CIVIL ENGINEERING FORMULAS

CONCRETE FORMULAS 119

where bwidth of beam [equals 12 in (304.8 mm) for slab], in (mm)
deffective depth of beam, measured from compressive face of beam
to centroid of tensile reinforcing (Fig. 5.1), in (mm)
Mbending moment, lb.in (k.Nm)
fccompressive stress in extreme fiber of concrete,lb/in^2 (MPa)
fsstress in reinforcement, lb/in^2 (MPa)
Ascross-sectional area of tensile reinforcing, in^2 (mm^2 )
jratio of distance between centroid of compression and centroid of
tension to depth d
kratio of depth of compression area to depth d
pratio of cross-sectional area of tensile reinforcing to area of the beam
(As/bd)

For approximate design purposes, jmay be assumed to be and k, For
average structures, the guides in Table 5.1 to the depth dof a reinforced concrete
beam may be used.

(^1) 
3.
(^7) 
8
Cross section of beam Stress diagram
C = fckbd
fc
kd
jd
d
b
fs/n
As
1
2
M =^12 fckjbd^2 =fs pjbd^2
T = Asfs=fspbd
FIGURE 5.1 Rectangular concrete beam with tensile reinforcing only.
TABLE 5.1 Guides to Depth dof Reinforced
Concrete Beam
Member d
Roof and floor slabs l/25
Light beams l/15
Heavy beams and girders l/12–l/10
lis the span of the beam or slab in inches (millimeters).
The width of a beam should be at least l/32.