Section Modulus calculation and optimization
OBJECTIVE
To calculate the section modulus of the hood for analyzing its strength and also optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a shape, the more it resist the bending .
EXPLANATION
Section Modulus is a geometric property used to calculate the bending stresses in a structural member.
Mathematically,
It is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.
It is denoted by Z.
Z = I/ymax
Mathematically By bending stress equation,
M/I = σmax/ymax
M = σmax × (I/ymax)
M = σmax × Z
Where,
I = Moment of Inertia(m⁴)
y = distance from NA to extreme layer(m)
The unit of section modulus is m³
The section modulus is classified into two types:-
1] Elastic section modulus:- The elastic section modulus is applicable up to the yield point of material.
It is used in most engineering applications.
2] Plastic section modulus:- The plastic section modulus is generally used for material in which plastic behavior is observed.
CALCULATION & OPTIMIZATION
CASE 1: DESIGN OF FIRST HOOD
MOI(min): 3.049126477e+04 mm^4
Y (distance): 1011.6mm/2= 505.8mm
Z =I(min)/Y(max)
Z = 3.049126477e+04 mm^4/505.8mm
Z = 6.028 mm^3
Z = 3.049126477e+04 mm^4/505.8mm
Z = 6.028 mm^3
CASE 2: OPTIMIZED DESIGN OF HOOD
MOI(min): 3.087483983e+04 mm^4
Y (distance): 1011.6mm/2= 505.8mm
Z =I(min)/Y(max)
Z = 3.087483983e+04 mm^4/505.8mm
Z = 6.104 mm^3
Z = 6.104 mm^3
Changes made: Increment by 0.5mm between the outer hood panel & the inner hood panel .
CONCLUSION
Here,the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the depth by 0.5mm.