Section Modulus calculation and optimization
Section Modulus calculation and optimizatio
Challenge : To calculate the section modulus of the hood designed & compare with modifing changes in order to improve the section modulus of hood.
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 of gyration for compression, and second moment of area and polar second moment of area 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.
Elastic section modulus
For general design, the elastic section modulus is used, applicable up to the yield point for most metals and other common materials.
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 fiber. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber.
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, and equal compressive and tensile yielding stress, the area above and below the PNA will be equal, but for composite sections.
The plastic section modulus is the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA.
Procedure.
- Create a datum plane at ceter of hood panel.
- Using the datum plane create a insection curve at hood outer & inner panel.
- Hide all solid surfaces.
- Go to sketch workbench.
- Using 2d project curve copy insection curve.
- Join all disconnected cuves using studio curve.
- Trim all unwanted lines
- Using section inertia analysis find the moment of inertia.
- Using the formula S=I/Y calculate section modulus
- Make some modifications in the hood design to improve the section modulus
Lenght of the hood
CASE-1 Calculating section modulus actual hood design.
Imin=1.567*104 mm4
Y=L/2=881.9/2=440.95
S=I/Y=1.567*10^4/440.95
S=35.5369mm3
CASE-2 Calculating the section modulus by modifying emboss
Imin=1.5855*104 mm4
Y=L/2=881.9/2=440.95
S=I/Y=1.5855*104/440.95
S= 35.9564 mm3
CASE-3 Calculating the section modulus by increasing gap beetween inner & outer hood by 0.5 mm
Imin=1.5928*104
Y=L/2=881.9/2=440.95
S=I/Y=1.5928*104/440.95
S= 36.1220 mm3
CONCLUTION : From the above camparison we can see that increasing in cross section of the hood, increases the section modulus.