (PNA) is the axis that bisects the cross-section such that the compressive force from the region in compression is equal to the tension force from the region under tension. So, for sections with a constant yield stress, the area above and below the PNA will be equal, but for mixed sections, this is not necessarily the case.

plastic modulus calculation for different plastic parts as follows,

Calculation:

To calculate the Section Modulus for the hood sheet metal, use the formula

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

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

To find an improved Section Modulus compared to the previous one,found that after extending of the lowermost edge of the inner panel & calculating the section modulus, the section modulus is improved.

So the lowermost edge has been offsetted to determine the better section modulus.

offset=0.5mm

offset=0.6mm

offset=0.7mm

offset=0.8mm

Comparison table of section modulus:

Conclusion:

While comparing the values in the above table, observed that section modulus of the optimized hood is increased.If there is increase the gap between the inner and outer panel of hood eventually section length will increase thus Moment of inertia will also increase.

Also infer that the value of section modulus is directly proportional to moment of inertia. If MOI increased,Section modulus also will increase and vice-versa.