Section Modulus calculation and optimization
- AIM :-
To calculate the section modulus of the previously designed 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 structure, the more the resistive it becomes to bending.
section modulus is defined as the ratio of moment of inertia of a section about the neutral axis to the distance of the outmost layer from the neutral axis.
it is the direct measure of the strength of the shaft section or beam section. higher the section modulus of a structure, the more resistive it becomes to bendin.
mathemetically it is expressed as
S=I/Y
where, S=section modulus
I=moment of inertia
Y= distance from neutral axis to extreme end
moment of inertia-
the moment of inertia is the capacity of a cross section to resist bending. when it is subjected to an external load.
it is directly propotional to the strength of the material, which can be calculated through section modulus.
section modulus of various cross section are given below in thefollowing table,
Section modulus calculation of the hood design -
case 1 : section modulus for the designed hood
here the section modulud is calculated by taking the intersection
moment of inertia (I-max) =9.185928726 * 10^7 mm^4
moment of inertia (I-min) = 2.927139033 * 10^5 mm^4
Y = 881.0923 / 2 = 440.54 mm
S(max) = I-max / y = 208.771* 10^3
S(min) = I-min / y = 0.665258 * 10^3
in this case the strength of the hood varies from 208.771*10^3 mm^3 to 0.665258 *10^3 mm3.
case -2 : section modulus for the modified hood design,
here the addistional emboss structure were created to calculated the section modulus.
moment of inertia (I-max)= 9.190096454 * 10^7 mm4
moment of inertia (I-min) = 3.004320534 * 10^5 mm4
Y= 881.0923/2= 440.54615 mm
S(max) = 208.606 * 10^3 mm3
S(min) = 0.681953 * 10^3 mm3
in this case the strength of the hood varies from 208.606 * 10^3 mm3 to 0.681953 * 10^3 mm3 .
Conclusion:
the strength of the section increases in area ion both maximum and minimum value.
by evaluting the above cases, we can say that moment of inertia is directly propotional to the strength of the material.