Section Modulus calculation and optimization

Aim: To calculate the section modulus and improve design by increasing section modulus

About 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 og gyration for compression, and moment of inertia and polar moment of inertia for stiffness.

Two types of Section Modulus:-

1) Elastic section modulus

2) Plastic section modulus

• Elastic section modulus

The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (M_y) such that M_y = S ⋅ σ_y, where σ_y is the yield strength of the material

Example Square section modulus:-

2) Plastic section modulus

The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.

The plastic section modulus depends on the location of the plastic neutral axis (PNA).The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.

First Design

Moment of inertia(max) =8.7034156583 ×10^5×mm^4

Moment of inertia(min) = 7.638457452×10^3×mm^4

Y=488.44/2=242.8799 mm

S=I/Y

S=7.638457452×10^3/244.22= 31.2759 mm^3

Hood Design Optimization

To improve design with consideration of only section modulus for strength purpose we to take moderate sectional area which is not to high or not to low which impact great impact on our strength of our hood.

By increasing the depth of the inner panel by 1 mm only in middle part of hood inner panel to incrase cross sectional area

Here,

Moment of inertia(max) =8.319556551 ×10^5×mm^4

Moment of inertia(min) = 7.928859545×10^3×mm^4

Y=488.44/2=244.22 mm

S=I/Y

S=7.928859545×10^3/244.22=32.466mm^3

Conclusion:-

Increase Sectional area increase moment of inertia and directly impact on section modulus and strength of hood.