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
1402518010ȳ = ?dimensions in mm

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

bf = 140 mmtf = 25 mmtw = 10 mmhw = 180 mm
ȳ = mm
2.Easy
240 mm240 mm120 mm60 mmØ50x̄ = ?

A 240 mm × 240 mm plate has a circular hole of diameter 50 mm whose centre is 60 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 240 mmh = 240 mmd = 50 mmhole centre: x = 60 mm
x̄ = mm
3.Medium
2602510010xdimensions in mm

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

bf = 260 mmtf = 25 mmtw = 10 mmhw = 100 mm
Ix = × 10⁶ mm⁴
4.Medium
200200t = 14ȳ = ?dimensions in mm

A channel section lies with its open side up: a base plate 200 mm wide with two upright legs, 200 mm high overall. Base and legs are all 14 mm thick. Find the height ȳ of the centroid above the bottom edge.

b = 200 mmh = 200 mmt = 14 mm
ȳ = mm
5.Hard
1401510014xM = 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 = 140 mmtf = 15 mmtw = 14 mmhw = 100 mmM = 25 kN·m
σtop = MPa
6.Hard
130300161901810xdimensions in mm

A welded I-section has a top flange 130 × 16 mm, a web 190 mm high and 10 mm thick, and a bottom flange 300 × 18 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 130 × 16 mmweb: 10 × 190 mmbottom flange: 300 × 18 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 157.7 mm
  2. 2. x̄ = 122.1 mm
  3. 3. Ix = 4.557 × 10⁶ mm⁴
  4. 4. ȳ = 72.03 mm
  5. 5. σtop = 191.4 MPa
  6. 6. Ix = 73.52 × 10⁶ mm⁴

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