Doubly Reinforced Beam Design to BS 8110

According to BS 8110, the concrete strain is limited to 0.0035 and the yielding of steel is considered as 0.002 for x/d value of 0.5. When the reinforcement strain reaches 0.002, it starts to yield, at that pint strain of the concrete is 0.002. After reaching concrete strain to a value of 0.002, we start providing compression reinforcement for the section as if the strain of the concrete reaches to 0.0035 concrete will fail and it will be a brittle failure which does not give sufficient warning at collapse.

Design example
Design Data

Bending Moment     = 250 kNm
Shear Force               = 200 kN

Beam width               = 225 mm
Beam height             = 500 mm

Grade of the concrete = 25 N/mm2
Strength of the steel    = 460 N/mm2
Cover to R/F                 = 30 mm
Shear links diameter    = 10 mm

No redistribution of the moment is assumed.

Calculations

effective depth      = 500-30-10-20/2
                                    = 450 mm

                     K            = M/bd2fcu
                                    = 250×106/(225×3502x25)
                                    = 0.219

                     K            > K’ = 0.156

Hence, section is doubly reinforced.

find d’ which is distance to center of compression reinforcement form the compression face
Assume T16 as compression reinforcements.

                     d’            = 30+10+16/2
                                    = 48 mm

Area of compression reinforcement As’

                     As’          = (K-K’)fcubd/{0.95fy(d-d’)}
                                    = (0.219-0.156)25x225x450/{0.95×460(450-48)}
                                    = 277 mm2

Provide 2T16 as compression reinforcement.

                     Z             = d[0.5+{0.25-K’/0.9}1/2]
                                    = 450[0.5+{0.25-0.156/0.9}1/2]
                                    = 349.599 mm

                     As           = {(K’fcubd2 / (0.95fyZ)} +As’

                                    = 0.156x25x225x4502 / (0.95x460x349.599) + 277
                                    = 1592 mm2

Provide three 25 mm bars in one layer and two 12 mm bars in a other layer.

Bottom reinforcements 3T25 + 2T12
Compression reinforcements 2T12

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