Doubly Reinforced Beams – BS 8110:1:1997 – Example 1

a) A reinforced concrete beam has a rectangular section of breadth b = 225 mm and effective depth d = 450 mm. It has to carry a design moment of 300.0 kNm. Show that compression reinforcement will be required.  

f_cu = 30 N/mm², f_y = 460 N/mm².

b) Calculate the number of 16 mm diameter steel bars that will be required as compression reinforcements. The distance of the center of compression reinforcement from the compression concrete surface may be taken as 40 mm.

c) Calculate the number of 25 mm diameter steel bars that will be required as tensile reinforcements.

Answer:

Given              b = 225 mm,               d = 450 mm,               d^’ = 40 mm,

M = 300.0 kNm,          f_cu= 30 N/mm²,          f_y=460 N/mm²

a)                     M         =          300.0 kNm      =          300 x 10⁶ Nmm

                                    Therefore, compression reinforcement will be required.

The compression steel will yield and the stress is equal to 0.95f_y.

*        The force in the compression reinforcement is dependent on the stress and consequently the strain ζ_cs. In order to ensure that this is greater than or equal to the yield stress, the ratio of (d′/x) is limited to 0.37 as shown below.

This value is given as 0.37 in the code to accommodate redistribution of moments in excess of 10%.