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Tips & Tricks - Rule of Thumb for Section Design

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For thin sections with the same outer dimensions, the Rule of Thumb is:

"double the weight (thickness) & double the strength"

It isn't always obvious how a change in thickness affects the section properties. In some cases an increase in thickness actually reduces the strength if the distance to the outer fiber (Y) increases faster than the moment of inertia (I). So this rule is very handy to use for thin sections when accurate calculations aren't required.

We have checked some standard section shapes to show that for practical purposes this rule holds true. The Multiplication Factors in the boxes on the right show the actual increases in section properties when the thickness is doubled i.e the doubling the channel thickness gives a 1.91 times increase in the channel area, where:

I = moment of inertia
A = area of section
Y = distance from centroid to outer fibre of section
S = section modulus (=I/Y)

The percentage errors compare these actual factors to the rule of thumb factor of 2.0.

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Channel Section (75 x 30 CH)

Investigate the effect of doubling the thickness on the section properties:

		Multiplication Factor % Error t = 2.0 0% A = 1.91 4.7% Ix = 1.75 12.4% Iy = 1.76 12.1% Sx = 1.84 7.8% Sy = 1.76 12.1%
t = 3 mm A = 387 mm2 Ix = 31212 mm4 Iy = 315542 mm4 Yx = 21.1 mm Yy = 37.5 mm	t = 6 mm A = 738 mm2 Ix = 54686 mm4 Iy = 55494 mm4 Yx = 22.2 mm Yy = 37.5 mm

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Square Hollow Section (65 x 65 SHS)

Investigate the effect of doubling the thickness on the section properties:

		Multiplication Factor % Error t = 2.0 0% A = 1.89 5.7% I = 1.74 13.2% S = 1.74 13.2%
t = 2 mm A = 492 mm2 I = 320933 mm4 Y = 32.5 mm	t = 4 mm A = 927 mm2 I = 557090 mm4 Y = 32.5 mm

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Pipe Section (70 CHS)

Investigate the effect of doubling the thickness on the section properties:

		Multiplication Factor % Error t = 2.0 0% A = 1.94 2.9% I = 1.83 8.3% S = 1.83 8.3%
t = 2 mm A = 427 mm2 I = 247168 mm4 Y = 35 mm	t = 4 mm A = 829 mm2 I = 453256 mm4 Y = 35 mm

The above results show that the rule of thumb gives a reasonable approximation to the actual numbers, and is sufficient for most purposes where accurate calculations are not required. Note also that this rule is proportional i.e. if the thickness is increased by a factor of 1.5, the strength will also increase by a factor of (approximately) 1.5.

Therefore, to reduce the shear, normal and bending stresses in a thin section, try increasing the section thickness as an easy solution!