### Bond stress and Development length

When the steel bars are embedded in concrete, the concrete after setting, adheres to the surface of the bars and resist any force that tends to pull or push this rod. The intensity of the adhesive force is called bond stress. It is the longitudinal shear stress acting on the surface between the steel and the concrete. The term bond  is used to describe the means by which slip between the steel and concrete is prevented. The bond is provided by anchoring the bars properly and extending the bars beyond the point of maximum shear.
OR
Bond stress is defined as the shear force per unit of Nominal surface area of a reinforcement bar acting parallel to the bar on the interface between the bars and surrounding concrete.
The bond between steel and concrete is mainly due to pure adhesive resistance, frictional resistance and mechanical resistance.
The bond stress developed in concrete around the steel reinforcement is given by

#### Design bond stress

• For deformed bars these values shall be increased by 60 percent.
• For bars in compression can be increased by 25 percent.

### Development length ( Ld)

Whenever some reinforcing bar is to anchored or two bars have to be given an overlap, it is essential that they must get sufficient length of embedment or overlap as the case may be, so that no slippage takes place. The length of embedment or overlap ( also known as development length or anchorage) is given by

Some Important Points:-
1. The deformed bars may be used without end anchorages (i.e. hooks) provided development length required is satisfied. The hooks should normally be provided for plain bars in tension.
2. When hooks are formed in deformed bars, the internal radius of the bend should be at least three times the diameter of the bar. The length of the straight bar beyond the end of the curve should be at least four times the diameter of bar.
3. The anchorage value of a standard U-type hook alone is equal to 16d, where d is diameter of a reinforcement bar.
4. The length of lap for reinforcement bars in tension shall not be less than Ld or 30d, whichever is greater
5. The length of lap for reinforcement bars in compression shall not be less than Ld or 24d, whichever is greater
6. When bars of two different diameters are to be spliced, the length of lap shall be calculated on the basis of diameter of the smaller bar.
7. The bond length  used for splicing bar in tension, for M15 grade concrete is equal to 58d, where d is diameter of reinforcing bar
8. The measurement of anchorage lengths of inclined bars, used to act as shear reinforcement is taken in tension zone from the end of the sloping portion of the bar and in compression zone from mid-depth of the beam.
9. The minimum spacing between horizontal parallel reinforcement of the same diameter should not be less than the diameter of bar.

### Correction due to curvature and refraction AND combined correction in surveying

In geodetic surveying, error due to curvature and refraction is taken into action when the area is greater than 256 km²   Correction due to curvature (Cc)             Error due to curvature is taken into action because during leveling with theodolite    or Autolevel the horizontal line and level line do not coincide. Level line is curved line parallel to the earth surface and horizontal line is straight line.               this correction is given by Cc =0.07849 d² OR 0.0785d²                                                                 here, d is the linear distance (in km)   Correction due to refraction (Cr)             Error due to refraction is taken into action due to the changing of medium of light either from a denser medium to lightier medium or viceversa.                    it is 1/7 of correction due to curvature                                               1/7x(0.785 d²)                                                   it is equals to 0.112d²

### Prestressed concrete

The basic concept of prestresssing the concrete consists in introducing the artificially the compressive stresses in a structure before it is loaded. The tensile stresses in the prestressed concrete structure may be reduced to a great extent or even entirely eliniminated depending upon the magnitude of prestressing. In a prestressed concrete structure, the cost of supporting structure and foundation is reduced, dead load of structure is reduced and cracking of concrete is avoided. The high strength concrete and high tensile steel should be used in a prestressed concrete member. According to Indian standards, the cube strength of the concrete used should bot be less  than 35N/mm 2 . The ultimate strength of high tensile steel wires used in prestressing varies from 1500N/mm 2 for 8mm diameter bars to 2350N/mm 2 for 1.5 mm diameter bars. The various methods adopted in prestresssing are as follows: Pre-tensioning The method of providing desired amount of compressive stress in

### Estimation of maximum flood discharge

The following empirical formulae may be adopted to compute the maximum flood discharge: Dicken's formula Ryve's formula Inglis formula Nawab Jang Bahadur formula Fanning's formula Fuller's formula  1) Dicken's formula According to Dicken's formula, the flood discharge (Q) in cumecs is given by The value of C taken as 11.4 for Northern India, 13.9 to 19.5 to Central India and 22.5 to 25 for Western Ghats 2) Ryve's formula According to Ryve's formula, for Madras catchments, the flood discharge (Q) in cumecs is given by The value of C is taken as 6.75 for areas within 24 km from the coast, 8.45 for areas within 24 km to 161 km form the coast and 10.1 for limited areas near hills 3) Inglis formula According to Inglis formula, the flood discharge (Q) in cumecs is given by This formula is used for estimating flood discharge for the catchments of former Bombay presidency. 4) Nawab Jang Bahadur formula According to Nawab Ja