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
xD = 210dimensions in mm

A solid circular bar has diameter D = 210 mm. Find its second moment of area Ix about a diameter.

D = 210 mm
Ix = × 10⁶ mm⁴
2.Easy
b = 200h = 175dimensions in mm

A rectangular section has width b = 200 mm and height h = 175 mm. Find its second moment of area Ibase about the axis along its bottom edge.

b = 200 mmh = 175 mm
Ibase = × 10⁶ mm⁴
3.Medium
150 mm150 mm105 mmØ50xIx​ = ?

A 150 mm × 150 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 105 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 150 mmd = 50 mmhole centre: y = 105 mm
Ix = × 10⁶ mm⁴
4.Medium
200 mm200 mm130 mmØ60xIx​ = ?

A 200 mm × 200 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 130 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 200 mmh = 200 mmd = 60 mmhole centre: y = 130 mm
Ix = × 10⁶ mm⁴
5.Hard
240201808xsagging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 60 MPa in tension and 120 MPa in compression. Find the largest sagging bending moment Mallow the beam can carry.

bf = 240 mmtf = 20 mmtw = 8 mmhw = 180 mmσt,allow = 60 MPaσc,allow = 120 MPa
Mallow = kN·m
6.Hard
260102208xM = 40 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 40 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 260 mmtf = 10 mmtw = 8 mmhw = 220 mmM = 40 kN·m
σbottom = MPa

Answer key

  1. 1. Ix = 95.47 × 10⁶ mm⁴
  2. 2. Ibase = 357.3 × 10⁶ mm⁴
  3. 3. Ix = 39.94 × 10⁶ mm⁴
  4. 4. Ix = 130 × 10⁶ mm⁴
  5. 5. Mallow = 5.437 kN·m
  6. 6. σbottom = 340.1 MPa

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