Flexural Analysis of Beams - Design of Reinforced Concrete - page 42

Figure 2.5

Then multiply the 25,000 by 12 to obtain in.-lbs as shown below:

(12 25,000)(9.00)
5832

f 463 psi

Since this stress is less than the tensile strength or modulus of rupture of the concrete of 474 psi, the
section is assumed not to have cracked.
(b) Cracking moment:

M cr f r I g (474)(5832)

9.00

307,152 in.- lb 25.6 ft- k

y t

2.3 ELASTIC STRESSES—CONCRETE CRACKED

When the bending moment is sufficiently large to cause the tensile stress in the extreme
fibers to be greater than the modulus of rupture, it is assumed that all of the concrete on
the tensile side of the beam is cracked and must be neglected in the flexure calculations.
The cracking moment of a beam is normally quite small compared to the service load
moment. Thus when the service loads are applied, the bottom of the beam cracks. The
cracking of the beam does not necessarily mean that the beam is going to fail. The reinforc-
ing bars on the tensile side begin to pick up the tension caused by the applied moment.
On the tensile side of the beam an assumption of perfect bond is made between the
reinforcing bars and the concrete. Thus the strain in the concrete and in the steel will be
equal at equal distances from the neutral axis. But if the strains in the two materials at a
particular point are the same, their stresses cannot be the same since they have different
moduli of elasticity. Thus their stresses are in proportion to the ratio of their moduli of
elasticity. The ratio of the steel modulus to the concrete modulus is called the modular
ratio n :

E s
E c

n

If the modular ratio for a particular beam is 10, the stress in the steel will be 10 times
the stress in the concrete at the same distance from the neutral axis. Another way of say-
ing this is that when n 10, one sq. in. of steel will carry the same total force as 10 in. 2 of

concrete.