Centroid & second moment of area worksheet with answers

Free printable Centroid & second moment of area worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
B = 160H = 250t = 12xdimensions in mm

A hollow rectangular (box) section has outer width B = 160 mm, outer height H = 250 mm and a uniform wall thickness t = 12 mm. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 160 mmH = 250 mmt = 12 mm
Ix = × 10⁶ mm⁴
2.Easy
b = 80h = 250xdimensions in mm

A rectangular section has width b = 80 mm and height h = 250 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 80 mmh = 250 mm
Sx = × 10³ mm³
3.Medium
140360108xdimensions in mm

A symmetric I-section has flanges 140 mm wide and 10 mm thick, an overall depth of 360 mm and a web 8 mm thick. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 140 mmH = 360 mmtf = 10 mmtw = 8 mm
Ix = × 10⁶ mm⁴
4.Medium
2401014020xdimensions in mm

Find the second moment of area Ix of the T-section about the horizontal axis x through its centroid.

bf = 240 mmtf = 10 mmtw = 20 mmhw = 140 mm
Ix = × 10⁶ mm⁴
5.Hard
1602522010xM = 20 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 20 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 160 mmtf = 25 mmtw = 10 mmhw = 220 mmM = 20 kN·m
σtop = MPa
6.Hard
100 mm300 mm195 mm40 × 30xIx​ = ?

A 100 mm × 300 mm plate has a rectangular cut-out 40 mm wide and 30 mm high, centred on the vertical centre line with its centre 195 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 300 mmcut-out: 40 × 30 mmhole centre: y = 195 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. Ix = 77.51 × 10⁶ mm⁴
  2. 2. Sx = 833.3 × 10³ mm³
  3. 3. Ix = 112 × 10⁶ mm⁴
  4. 4. Ix = 11.86 × 10⁶ mm⁴
  5. 5. σtop = 36.84 MPa
  6. 6. Ix = 222.4 × 10⁶ mm⁴

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