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
200 mm200 mm100 mm60 mmØ40x̄ = ?

A 200 mm × 200 mm plate has a circular hole of diameter 40 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 = 200 mmh = 200 mmd = 40 mmhole centre: x = 60 mm
x̄ = mm
2.Easy
200190t = 20x̄ = ?dimensions in mm

An L-shaped angle section has a horizontal leg 200 mm wide and a vertical leg 190 mm high (both measured overall). Both legs are 20 mm thick. Find the distance x̄ of the centroid from the left (outer) edge of the vertical leg.

B = 200 mmH = 190 mmt = 20 mm
x̄ = mm
3.Medium
200180t = 20xdimensions in mm

A channel section lies with its open side up: a base plate 200 mm wide with two upright legs, 180 mm high overall. Base and legs are all 20 mm thick. Find its second moment of area Ix about the horizontal axis x through its centroid.

b = 200 mmh = 180 mmt = 20 mm
Ix = × 10⁶ mm⁴
4.Medium
1203022014xdimensions in mm

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

bf = 120 mmtf = 30 mmtw = 14 mmhw = 220 mm
Ix = × 10⁶ mm⁴
5.Hard
110260102301612xdimensions in mm

A welded I-section has a top flange 110 × 10 mm, a web 230 mm high and 12 mm thick, and a bottom flange 260 × 16 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 110 × 10 mmweb: 12 × 230 mmbottom flange: 260 × 16 mm
Ix = × 10⁶ mm⁴
6.Hard
1201014012xhogging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 50 MPa in tension and 100 MPa in compression. Find the largest hogging bending moment Mallow the beam can carry (give its size).

bf = 120 mmtf = 10 mmtw = 12 mmhw = 140 mmσt,allow = 50 MPaσc,allow = 100 MPa
Mallow = kN·m

Answer key

  1. 1. x̄ = 101.3 mm
  2. 2. x̄ = 58.65 mm
  3. 3. Ix = 33.73 × 10⁶ mm⁴
  4. 4. Ix = 38.63 × 10⁶ mm⁴
  5. 5. Ix = 73.07 × 10⁶ mm⁴
  6. 6. Mallow = 6.609 kN·m

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