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
1002028018ȳ = ?dimensions in mm

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

bf = 100 mmtf = 20 mmtw = 18 mmhw = 280 mm
ȳ = mm
2.Easy
B = 160H = 350t = 16xdimensions in mm

A hollow rectangular (box) section has outer width B = 160 mm, outer height H = 350 mm and a uniform wall thickness t = 16 mm. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 160 mmH = 350 mmt = 16 mm
Ix = × 10⁶ mm⁴
3.Medium
xD = 170d = 138dimensions in mm

A circular tube has outside diameter D = 170 mm and inside diameter d = 138 mm. Find its radius of gyration r about the horizontal centroidal axis.

D = 170 mmd = 138 mm
r = mm
4.Medium
B = 300H = 375t = 14xdimensions in mm

A hollow rectangular (box) section has outer width B = 300 mm, outer height H = 375 mm and a uniform wall thickness t = 14 mm. Find its radius of gyration r about the horizontal centroidal axis.

B = 300 mmH = 375 mmt = 14 mm
r = mm
5.Hard
180290103701016xdimensions in mm

A welded I-section has a top flange 180 × 10 mm, a web 370 mm high and 16 mm thick, and a bottom flange 290 × 10 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 180 × 10 mmweb: 16 × 370 mmbottom flange: 290 × 10 mm
Ix = × 10⁶ mm⁴
6.Hard
2801022018xM = 30 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 30 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 280 mmtf = 10 mmtw = 18 mmhw = 220 mmM = 30 kN·m
σbottom = MPa

Answer key

  1. 1. ȳ = 182.6 mm
  2. 2. Ix = 228.7 × 10⁶ mm⁴
  3. 3. r = 54.74 mm
  4. 4. r = 143.2 mm
  5. 5. Ix = 233.1 × 10⁶ mm⁴
  6. 6. σbottom = 125.5 MPa

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