Section Modulus calculation and optimization

1). Section modulus -

A geometric property for a given cross-section used in the design of beams.

Other geometric property used in design using include areaof tension & shear,radius of gyration for compression

second moment of area & polar second moment of area stiffness.

- Two types of section modulus -

a). Elastic section modulus.

b). plastic section modulus.

Elastic section modulus(S)-

A ratio of the second moment of area(I) to the distance from the neutral axis(Y) to any given fibre.

S=I/Y.

Plastic section modulus(Zp)-

The sum of the area of the cross section on each side of PNA(plastic neutral axis) multiplied by the distance from the local centroid of the two areas to the PNA.

*). Shape factor(SF)-

A ratio of the plastic moment of area to the elastic moment of area.

Before optimization -

Section modulus(S)=I/Y

I= Moment of inertia(max.)

y= Distance from neutral axis to any given fibre.

= y/2=2000/2=1000 mm.

I(max)= 5.887875292x10⁷mm⁴

so, S=5.887875292x10⁷ /1000

= 58878 mm³

^&

I(min)= 1.433415820x10⁵mm⁴

so, S=1.433415820x10⁵ /1000

= 14334 mm³

^{After optimization -}

Section modulus(S)=I/Y

I= Moment of inertia(max.)

y= Distance from neutral axis to any given fibre.

= y/2=2000/2=1000 mm.

I(max)= 5.972681541x10⁷mm⁴

so, S= 5.97268154x10⁷ /1000

= 59726mm³

^&

I(min)= 1.500545987x10⁵mm⁴

so, S=1.500545987x10⁵ /1000

= 15005 mm³

COMPARISON CHART

Description	Before Optimization	After Optimization
I (Max)	8.9743938787 x 107mm4	8.959469530 x 107mm4
I (Min)	2.798862838 x 105mm4	2.859755347 x 105mm4
S (max)	203593.325 mm3	203254.753 mm3
S (Min)	634.950735 mm3	648.764825 mm3