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Splitting tensile strength of cylinder and cube (500 kN)

Short answer

For cylinder: f_sp = 2P/(pi L d) = 2*500000/(pi*300*150) = 7.07 N/mm^2. For cube: f_sp = 2P/(pi a^2) = 2*500000/(pi*150^2) = 14.15 N/mm^2. The cube value is higher due to the smaller loaded plane.

Calculate the splitting tensile strength of a concrete cylinder (300 mm ×\times 150 mm dia) and a cube (150 mm ×\times 150 mm ×\times 150 mm) under the standard splitting test, if the load shown by the testing machine is 500 kN.

Formulae: cylinder fsp=2PπLdf_{sp} = \dfrac{2P}{\pi L d}; cube (load along the centre line of a face) fsp=2Pπa2f_{sp} = \dfrac{2P}{\pi a^2}, where aa is the side.

P=500P = 500 kN =500 000= 500\,000 N.

Cylinder 300 mm × 150 mm dia

fsp=2×500000π×300×150=1000000141371.7=7.07 N/mm2f_{sp} = \frac{2\times500000}{\pi\times300\times150} = \frac{1000000}{141371.7} = 7.07\ \text{N/mm}^2

Cube 150 mm

fsp=2×500000π×150×150=100000070685.8=14.15 N/mm2f_{sp} = \frac{2\times500000}{\pi\times150\times150} = \frac{1000000}{70685.8} = 14.15\ \text{N/mm}^2

Answer: cylinder 7.07 N/mm2^2; cube 14.15 N/mm2^2. The cube gives the higher value because the same load acts over a smaller splitting plane (150 × 150 mm against 300 × 150 mm). The cylinder result is the standard one.

✓ Answer checked by Claude Sonnet 5.5

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