A cantilever beam of rectangular section 250mm wide and 500mm overall depth has to carry an udl of 30kN/m (inclusive of self weight) over an effective span of 3.5 metre. M25 grade concrete and Fe415 grade steel are to be used. Design the reinforcement for flexure by limit state method.
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Solution:
(i) Characteristics strength of concrete, fck=20 N/mm2
(ii) Characteristics strength of reinforcing steel, fy=415 N/mm2
(iii) Width, b=250 mm
(iv) Effective depth, d=317 mm
(v) Neutral axis factor, xub
d
=
c
c+s
=
0.0035
0.0035+0.0038
=0.48
(vi) Coefficient, Qub
=k1
xub
d
(1 − k2
xub
d
)
=0.36 × 0.48 × (1 − 0.42 × 0.48)
=0.138
(vii) Moment of resistance due to concrete, Mucb
=Qub f ck b d2
=0.138 × 20 × 250 × 3172
=69.395 kNm
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