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
120150t = 18ȳ = ?dimensions in mm

An L-shaped angle section has a horizontal leg 120 mm wide and a vertical leg 150 mm high (both measured overall). Both legs are 18 mm thick. Find the height ȳ of the centroid above the bottom edge.

B = 120 mmH = 150 mmt = 18 mm
ȳ = mm
2.Easy
1802020012ȳ = ?dimensions in mm

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

bf = 180 mmtf = 20 mmtw = 12 mmhw = 200 mm
ȳ = mm
3.Medium
20090t = 14xdimensions in mm

A channel section lies with its open side up: a base plate 200 mm wide with two upright legs, 90 mm high overall. Base and legs are all 14 mm thick. Find its second moment of area Ix about the horizontal axis x through its centroid.

b = 200 mmh = 90 mmt = 14 mm
Ix = × 10⁶ mm⁴
4.Medium
1402530016xdimensions in mm

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

bf = 140 mmtf = 25 mmtw = 16 mmhw = 300 mm
Ix = × 10⁶ mm⁴
5.Hard
1803028010xM = 50 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 50 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 180 mmtf = 30 mmtw = 10 mmhw = 280 mmM = 50 kN·m
σtop = MPa
6.Hard
1504201212xM = 200 kN·mdimensions in mm

A symmetric I-section has flanges 150 mm wide and 12 mm thick, an overall depth of 420 mm and a web 12 mm thick. It carries a bending moment of 200 kN·m about the axis x. Find the size of the bending stress σj at the junction of the web and the top flange.

B = 150 mmH = 420 mmtf = 12 mmtw = 12 mmM = 200 kN·m
σj = MPa

Answer key

  1. 1. ȳ = 48.29 mm
  2. 2. ȳ = 166 mm
  3. 3. Ix = 3.518 × 10⁶ mm⁴
  4. 4. Ix = 89.63 × 10⁶ mm⁴
  5. 5. σtop = 53.91 MPa
  6. 6. σj = 186.8 MPa

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