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 mm72 mmØ80x̄ = ?

A 240 mm × 300 mm plate has a circular hole of diameter 80 mm whose centre is 72 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 240 mmh = 300 mmd = 80 mmhole centre: x = 72 mm
x̄ = mm
2.Easy
b = 200h = 200dimensions in mm

A rectangular section has width b = 200 mm and height h = 200 mm. Find its second moment of area Ibase about the axis along its bottom edge.

b = 200 mmh = 200 mm
Ibase = × 10⁶ mm⁴
3.Medium
B = 240H = 325t = 14xdimensions in mm

A hollow rectangular (box) section has outer width B = 240 mm, outer height H = 325 mm and a uniform wall thickness t = 14 mm. Find its radius of gyration r about the horizontal centroidal axis.

B = 240 mmH = 325 mmt = 14 mm
r = mm
4.Medium
1401012018xdimensions in mm

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

bf = 140 mmtf = 10 mmtw = 18 mmhw = 120 mm
Ix = × 10⁶ mm⁴
5.Hard
120260183802214xdimensions in mm

A welded I-section has a top flange 120 × 18 mm, a web 380 mm high and 14 mm thick, and a bottom flange 260 × 22 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 120 × 18 mmweb: 14 × 380 mmbottom flange: 260 × 22 mm
Ix = × 10⁶ mm⁴
6.Hard
1402012020xM = 10 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 10 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 140 mmtf = 20 mmtw = 20 mmhw = 120 mmM = 10 kN·m
σtop = MPa

Answer key

  1. 1. x̄ = 123.6 mm
  2. 2. Ibase = 533.3 × 10⁶ mm⁴
  3. 3. r = 122 mm
  4. 4. Ix = 6.193 × 10⁶ mm⁴
  5. 5. Ix = 341.7 × 10⁶ mm⁴
  6. 6. σtop = 45.46 MPa

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