# Working Stress Method

## Permissible Stresses in Steel Reinforcement:

Permissible stresses in steel reinforcement for dissimilar grades of steel, diameters of bars and the types of stress in steel reinforcement are provided in IS 456.  Involving values of permissible stresses of steel of grade (Fe 250) mild steel and (Fe 415) high yield strength deformed bars in tension (σst and σsh) and compression in column (σsc) are enhanced. It may be written from the values that the factor of safety in steel for these stresses is about 1.8 much less than concrete due to high-quality control during the manufacture of steel in the industry in differentiation to make concrete.

Type of stress                            Mild steel bars,         High yield                                                                        Fe 250                strength                                                                                                       deformed                                                                                                         bars,

(N/mm2)          Fe415(N/mm2)

Tension σstorσss

(a) up to and including                      140                                   230

20 mm diameter

(b) over 20 mm diameter                 130                                    230

## Permissible Stresses in Concrete:

The permissible stress of concrete in direct tension is indicated by σtd.

The permissible stresses of concrete in bending compression σcbc and indirect compression σcc.  The mean bond for plain bars in tension τbd is provided for various grades of concrete. The Table presents these values for select grades of concrete, as a good remark. The components of the safety of concrete in bending compression, direct compression and the average bond for plain bars are 3, 4 and from 25 to 35, respectively. For plain bars in compression, the values of mean bond stress are acquired by getting bigger the respective value in tension by 25 percent. For deformed bars, the values are to be increased by 60 percent.

## # Modular Ratio (m):

In the reinforced concrete structure, concrete and reinforcing steel are converted into one material. This is done by modification using the modular ratio (m) which is the ratio of modulus of elasticity of both steel and concrete.

m = Es/Ec.

where Es is the modulus of elasticity of steel which is about 200000 N/mm2. However, concrete has different modules, as concrete is not a perfectly elastic material. The limit modulus of concrete is       Ec = 5000 fck in N/mm2, where fck is the characteristic strength of concrete. The short-term modulus does not take into account the effects of creep, shrinkage and other long-term effects. According, to the modular ratio (m), is not calculated as m = Es/Ec

m = 200000/(500), m=400

## Assumptions for  Working Stress Method:

The working stress method is established on elastic theory, where the following assumptions are made which are as follows:

(a) The plane sections before bending remain plane after bending also.

(b) Concrete is not good for taking the tensile stresses except otherwise specifically permitted. Therefore, all tensile stresses are upheld by reinforcement only.

(c) The stress-strain relationship of steel and concrete is a straight line below working loads.

(d) The modular ratio m has a value of about 280/3σcbc

where σcb cis the permissible compressive stress in concrete because of bending in N/mm2

The values of σcbc are given in IS 456.