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
2402514014ȳ = ?dimensions in mm

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

bf = 240 mmtf = 25 mmtw = 14 mmhw = 140 mm
ȳ = mm
2.Easy
b = 300h = 375xdimensions in mm

A rectangular section has width b = 300 mm and height h = 375 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 300 mmh = 375 mm
Sx = × 10³ mm³
3.Medium
200303008xdimensions in mm

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

bf = 200 mmtf = 30 mmtw = 8 mmhw = 300 mm
Ix = × 10⁶ mm⁴
4.Medium
150 mm300 mm180 mmØ60xIx​ = ?

A 150 mm × 300 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 180 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 300 mmd = 60 mmhole centre: y = 180 mm
Ix = × 10⁶ mm⁴
5.Hard
2602020010xM = 15 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 15 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 260 mmtf = 20 mmtw = 10 mmhw = 200 mmM = 15 kN·m
σtop = MPa
6.Hard
1403018018xM = 30 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 30 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 140 mmtf = 30 mmtw = 18 mmhw = 180 mmM = 30 kN·m
σbottom = MPa

Answer key

  1. 1. ȳ = 132.2 mm
  2. 2. Sx = 7031 × 10³ mm³
  3. 3. Ix = 65.12 × 10⁶ mm⁴
  4. 4. Ix = 334.1 × 10⁶ mm⁴
  5. 5. σtop = 25.02 MPa
  6. 6. σbottom = 153.2 MPa

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