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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
2201516018ȳ = ?dimensions in mm

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

bf = 220 mmtf = 15 mmtw = 18 mmhw = 160 mm
ȳ = mm
2.Easy
b = 200h = 325xdimensions in mm

A rectangular section has width b = 200 mm and height h = 325 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 200 mmh = 325 mm
Sx = × 10³ mm³
3.Medium
B = 240H = 400t = 10xdimensions in mm

A hollow rectangular (box) section has outer width B = 240 mm, outer height H = 400 mm and a uniform wall thickness t = 10 mm. Find its radius of gyration r about the horizontal centroidal axis.

B = 240 mmH = 400 mmt = 10 mm
r = mm
4.Medium
200 mm150 mm90 mmØ50xIx​ = ?

A 200 mm × 150 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 90 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 200 mmh = 150 mmd = 50 mmhole centre: y = 90 mm
Ix = × 10⁶ mm⁴
5.Hard
2601526010xM = 5 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 5 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 260 mmtf = 15 mmtw = 10 mmhw = 260 mmM = 5 kN·m
σtop = MPa
6.Hard
2401024014xM = 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 = 240 mmtf = 10 mmtw = 14 mmhw = 240 mmM = 25 kN·m
σtop = MPa

Answer key

  1. 1. ȳ = 126.7 mm
  2. 2. Sx = 3521 × 10³ mm³
  3. 3. r = 148.7 mm
  4. 4. Ix = 55.47 × 10⁶ mm⁴
  5. 5. σtop = 7.068 MPa
  6. 6. σtop = 51.23 MPa

Full step-by-step solutions: practise this topic on examproblems.com.