multiplied with the modification factor depending on reinforcement percentage and type.
Figures 4 and 5 of IS 456 give the different values of modification factors. The total depth D
can be determined by adding 40 to 80 mm to the effective depth.
(iii) Selection of the amount of steel reinforcement A
st
The amount of steel reinforcement should provide the required tensile force T to resist the
factored moment M
u
of the beam. Further, it should satisfy the minimum and maximum
percentages of reinforcement requirements also. The minimum reinforcement A
s
is provided
for creep, shrinkage, thermal and other environmental requirements irrespective of the
strength requirement. The minimum reinforcement A
s
to be provided in a beam depends on
the f
y
of steel and it follows the relation: (cl. 26.5.1.1a of IS 456)
The maximum tension reinforcement should not exceed 0.04 bD (cl. 26.5.1.1b of IS 456),
where D is the total depth.
Besides satisfying the minimum and maximum reinforcement, the amount of reinforcement
of the singly reinforced beam should normally be 75 to 80% of p
t, lim
. This will ensure that
strain in steel will be more than (
) as the design stress in steel will be 0.87 f
y
.
Moreover, in many cases, the depth required for deflection becomes more than the limiting
depth required to resist M
u, lim
. Thus, it is almost obligatory to provide more depth. Providing
more depth also helps in the amount of the steel which is less than that required for M
u, lim
.
This helps to ensure ductile failure. Such beams are designated as under-reinforced beams.
(iv) Selection of diameters of bar of tension reinforcement
Reinforcement bars are available in different diameters such as 6, 8, 10, 12, 14, 16, 18, 20,
22, 25, 28, 30, 32, 36 and 40 mm. Some of these bars are less available. The selection of the
diameter of bars depends on its availability, minimum stiffness to resist while persons walk
over them during construction, bond requirement etc. Normally, the diameters of main tensile
bars are chosen from 12, 16, 20, 22, 25 and 32 mm.
(v) Selection of grade of concrete