CIVIL ENGINEERING FORMULAS

CONCRETE FORMULAS 133

Development of Tensile Reinforcement

At least one-third of the positive-moment reinforcement in simple beams and one-
fourth of the positive-moment reinforcement in continuous beams should extend
along the same face of the member into the support, in both cases, at least 6 in
(152.4 mm) into the support. At simple supports and at points of inflection, the
diameter of the reinforcement should be limited to a diameter such that the develop-
ment length ldsatisfies

(5.54)

whereMncomputed flexural strength with all reinforcing steel at section
stressed to fy
Vuapplied shear at section
laadditional embedment length beyond inflection point or center of
support

At an inflection point, lais limited to a maximum of d, the depth of the centroid
of the reinforcement, or 12 times the reinforcement diameter.

Hooks on Bars

The basic development length for a hooked bar with fy60 ksi (413.7 MPa) is
defined as

(5.55)

wheredbis the bar diameter, in (mm), and is the 28-day compressive
strength of the concrete, lb/in^2 (MPa).

WORKING-STRESS DESIGN OF RECTANGULAR BEAMS
WITH TENSION REINFORCEMENT ONLY

From the assumption that stress varies across a beam section with the distance
from the neutral axis, it follows that

(5.56)

where nmodular ratio Es/Ec
Esmodulus of elasticity of steel reinforcement, ksi (MPa)
Ecmodulus of elasticity of concrete, ksi (MPa)
fccompressive stress in extreme surface of concrete, ksi (MPa)
fsstress in steel, ksi (MPa)

nfc

fs



k

1 k

fc

lhb

1200 db

fc

ld

Mn

Vu

la