**Method of RCC design**

A reinforced concrete structure should be designed to satisfy the following design criteria-

Adequate safety required, in items of stiffness and durability

Reasonable economy for construction.

The following design methods are generally used for the design of RCC Structures.

The working stress method (WSM)

The ultimate load method (ULM)

The limit state method (LSM)

Working Stress Method (WSM)

This method is based upon linear elastic theory or depend on the classical elastic theory. This method ensured the adequate safety by suitably restricting the stress in the materials induced by the expected working leads on the structures. The basic assumption of linear elastic behaviour is considered justifiable since the specified permissible stresses are kept in well below the ultimate strength of the material. The ratio of the yield stress of the steel reinforcement or the concrete cube strength to the corresponding permissible or working stress value is usually called as factor of safety.

The WSM uses a factor of safety of about 3 with respect to the cube strength of concrete and a factor of safety of about 1.8 with respect to the yield strength of steel considered.

Ultimate load method (ULM)

This method is based on the ultimate strength of reinforced concrete at ultimate load is obtained by enhancing the service load by some factor called as load factor for giving a desired margin of safety .Hence the method is also referred to as the load factor method or the ultimate strength method.

In the ULM, the stress condition at the state of in pending collapse of the structure is analysed, thus using, the non-linear stress – strain curves of concrete and steel. The safely measure in the design is obtained by the use of the proper load factor. The satisfactory strength of performance at ultimate loads does not guarantee the satisfactory strength performance at ultimate loads does not guarantee the satisfactory serviceability performance at normal service loads.

Limit state method (LSM)

Limit states are the acceptable limits for the safety and serviceability requirements of the structure before failure occurs. The design of structures by this method will thus ensure that they will not reach limit states and will not become unfit for the use for which they are intended. It is worth mentioning that structures will not just fail or collapse by violating (exceeding) the limit states. Failure, therefore, implies that clearly defined limit states of structural usefulness has been exceeded.

Limit state are two types

Limit state of collapse

Limit state of serviceability.

Limit states of collapse

The limit state of collapse of the structure or part of the structure could be assessed from rupture of one or more critical sections and from bucking due to elastic bending, shear, torsion and axial loads at every section shall not be less than the appropriate value at that section produced by the probable most unfavourable combination of loads on the structure using the appropriate factor of safely.

Limit state of serviceability

Limit state of serviceability deals with deflection and crocking of structures under service loads, durability under working environment during their anticipated exposure conditions during service, stability of structures as a whole, fire resistance etc.

Characteristic and design values and partial safety factor

- Characteristic strength of the materials.

The word characteristic strength‘ means that value of the strength of material below which not more than minimum acceptable percentage of test results are expected to fall. The minimum acceptable percentage as 5% for reinforced concrete structures. This means that there is 5% for probability or chance of the actual strength being less than the characteristic strength value.

Figure 1: Frequency distribution curve for strength

Figure shows frequency distribution curve of strength material (concrete or steel). The value of K corresponding to 5% area of the curve is 1.65.

The design strength should be lower than the mean strength (fm) Characteristic strength = Mean strength –K x standard deviation or

fk=fm-KSd

Where, fk=characteristic strength of the material

fm=mean strength

K=constant =1.65

Sd=standard deviation for a set of test results.

The value of standard deviation (Sd) is given by

Sd

2

n 1

Where, δ=deviation of the individual test strength from the average or mean strength of n samples.

n= number of test results.

The recommended minimum value of n=30.

Characteristic strength of concrete

Characteristic strength of concrete is denoted by fck (N/mm2) and its value is different for different grades of concrete e.g. M 15, M25 etc. In the symbol ‗M‘ used for designation of concrete mix, refers to the mix and the number refers to the specified characteristic compressive strength of 150 mm size cube at 28 days expressed in N/mm2

Characteristic strength of steel

Until the relevant Indian Standard specification for reinforcing steel are modified to include the concept of characteristic strength, the characteristic value shall be assumed as the minimum yield stress or 0.2% proof stress specified in the relevant Indian Standard specification. The characteristic strength of steel designated by symbol fy (N/mm2)

Characteristic loads

The term ‗Characteristic load‘ means that values of load which has a 95% probability of not being exceeded during that life of the structure.

Figure 1.2Frequency distribution curve for load

The design load should be more than average load obtained from statistic, we have

Fk=Fm+KSd

Where, Fk=characteristic load;

Fm= mean load

K=constant=2.65;

Sd=standard deviation for the load.

Since data are not available to express loads in statistical terms, for the purpose of this standard, dead loads , imposed loads , wind loads, snow load and seismic forces shall be assumed as the characteristic loads.

Design strength of materials

The design strength of materials (fd) is given by

fd fk

m

Where, fk=characteristic strength of material.

m =partial safety factor appropriate to the material and the limit state being considered

Design loads

The design load ( Fd) is given by.

Fd=Fk./ f

f =partial safety factor appropriate to the nature of loading and the limit state being considered.

The design load obtained by multi plying the characteristic load by the partial safety factor for load is also known as factored load.

Partial safety factor ( m) for materials

When assessing the strength of a structure or structural member for the limit state of collapse, the values of partial safety factor, m should be taken as 1.15 for steel.

Thus, in the limit state method , the design stress for steel reinforcement is given by fy / ms = fy/1.15=0.87fy.

For design purpose the compressive strength of concrete in the structure shall be assumed to be 0.67 times the characteristic strength of concrete in cube and partial safety factor mc =1.5 shall be applied in addition to this. Thus, the design stress in concrete is given by

0.67 f ck / mc =0.67 f ck / 1.5 =0.446 fck

Partial safety factor for loads

Limit State of Serviceability

Limit state of collapse in flexure

The behaviour of reinforced concrete beam sections at ultimate loads has been explained in detail in previous section. The basic assumptions involved in the analysis at the ultimate limit state of flexure are listed here.

Plane sections normal to the beam axis remain plane after bending, i.e., in an initially straight beam, strain varies linearly over the depth of the section.

The maximum compressive strain in concrete (at the outermost fibre) cu shall be taken as

0.0035 in bending.

The relationship between the compressive stress distribution in concrete and the strain in concrete may be assumed to be rectangle, trapezoid, parabola or any other shape which results in prediction of strength in substantial agreement with the results of test. An acceptable stress-strain curve is given below in figure 1.6. For design purposes, the compressive strength of concrete in the structure shall be assumed to be 0.67 times the characteristic strength. The partial safety factor y, = 1.5 shall be applied in addition to this.

Figure Stress-strain curve for concrete

The tensile strength of the concrete is ignored.

The stresses in the reinforcement are derived from representative stress-strain curve for the

type of steel used. Typical curves are given in figure . For design purposes the partial safety factor m equal to 1.15 shall be applied.

The maximum strain in the tension reinforcement in the section at failure shall not be less

than:

f y/1.15 E

+0.002

s

Limiting Depth of Neutral Axis