Multiple choice

A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2 respectively.

Ignoring the presence of tension reinforcement, find the value of load P in kN when the first flexure crack will develop in the beam.

  1. 4.5

  2. 5.0

  3. 6.6

  4. 7.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first flexure crack occurs when the extreme fiber stress reaches the modulus of rupture (bending tensile strength). Using the section modulus of the uncracked rectangular section, M = f * Z, where Z = (b * d^2) / 6. Solving for P gives 6.6 kN.

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