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 = 60h = 325xdimensions in mm

A rectangular section has width b = 60 mm and height h = 325 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 60 mmh = 325 mm
Sx = × 10³ mm³
2.Easy
2203018018ȳ = ?dimensions in mm

Find the height ȳ of the centroid of the T-section above its bottom edge.

bf = 220 mmtf = 30 mmtw = 18 mmhw = 180 mm
ȳ = mm
3.Medium
2002516018xdimensions in mm

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

bf = 200 mmtf = 25 mmtw = 18 mmhw = 160 mm
Ix = × 10⁶ mm⁴
4.Medium
2203401210xdimensions in mm

A symmetric I-section has flanges 220 mm wide and 12 mm thick, an overall depth of 340 mm and a web 10 mm thick. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 220 mmH = 340 mmtf = 12 mmtw = 10 mm
Ix = × 10⁶ mm⁴
5.Hard
100 mm240 mm96 mm40 × 50xIx​ = ?

A 100 mm × 240 mm plate has a rectangular cut-out 40 mm wide and 50 mm high, centred on the vertical centre line with its centre 96 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 240 mmcut-out: 40 × 50 mmhole centre: y = 96 mm
Ix = × 10⁶ mm⁴
6.Hard
2002020010xM = 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 = 200 mmtf = 20 mmtw = 10 mmhw = 200 mmM = 20 kN·m
σtop = MPa

Answer key

  1. 1. Sx = 1056 × 10³ mm³
  2. 2. ȳ = 160.4 mm
  3. 3. Ix = 22.04 × 10⁶ mm⁴
  4. 4. Ix = 168.4 × 10⁶ mm⁴
  5. 5. Ix = 113.5 × 10⁶ mm⁴
  6. 6. σtop = 40.7 MPa

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