Second Moment of Area about x-x Centroidal Axis

Sep 2012
66
0
Scotland
Having problems with (b) and (f) here.

For (b) I've done the following:

A1 = 600 mm^2
y1 = 50 mm
h1 = 27.78 mm

A2 = 1000 mm^2
y2 = 30 mm
h2 = 7.78 mm

A3 = 2000 mm^2
y3 =10 mm
h3 = 12.22 mm

I = bd^3/12 + Ah^2

= (30 * 20^3/12 + 60 * 27.78^2) + (50*20^3/12 + 1000 * 7.78^2) + (100*20^3/12 + 2000*12.22^2)
= 483, 037.04 + 93,861.73 + 365323.47
= 0.942 x10^6

Correct solution is 1.12x10^6 mm^4.

Any idea where I've gone wrong?

For (f):

I = bd^3/12

d will remain 60

So b = I*12/ d^3

Using the correct I value

1.12x10^6 * 12/ 60^3

b = 62.22 mm

The correct solution is 60.5 mm.