Handbook of Civil Engineering Calculations

PARTl

REINFORCED CONCRETE

The design of reinforced-concrete members in this handbook is executed in accordance
with the specification titled Building Code Requirements for Reinforced Concrete of the
American Concrete Institute (ACI). The ACI Reinforced Concrete Design Handbook
contains many useful tables that expedite design work. The designer should become thor-
oughly familiar with this handbook and use the tables it contains whenever possible.
The spacing of steel reinforcing bars in a concrete member is subject to the restrictions
imposed by the ACI Code. With reference to the beam and slab shown in Fig. 1, the rein-
forcing steel is assumed, for simplicity, to be concentrated at its centroidal axis, and the
effective depth of the flexural member is taken as the distance from the extreme compres-
sion fiber to this axis. (The term depth hereafter refers to the effective rather than the over-
all depth of the beam.) For design purposes, it is usually assumed that the distance from
the exterior surface to the center of the first row of steel bars is 2
1
A in (63.5 mm) in a beam
with web stirrups, 2 in (50.8 mm) in a beam without stirrups, and 1 in (25.4 mm) in a slab.
Where two rows of steel bars are provided, it is usually assumed that the distance from
the exterior surface to the centroidal axis of the reinforcement is 3
1
A in (88.9 mm). The
ACI Handbook gives the minimum beam widths needed to accommodate various combi-
nations of bars in one row.
In a well-proportioned beam, the width-depth ratio lies between 0.5 and 0.75. The
width and overall depth are usually an even number of inches.
The basic notational system pertaining to reinforced concrete beams is as follows:
fc = ultimate compressive strength of concrete, lb/in^2 (kPa); fc = maximum compressive
stress in concrete, lb/in
2
(kPa);^ = tensile
stress in steel, lb/in
2
(kPa);^, = yield-point
stress in steel, lb/in
2
(kPa); ec = strain of
extreme compression fiber; es = strain of
steel; b = beam width, in (mm); d = beam
depth, in (mm); A 3 = area of tension rein-
forcement, in
2
(cm
2
); p = tension-
reinforcement ratio, Asl(bd)\ q = tension-
reinforcement index, pfylfc'\ n — ratio of
modulus of elasticity of steel to that of
concrete, EJEC\ C = resultant compressive
force on transverse section, Ib (N); T= re-
sultant tensile force on transverse section,
Ib (N).
Where the subscript b is appended to a
symbol, it signifies that the given quantity
is evaluated at balanced-design conditions.

Design of Flexural Members by

Ultimate-Strength Method

In the ultimate-strength design of a rein-

FIGURE 1. Spacing of reinforcing bars. forced-concrete structure, as in the plastic

(a) Beam with stirrups

Stirrup

clear

d =

effective depth

clear