Reinforcement steel possesses excellent tensile strength, unlike concrete. Therefore it is common sense to place reinforcement in an area subjected to tensile stress. Occasionally steel is placed in the compression side of beams. Beams with reinforcement in tensile and compression side known as a doubly reinforced beam.

*Figure 1*

In some cases, the size of the beam is reduced due to aesthetic or space requirement. Therefore we use compression reinforcement to increase the resisting moment of the beam. Adding reinforcement in the compression side will result in a beam with higher moment capacity compared to beam with a limited maximum reinforcement in the tensile side. By introducing steel in the compression side. Another resisting couple introduced to the beam. Also, compression reinforcement will increase the amount of curvature that a beam can stand before flexural failure. This means producing a beam with higher ductility.

Shrinkage and creep deformation can be reduced by adding compression steel. Compression steel will help in placing the stirrups by tying the steel bar to stirrups. Also, it will help in maintaining the location of stirrups during the placing and consolidating of concrete.

If the concrete crushed and fail. The beam will not collapse if compression reinforcement is provided and enclosed in stirrups. Once the concrete reaches the crushing strain. The concrete cover will crack and spall off, exposing the compression reinforcement. The compression reinforcement will not buckle until an additional moment is applied.

The compression steel is assumed to yields similarly as in tensile steel. Tensile steel assumed to yield to met the ductility requirement specified by ACI code. If the strain at the extreme compression fiber assumed to be 0.003. And the compression steel is placed at 3/4 from the neutral axis. Strain in compression reinforcement equal 3*0.003/4=0.00225. If the steel E=200,000Mpa and fy=420Mpa. The strain equals 420/200,000=0.0021, and this means steel yields.

The nominal resisting moment for doubly reinforced beam consists of two components. The first component is the resistance of compression concrete and the balancing tensile reinforcement. The second component is the resistance of compressive steel and the additional of tensile reinforcement, as shown in figure 2.

*Figure 2*

Mn=Mn1+Mn2

Mn1=As1fy(d-a/2)Mn2=As’fs'(d-d’)=As’fy(d-d’)

Mn=As1fy(d-a/2)+As’fy(d-d’)

Up to this point compression steel assumed to yield. If the assumption is valid. This means As2 equal As’ to achieve the equilibrium. If compression steel has not yielded this means As’ is larger than As2.

Mn=As1fy(d-a/2)+As’fs'(d-d’)

ΦMn=Φ[As1fy(d-a/2)+As’fy(d-d’)]

Equilibrium equations are used to determine the magnitude of strain and the location of the neutral axis. From figure 3. initially, we all assume the steel at the compression side yield. Then we will verify if the steel yield or no.

As fy = 0.85f c’β1cb + As’fy

C=(Asfy-As’fy)/(0.85fc’β1b)

from the strain diagram in figure 3

ε’s=(c-d’)*0.003/c

If ε’s>εy=As/fy then the assumption is valid and the steel yields. If no then the steel is not yielding. in this case, a new equilibrium equation is required

As fy = 0.85f c’β1cb + As'((c-d’)/c)*0.003*Es

*Figure 3*