Section Modulus calculation and optimization

Section Modulus calculation and optimization

The section modulus is a concept in structural design that measures the bending strength of a cross-section.

It’s a area of moment od inertia about the neutral axis and to the distance of outermost fiber from the neutral axis

Z = I/y

Z is section modulus

I is moment of inertia

y is distance from the neutral axis to end

Example:

Rectangular bar

For stronger Axis,

I₁ = bd³ / 12

Z₁ = I₁ / y₁ = (bd³ / 12) / (d/2) = bd²/6

For weaker Axis,

I₂ = b³d / 12

Z₂ = I₂ / y₂ = (db³ / 12) / (d/2) = db²/6

For Hood,

y=d/2

d=875.9309

y=875.9309/2 = 438 mm

For first case,

I_max = 9.0958944*10⁷ mm⁴ I_min = 2.93894039*10⁵ mm⁴

y= 438 mm y= 438 mm

Z_max = I_max / y Z_min = I_min / y

Z_max = 9.0958944*10⁷ / 438 Z_min = 2.93894039*10⁵ / 438

Z_max = 207*10³ mm³ Z_min = 0.67*10³ mm³

For second case,

I_max = 9.1127054*10⁷ mm⁴ I_min = 2.9020776*10⁵ mm⁴

y= 438 mm y= 438 mm

Z_max = I_max / y Z_min = I_min / y

Z_max = 9.1127054*10⁷ / 438 Z_min = 2.9020776*10⁵ / 438

Z_max = 208*10³ mm³ Z_min = 0.6*10³ mm³

Conclusion:

The greater the section modulus, the greater the bending resistance of a structural element.

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