F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

Characteristics of some proposed stress blocks 93
assume for simplicity that Ecu has a definite value irrespective of the
concrete strength.
(b) Whitney's equivalent rectangular block
Both BS 8110 and the ACI Building Code [10] make use of the concept of
an equivalent rectangular stress block, which was pioneered by Whitney
[11]. Whitney found that if the actual stress block was replaced by a
fictitious rectangular block of intensity 0.85 times the cylinder strength 1~
and of such a depth Xw that the area of 0.851~xw was equal to that of the
actual block, then the centroids of the two blocks were very nearly at the
same level (Fig. 4.4-2). The depth Xw of Whitney's block is not directly
related to the neutral axis depth x; x is determined by the strain
distribution ( eqns 4.2-1 and 4.2-7), but xw is to be determined from the
condition of equilibrium. For a rectangular beam of width b having tension
reinforcement As,
0.85l~bxw = Asls
where Is is the steel stress at collapse. For a primary tension failure, Is is
equal to the yield stress IY; therefore
As/y ly d ( )
xw = 0.85l~b = 0.85/~e 4.4-1
where e is the steel ratio As! bd. The ultimate moment of resistance may be
obtained by taking moments about the centroid of the stress block or about
that of the tension reinforcement:
Mu = As/y(d- Xi)
(4.4-2(a))
T
X
l
I
~
Stress block
(a)
Whitney's
equivalent block
(b)
Fig. 4.4-2 Whitney's equivalent rectangular stress block