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
xD = 190d = 166dimensions in mm

A circular tube has outside diameter D = 190 mm and inside diameter d = 166 mm. Find its second moment of area Ix about a diameter.

D = 190 mmd = 166 mm
Ix = × 10⁶ mm⁴
2.Easy
150 mm240 mm120 mm45 mmØ40x̄ = ?

A 150 mm × 240 mm plate has a circular hole of diameter 40 mm whose centre is 45 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 150 mmh = 240 mmd = 40 mmhole centre: x = 45 mm
x̄ = mm
3.Medium
1404002014xdimensions in mm

A symmetric I-section has flanges 140 mm wide and 20 mm thick, an overall depth of 400 mm and a web 14 mm thick. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

B = 140 mmH = 400 mmtf = 20 mmtw = 14 mm
Sx = × 10³ mm³
4.Medium
2504801412xdimensions in mm

A symmetric I-section has flanges 250 mm wide and 14 mm thick, an overall depth of 480 mm and a web 12 mm thick. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

B = 250 mmH = 480 mmtf = 14 mmtw = 12 mm
Sx = × 10³ mm³
5.Hard
2602526018xM = 30 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 30 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 260 mmtf = 25 mmtw = 18 mmhw = 260 mmM = 30 kN·m
σtop = MPa
6.Hard
1602018010xM = 40 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 40 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 160 mmtf = 20 mmtw = 10 mmhw = 180 mmM = 40 kN·m
σtop = MPa

Answer key

  1. 1. Ix = 26.7 × 10⁶ mm⁴
  2. 2. x̄ = 76.09 mm
  3. 3. Sx = 1284 × 10³ mm³
  4. 4. Sx = 1969 × 10³ mm³
  5. 5. σtop = 26.41 MPa
  6. 6. σtop = 111.6 MPa

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