1.Easy
A 200 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 = 200 mmh = 240 mmd = 50 mmhole centre: x = 60 mm
x̄ = mm
Centroid & second moment of area worksheet with answers
2.Easy
Find the height ȳ of the centroid of the T-section above its bottom edge.
bf = 100 mmtf = 30 mmtw = 12 mmhw = 180 mm
ȳ = mm
3.Medium
A 150 mm × 240 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 168 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 150 mmh = 240 mmd = 50 mmhole centre: y = 168 mm
Ix = × 10⁶ mm⁴
4.Medium
A circular tube has outside diameter D = 190 mm and inside diameter d = 182 mm. Find its radius of gyration r about the horizontal centroidal axis.
D = 190 mmd = 182 mm
r = mm
5.Hard
A 200 mm × 240 mm plate has a rectangular cut-out 30 mm wide and 20 mm high, centred on the vertical centre line with its centre 168 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 200 mmh = 240 mmcut-out: 30 × 20 mmhole centre: y = 168 mm
Ix = × 10⁶ mm⁴
6.Hard
A symmetric I-section has flanges 160 mm wide and 10 mm thick, an overall depth of 360 mm and a web 6 mm thick. It carries a bending moment of 80 kN·m about the axis x. Find the size of the maximum bending stress σmax in the section.
B = 160 mmH = 360 mmtf = 10 mmtw = 6 mmM = 80 kN·m
σmax = MPa
Answer key
- 1. x̄ = 101.7 mm
- 2. ȳ = 151 mm
- 3. Ix = 167.7 × 10⁶ mm⁴
- 4. r = 65.78 mm
- 5. Ix = 229 × 10⁶ mm⁴
- 6. σmax = 122.4 MPa
Full step-by-step solutions: practise this topic on examproblems.com.