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 = 400dimensions in mm

A rectangular section has width b = 60 mm and height h = 400 mm. Find its second moment of area Ibase about the axis along its bottom edge.

b = 60 mmh = 400 mm
Ibase = × 10⁶ mm⁴
2.Easy
B = 280H = 350t = 10xdimensions in mm

A hollow rectangular (box) section has outer width B = 280 mm, outer height H = 350 mm and a uniform wall thickness t = 10 mm. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 280 mmH = 350 mmt = 10 mm
Ix = × 10⁶ mm⁴
3.Medium
120 mm200 mm130 mmØ60xIx​ = ?

A 120 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 = 120 mmh = 200 mmd = 60 mmhole centre: y = 130 mm
Ix = × 10⁶ mm⁴
4.Medium
2001030010xdimensions in mm

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

bf = 200 mmtf = 10 mmtw = 10 mmhw = 300 mm
Ix = × 10⁶ mm⁴
5.Hard
150 mm240 mm72 mm30 × 20xIx​ = ?

A 150 mm × 240 mm plate has a rectangular cut-out 30 mm wide and 20 mm high, centred on the vertical centre line with its centre 72 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 240 mmcut-out: 30 × 20 mmhole centre: y = 72 mm
Ix = × 10⁶ mm⁴
6.Hard
2003012020xM = 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 = 30 mmtw = 20 mmhw = 120 mmM = 20 kN·m
σtop = MPa

Answer key

  1. 1. Ibase = 1280 × 10⁶ mm⁴
  2. 2. Ix = 221.8 × 10⁶ mm⁴
  3. 3. Ix = 76.48 × 10⁶ mm⁴
  4. 4. Ix = 51.35 × 10⁶ mm⁴
  5. 5. Ix = 171.4 × 10⁶ mm⁴
  6. 6. σtop = 56.16 MPa

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