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 = 140h = 125xdimensions in mm

A rectangular section has width b = 140 mm and height h = 125 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 140 mmh = 125 mm
Sx = × 10³ mm³
2.Easy
1001518016ȳ = ?dimensions in mm

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

bf = 100 mmtf = 15 mmtw = 16 mmhw = 180 mm
ȳ = mm
3.Medium
1802512018xdimensions in mm

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

bf = 180 mmtf = 25 mmtw = 18 mmhw = 120 mm
Ix = × 10⁶ mm⁴
4.Medium
150 mm240 mm72 mmØ40xIx​ = ?

A 150 mm × 240 mm plate has a circular hole of diameter 40 mm on its 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 mmd = 40 mmhole centre: y = 72 mm
Ix = × 10⁶ mm⁴
5.Hard
1001520018xM = 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 = 100 mmtf = 15 mmtw = 18 mmhw = 200 mmM = 20 kN·m
σtop = MPa
6.Hard
160302408xM = 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 = 160 mmtf = 30 mmtw = 8 mmhw = 240 mmM = 25 kN·m
σtop = MPa

Answer key

  1. 1. Sx = 364.6 × 10³ mm³
  2. 2. ȳ = 123.4 mm
  3. 3. Ix = 10.5 × 10⁶ mm⁴
  4. 4. Ix = 169.7 × 10⁶ mm⁴
  5. 5. σtop = 68.73 MPa
  6. 6. σtop = 38.74 MPa

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