# D. SP52-101-03 Beam Design Principles

Design of the multi-span reinforced concrete beam is performed according to the Russian design code SP52-101-2003 Concrete And Reinforced Concrete Structures Without Prestressing, 2004. The program computes required reinforcement areas and performs necessary RC detailing operations. The ultimate limit state and serviceability limit state verification as well as detailing requirements of the SP52-101-2003 are provided in this program.

Present Russian RC design code, SP52-101-2003 Concrete And Reinforced Concrete Structures Without Prestressing, coincides with 1990 CEB – FIB Model Code for Concrete Structures in the part of normal section analysis. However, shear and torsion analysis and cracking calculations are based on rather different principles.

## Design for Bending

Analytical model for planar bending is based on the following figure:

### Planar bending of RC section

where
 Rb = design strength of concrete Rs = design strength of steel x = depth of neutral axis, constrained by the limiting quantity , depending on steel strength

In the program the small value of the axial force can be taken into account, provided the compression force does not cause the neutral axis depth greater than the limiting value , and in the tension case, the hog zone remains compressed.

The bending strength of the section and the layout of the longitudinal reinforcing steel are interrelated through the effective depth of the section. The crack width limitation must also be taken into account when choosing the longitudinal reinforcement. On the other hand, one must try all possible load combinations having in mind the interaction of the axial force and bending moment.

Strength and crack width verification is performed for the set of design sections uniformly spaced in a span. The user can introduce additional checking points for each span where he presumes the existence the sharp maximum of the moment caused by the concentrated force. The critical load combination is defined by the maximum value of the required tension steel area for each design section. The sag- and hog-critical sections are defined by the maximum of required tension reinforcement. The layout of tension steel bars is defined for both sag- and hog-critical section of the beam.

All admissible bar diameters are tried during design of critical section; the diameter resulting in minimum steel area is adopted as optimal one. As the result, the optimum layout for critical sag reinforcement and critical hog reinforcement is obtained.

The tension bar layouts are produced only for critical sections. For other design sections, the bar layouts are obtained during bar curtailment procedure as illustrated in the following figure. Required steel areas, computed previously, are used during this procedure.

### Bars curtailment procedure. The additional tensile force due to shear ΔFtd is ignored according to SP52.

1. Envelope of MEd/z + NEd
2. acting tensile force Fs
3. resisting tensile force FRs

The use of this design method is restricted to beams with predominantly downward-directed loads, when maximum sag moments are located in about the middle of span and maximum hog moments (if any) are at the supports. In this case the provided steel areas at all design sections are straightforwardly obtained in the sequential bars curtailment procedure.

## Design for Shear

It is assumed that the shear resistance of member consists of the following two factors:

• concrete compression zone shear Qb

The contribution of inclined reinforcing steel is not considered.

### Shearing of RC member

The following formula is used to calculate crack width:

 acrc = φ1φ2ψs(σs/Es)ls

where
 σs = steel stress computed according to elastic formulas, excluding concrete tension zone ls = spacing of cracks φ1 = 1.0 for short term loading, = 1.4 for long term loading φ2 = 0.5 for high bond bars, = 0.8 for bars with plain surface ψs = factor allowing for steel-concrete interaction in the tension zone ≤ 1.0,

The spacing of cracks is calculated from the expression

 ls = 0.5(Abt/AS)ds

where
 Abt = concrete tension area AS = steel tension area ds = diameter of reinforcing bars

The torsional strength includes the contributions of both the longitudinal and transverse reinforcement.

The longitudinal reinforcement is checked according to strength and crack width conditions. The transverse bars must comply with the inclined sections strength and maximum allowable spacing conditions. Additionally, in the presence of torsion moments the combined action of bending, shear and torsion must be taken into account.

## Design Procedure

The design process is summarized by the following steps:

1. Find the sag- and hog-critical sections of the continuous beam, according to the maximum required tension steel area. Typically, these sections are situated at a support and at about the middle of a span.
2. Produce the layouts of tension reinforcing steel for these two critical sections.
3. Produce the derived layouts for all supports and most adverse middle span sections of each beam.
4. Carry out the reinforcing steel curtailment procedure for each span of the continuous beam.
5. Compute the required stirrup spacing for each section of the continuous beam. In the detailing procedure, the stirrup spacing may be manually defined for each part of the span.
6. The final strength check is performed for the obtained layout for each design section.

The assumptions adopted for the beam design procedure, can be summarized as follows:

1. The diameters of bottom and top reinforcing bars may be different; all bars in the bottom or top of the continuous beam are of the same diameter.
2. The sag- and hog-critical sections of the continuous beam are selected according to the most adverse load conditions; basic reinforcement layouts are produced for these two critical sections.
3. The diameters of the bars for the sag- and hog-critical reinforcement are chosen according to the minimum steel area criterion, within the reasonable boundaries you have imposed.
4. The tension bars compatibility is retained at support sections of the continuous beam. The sag bars layouts and diameters in each span can be different.
5. In each span of the continuous beam the derived layouts, compatible with the basic layouts, are to be produced.
6. Derived layouts are based on the same reinforcing bar diameters as basic ones.
7. Bar curtailment is based on the loading and strength conditions of the set of the beam cross-sections; these cross-sections must not coincide with definite nodes of the finite element mesh.