If the reinforced bars are provided only on tension side in the beam section, it is called as singly reinforced beams.
Consider a simply supported beam subjected to bending under working loads. Since plane sections are assumed to remain plane after bending, strain is proportional to distance from the neutral axis. All the tensile stresses are assumed to be resisted by the steel bars as the
tensile strength of concrete is ignored. The resultant tensile forces, thus acts the centroid of reinforcing bars.
EFFECTIVE DEPTH
Effective depth of a beam is the distance between the centroid of tension reinforcement and the maximum compression fibre, excluding the thickness of finishing material not placed, monolithically with the member
Effective depth d = D-clear cover- Φ/2
where
D= Gross depth or overall depth
Φ= Diameter of the bar.
NEUTRAL AXIS (n)
Neutral axis is the axis at which the stresses are zero in the section. Locating the position of neutral axis is of great importance to the designer. This helps in knowing the amount of strains both in concrete and steel. This position of neutral axis in a section can be found by either of the following two ways depending upon the situation. 1. When the stresses developed in the concrete section are known
Consider a rectangular section as shown in Fig subjected to a moment M under working loads.
2. When the Dimensions of the Beam and the Reinforcements are given: The depth of neutral axis can be obtained by considering the equilibrium of internal forces of compression and tension.
LEVER ARM
The forces of compression and tension form a couple. The distance between the lin of action of Compression and Tension forces is called as lever arm.
Lever arm,
Z = d – n/3
= d – (kd)/3
= d(1 – k/3)
= j×d
where J = 1 – k/3 called lever arm factor
MOMENT OF RESISTANCE
Moment of resistance = Total compression or tension x lever arm
TYPES OF SECTIONS YPES OF SECTIONS
1. Balanced or Critical Section: A reinforced concrete section in which steel and concrete reach their maximum allowable stress simultaneously is called as balanced or critical section. The neutral axis corresponding to balanced section is called as critical neutral axis n(c) . The percentage of steel corresponding to balanced section is called critical percentage of steel.
Critical depth of neutral axis
Under Reinforced Section: A section in which the area of steel reinforcement provided is less than that is required for a balanced section is called an under reinforced section. In this d section when the stress in steel reaches its maximum allowable value, the extreme compressive stress in concrete is less than the maximum permissible stress in concrete and the depth of actual neutral axis (n_{a}) is less than the depth of critical neutral axis.
The moment of resistance of an under reinforced section is given by M.R= σst × Ast (d- na/ 3 )
Where n_{a} = depth of actual neutral axis
3. Over Reinforced Section: A section in which the area of steel reinforcement provided is more than that is required for a balanced section is called over reinforced section In this section when the stress in concrete reaches its maximum allowable value, the stress in steel will be less than its allowable value and the depth of actual neutral axis ( n ) is more than the depth of critical neutral axis.
The moment of resistance of an under reinforced section is given by
M.R= 1/ 2 σcbc b×n{a} (d – n{a}/3)
The critical, under reinforced and over reinforced sections In actual application, it is desirable to obtain an under reinforced section because in this case the steel will yield first and after that concrete starts yielding which gives sufficient warning before failure, where as in over reinforced section concrete will attain its maximum stress first and hence the failure will be sudden.
