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
15090t = 12ȳ = ?dimensions in mm

An L-shaped angle section has a horizontal leg 150 mm wide and a vertical leg 90 mm high (both measured overall). Both legs are 12 mm thick. Find the height ȳ of the centroid above the bottom edge.

B = 150 mmH = 90 mmt = 12 mm
ȳ = mm
2.Easy
90180t = 18x̄ = ?dimensions in mm

An L-shaped angle section has a horizontal leg 90 mm wide and a vertical leg 180 mm high (both measured overall). Both legs are 18 mm thick. Find the distance x̄ of the centroid from the left (outer) edge of the vertical leg.

B = 90 mmH = 180 mmt = 18 mm
x̄ = mm
3.Medium
xD = 240d = 228dimensions in mm

A circular tube has outside diameter D = 240 mm and inside diameter d = 228 mm. Find its radius of gyration r about the horizontal centroidal axis.

D = 240 mmd = 228 mm
r = mm
4.Medium
100 mm240 mm156 mmØ30xIx​ = ?

A 100 mm × 240 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 156 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 240 mmd = 30 mmhole centre: y = 156 mm
Ix = × 10⁶ mm⁴
5.Hard
120 mm300 mm180 mm80 × 30xIx​ = ?

A 120 mm × 300 mm plate has a rectangular cut-out 80 mm wide and 30 mm high, centred on the 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 = 120 mmh = 300 mmcut-out: 80 × 30 mmhole centre: y = 180 mm
Ix = × 10⁶ mm⁴
6.Hard
2002530018xM = 10 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 10 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 200 mmtf = 25 mmtw = 18 mmhw = 300 mmM = 10 kN·m
σbottom = MPa

Answer key

  1. 1. ȳ = 21.39 mm
  2. 2. x̄ = 21.86 mm
  3. 3. r = 82.76 mm
  4. 4. Ix = 114.2 × 10⁶ mm⁴
  5. 5. Ix = 267.5 × 10⁶ mm⁴
  6. 6. σbottom = 20.87 MPa

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