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

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

2.Easy

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

b_f = 220 mmt_f = 30 mmt_w = 12 mmh_w = 240 mm

ȳ = mm

3.Medium

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

b_f = 200 mmt_f = 20 mmt_w = 10 mmh_w = 120 mm

I_x = × 10⁶ mm⁴

4.Medium

A 200 mm × 240 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 72 mm above the bottom. Find the second moment of area I_x about the horizontal axis through the centroid.

b = 200 mmh = 240 mmd = 60 mmhole centre: y = 72 mm

I_x = × 10⁶ mm⁴

5.Hard

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 10 kN·m. Find the size of the bending stress σ_top at the top edge.

b_f = 100 mmt_f = 30 mmt_w = 16 mmh_w = 260 mmM = 10 kN·m

σ_top = MPa

6.Hard

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 50 kN·m. Find the bending stress σ_bottom at the bottom edge.

b_f = 220 mmt_f = 15 mmt_w = 8 mmh_w = 260 mmM = 50 kN·m

σ_bottom = MPa

Answer key

1. x̄ = 101.7 mm
2. ȳ = 214 mm
3. I_x = 6.096 × 10⁶ mm⁴
4. I_x = 222.8 × 10⁶ mm⁴
5. σ_top = 16.46 MPa
6. σ_bottom = 298.5 MPa

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