Reinforced concrete - The Design of Prestressed Concrete Bridges - page 37

Figure 3.3 Stress-strain curve for high yield reinforcing steel
3.4 Reinforced concrete in bending
3.4.1 General
A reinforced concrete member has to satisfy both the Serviceability Limit State
and the Ultimate Limit State. The SLS criteria include considerations of defl ection,
vibration and of control of the width of cracks ( 3.5 ), while the ULS is principally
the consideration of the collapse of the member in bending, by yield of the steel or
crushing of the concrete, or in shear. Although beams are usually designed at the ULS,
the beam actually spends its life at working loads, and its performance at the SLS is
just as important.
Most correctly designed beams are 'under-reinforced' in bending. This means that
the steel reinforcement yields before the concrete crushes, and the mode of failure is
ductile. The simple methods described below are aimed at demystifying the preliminary
sizing of under-reinforced concrete members at the ULS. Clearly the detailed design
and verifi cation of a beam involve much more extensive and careful calculations, at
both the SLS and the ULS.
3.4.2 Preliminary sizing of bending reinforcement in beams and slabs
When designing a reinforced concrete beam to resist specifi ed superimposed loads, the
fi rst step is to guess a size. For a lightly loaded beam, the depth is likely to be of the
order of the span/20, while for more heavily loaded beams it may be twice that fi gure.
The width of the beam will be determined by the space required to accommodate the
reinforcement, by the shear stresses or by the need to provide an adequate area of
concrete in compression. This guessed size allows a dead load to be calculated, to give
a total load and a total bending moment. A preliminary calculation is then necessary
to make a fi rst estimate of the area of reinforcing steel required, and to check that the
depth and width of the beam are adequate.