*Singly Reinforced Beam: *

*Singly Reinforced Beam:*

*The beam that is long reinforced only in tension zone, it is called a singly reinforced beam. In Such beams, the* concluding bending moment and the tension due to bending are taken* by the reinforcement, while the compression is taken by the concrete.*

*Singly reinforced beams are utilized in any building framed as well as composite structures. The main profit of a single reinforced beam is that it decreases the economy. It is utilized when there is no need for **appending the steel reinforcement in the compression zone.*

* **Practically, it is impossible to give reinforcement only in the tension zone, because we need to tie the stirrups. Therefore, two rebars are used in the compression zone to tie the stirrups and the rebars act as wrong members just for** possessions the stirrups.*

**ASSUMPTIONS OF SINGLY REINFORCED BEAM: **

**ASSUMPTIONS OF SINGLY REINFORCED BEAM:**

- The plane before bending remains the same as plane after bending, at any cross-section.
- All tensile stresses are taken up by steel reinforcement and not by concrete.
- The stress to strain relationship of steel and concrete below the functioning load is a straight line.
- The modular ratio (m) has a value of 280/3σcbc.
- There is a perfect union between steel and concrete and no-slip hold place between steel and concrete.

**Calculate the moment of resistance (M.O.R) of an Reinforced Concrete beam 250mm wide, the depth of the centre of reinforcement being 500mm. Assume σcbc = 5N/mm2, σst = 140 N/mm2 and modular ratio = 18.66**

#### Given that,

b = width of the beam = 250mm

d = depth of the beam = 500mm

σ_{cbc} = 5N/mm^{2}

σ_{st} = 140 N/mm^{2 }

m = 18.66

**To calculate Neutral Axis (NA)**

σ

_{cbc}/(σ_{st}/m) = x_{c}/(d – x_{c})

5/(140/18.66) = x_{c}/(500 – x_{c})

X_{c} = 199.95mm = 200mm

*To calculate lever arm*

z = d – x

_{c}/3

= 500 – 200/3

= 433.33mm

**To calculate Moment of resistance**

M

_{r}= C x z= bx

_{c}(σ_{cbc}/2)z

= 250 x 200 x 5/2 x 433.33

= 54166250 N-mm

= 54.166 kN-m

OR

M

_{r}= T x z= A

_{st}. σ_{st}.z…………………equation 1

**To calculate A _{st}**

Equating, C = T

bx

_{c}.σ_{cbc}/2 = A_{st}. σ_{st}Therefore, A

_{st}= bx_{c}.σ_{cbc}/2 σ_{st}

A_{st} = (250 x 200 x 5/2)/140

A_{st }= 892.85 mm2

**Substituting the value of A _{st} in equation 1;**

M

_{r}= T x z= A

_{st}. σ_{st}.z

= 892.85 x 140 x 433.33

= 54165817 N-mm

= 54.1658 kN-m

**Doubly Reinforced Beams**

**Doubly Reinforced Beams**

Concrete has high compressive strength and almost negligible tensile strength. steel reinforcement is utilized on the tensile side of the concrete. Thus, singly reinforced beams reinforced on the tensile are best in both compression and tension. These beams have their individual limiting moments of resistance with detailed width, depth, and grades of concrete, steel. The amount of steel reinforcement needed is called as Ast,lim. The problem will increase if such a section is experienced to bending moment greater than its limiting moment of resistance as a singly reinforced section. There are two ways to answer this problem. First, we may arise in the depth of the beam, which may not be feasible in more situations. In those cases, it is possible to arise both the compressive and tensile forces of the beam by admitting steel reinforcement in compression face and additional reinforcement in the tension face of the beam without arising the depth. The total compressive force of these beams contain:

(i) force due to concrete in compression

(ii) force due to steel in compression.

**The tensile force has two components: **

(i) The first provided by Ast,lim which is uniform to the compressive force of concrete in compression.

(ii) this is due to the sum of steel in tension, its force will be uniform to the compressive force of steel in compression. Those reinforced concrete beams having steel reinforcement both on tensile and compressive faces are called doubly reinforced beams. Doubly reinforced beams have a moment of resistance more than the singly reinforced beams of a similar depth for particular grades of steel and concrete. Many architectural or functional needed may restrict the overall depth of the beams.

**Differently in doubly reinforced beams compression steel reinforcement is acceptable when:**

(i) A few sections of an unceasing beam with active loads undergo a change of sign of the bending moment which manufactures compression zone as tension zone or vice versa.

(ii)The ductility requirement has to be followed.

(iii)The reduction of long term deflection is needed. It may be detailed that even in so, called singly reinforced beams there could be a long hanger reinforced bars in the compression zone for locating and fixing stirrups.

* The assumption made by the doubly reinforced beam is as follows:*

In the case of doubly reinforced beam:

- First of all, concrete is completely neglected.
- The value of the moment of resistance is taken equal to the amount of a couple of compressive and tensile steel.
- The permissible stress in compressive steel will be taken equal to the permissible stress in tensile steel.

**{ ****Note:**

Actually, in the case of a steel beam, you can see the amount of tension & compression steel is the same. But in the theoretical cases, you can never get the same amount of tension and compression steel.**}**

**Advantages of the doubly reinforced beam over singly reinforced beam are:**

**Advantages of the doubly reinforced beam over singly reinforced beam are:**

*Doubly reinforced beams can be utilized in place of singly reinforced beams when you have to decrease the depth of the beam but at the same time, this process will be more expensive than the singly reinforced beam.*

*Theoretically, the singly reinforced beam doesn’t have compression steel but on the other hand, doubly reinforced beam have compression steel.*

*For both types of beams, on-site, under reinforced beams are preferred because we can’t design a balanced section. Over reinforced beams are more dangerous and expensive too.*

* *