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 = 180h = 425xdimensions in mm

A rectangular section has width b = 180 mm and height h = 425 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 180 mmh = 425 mm
Sx = × 10³ mm³
2.Easy
xD = 130d = 102dimensions in mm

A circular tube has outside diameter D = 130 mm and inside diameter d = 102 mm. Find its second moment of area Ix about a diameter.

D = 130 mmd = 102 mm
Ix = × 10⁶ mm⁴
3.Medium
200 mm240 mm144 mmØ50xIx​ = ?

A 200 mm × 240 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 144 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 200 mmh = 240 mmd = 50 mmhole centre: y = 144 mm
Ix = × 10⁶ mm⁴
4.Medium
2401014018xdimensions in mm

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

bf = 240 mmtf = 10 mmtw = 18 mmhw = 140 mm
Ix = × 10⁶ mm⁴
5.Hard
1704801414xM = 150 kN·mdimensions in mm

A symmetric I-section has flanges 170 mm wide and 14 mm thick, an overall depth of 480 mm and a web 14 mm thick. It carries a bending moment of 150 kN·m about the axis x. Find the size of the maximum bending stress σmax in the section.

B = 170 mmH = 480 mmtf = 14 mmtw = 14 mmM = 150 kN·m
σmax = MPa
6.Hard
120252408xM = 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 bending stress σbottom at the bottom edge.

bf = 120 mmtf = 25 mmtw = 8 mmhw = 240 mmM = 20 kN·m
σbottom = MPa

Answer key

  1. 1. Sx = 5419 × 10³ mm³
  2. 2. Ix = 8.706 × 10⁶ mm⁴
  3. 3. Ix = 228.9 × 10⁶ mm⁴
  4. 4. Ix = 11.05 × 10⁶ mm⁴
  5. 5. σmax = 98.3 MPa
  6. 6. σbottom = 134.2 MPa

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