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
200 mm240 mm60 mmØ30ȳ = ?

A 200 mm × 240 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 60 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 200 mmh = 240 mmd = 30 mmhole centre: y = 60 mm
ȳ = mm
2.Easy
b = 160h = 175xdimensions in mm

A rectangular section has width b = 160 mm and height h = 175 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 160 mmh = 175 mm
Sx = × 10³ mm³
3.Medium
200 mm300 mm180 mmØ50xIx​ = ?

A 200 mm × 300 mm plate has a circular hole of diameter 50 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 = 200 mmh = 300 mmd = 50 mmhole centre: y = 180 mm
Ix = × 10⁶ mm⁴
4.Medium
xD = 300d = 280dimensions in mm

A circular tube has outside diameter D = 300 mm and inside diameter d = 280 mm. Find its radius of gyration r about the horizontal centroidal axis.

D = 300 mmd = 280 mm
r = mm
5.Hard
280152808xM = 25 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 25 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 280 mmtf = 15 mmtw = 8 mmhw = 280 mmM = 25 kN·m
σtop = MPa
6.Hard
200 mm300 mm210 mm60 × 50xIx​ = ?

A 200 mm × 300 mm plate has a rectangular cut-out 60 mm wide and 50 mm high, centred on the vertical centre line with its centre 210 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 200 mmh = 300 mmcut-out: 60 × 50 mmhole centre: y = 210 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 120.9 mm
  2. 2. Sx = 816.7 × 10³ mm³
  3. 3. Ix = 447.9 × 10⁶ mm⁴
  4. 4. r = 102.6 mm
  5. 5. σtop = 31.62 MPa
  6. 6. Ix = 438 × 10⁶ mm⁴

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