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
240 mm300 mm150 mm180 mmØ40x̄ = ?

A 240 mm × 300 mm plate has a circular hole of diameter 40 mm whose centre is 180 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 240 mmh = 300 mmd = 40 mmhole centre: x = 180 mm
x̄ = mm
2.Easy
150250t = 18x̄ = ?dimensions in mm

An L-shaped angle section has a horizontal leg 150 mm wide and a vertical leg 250 mm high (both measured overall). Both legs are 18 mm thick. Find the distance x̄ of the centroid from the left (outer) edge of the vertical leg.

B = 150 mmH = 250 mmt = 18 mm
x̄ = mm
3.Medium
xD = 140d = 112dimensions in mm

A circular tube has outside diameter D = 140 mm and inside diameter d = 112 mm. Find its radius of gyration r about the horizontal centroidal axis.

D = 140 mmd = 112 mm
r = mm
4.Medium
2602030014xdimensions in mm

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

bf = 260 mmtf = 20 mmtw = 14 mmhw = 300 mm
Ix = × 10⁶ mm⁴
5.Hard
1204402414xM = 120 kN·mdimensions in mm

A symmetric I-section has flanges 120 mm wide and 24 mm thick, an overall depth of 440 mm and a web 14 mm thick. It carries a bending moment of 120 kN·m about the axis x. Find the size of the maximum bending stress σmax in the section.

B = 120 mmH = 440 mmtf = 24 mmtw = 14 mmM = 120 kN·m
σmax = MPa
6.Hard
2401012016xsagging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 60 MPa in tension and 100 MPa in compression. Find the largest sagging bending moment Mallow the beam can carry.

bf = 240 mmtf = 10 mmtw = 16 mmhw = 120 mmσt,allow = 60 MPaσc,allow = 100 MPa
Mallow = kN·m

Answer key

  1. 1. x̄ = 118.9 mm
  2. 2. x̄ = 34.92 mm
  3. 3. r = 44.82 mm
  4. 4. Ix = 91.15 × 10⁶ mm⁴
  5. 5. σmax = 82.56 MPa
  6. 6. Mallow = 4.264 kN·m

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