1.Easy
A rectangular section has width b = 200 mm and height h = 425 mm. Find its second moment of area Ibase about the axis along its bottom edge.
b = 200 mmh = 425 mm
Ibase = × 10⁶ mm⁴
Centroid & second moment of area worksheet with answers
2.Easy
A 150 mm × 200 mm plate has a circular hole of diameter 60 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 = 200 mmd = 60 mmhole centre: x = 45 mm
x̄ = mm
3.Medium
Find the second moment of area Ix of the T-section about the horizontal axis x through its centroid.
bf = 180 mmtf = 25 mmtw = 16 mmhw = 140 mm
Ix = × 10⁶ mm⁴
4.Medium
A 100 mm × 300 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 105 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 100 mmh = 300 mmd = 30 mmhole centre: y = 105 mm
Ix = × 10⁶ mm⁴
5.Hard
A welded I-section has a top flange 200 × 24 mm, a web 170 mm high and 16 mm thick, and a bottom flange 290 × 20 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.
top flange: 200 × 24 mmweb: 16 × 170 mmbottom flange: 290 × 20 mm
Ix = × 10⁶ mm⁴
6.Hard
A symmetric I-section has flanges 200 mm wide and 12 mm thick, an overall depth of 260 mm and a web 12 mm thick. It carries a bending moment of 100 kN·m about the axis x. Find the size of the maximum bending stress σmax in the section.
B = 200 mmH = 260 mmtf = 12 mmtw = 12 mmM = 100 kN·m
σmax = MPa
Answer key
- 1. Ibase = 5118 × 10⁶ mm⁴
- 2. x̄ = 78.12 mm
- 3. Ix = 14.07 × 10⁶ mm⁴
- 4. Ix = 223.5 × 10⁶ mm⁴
- 5. Ix = 103.9 × 10⁶ mm⁴
- 6. σmax = 149.4 MPa
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