CIVIL ENGINEERING FORMULAS

120 CHAPTER FIVE

For a balanced design, one in which both the concrete and the steel are
stressed to the maximum allowable stress, the following formulas may be used:

(5.7)

Values of K,k,j, and pfor commonly used stresses are given in Table 5.2.

T-Beams with Tensile Reinforcing Only When a concreteslab is constructed
monolithically with the supporting concrete beams, a portion of the slab acts as the
upper flange of the beam. The effective flange width should not exceed (1) one-
fourth the span of the beam, (2) the width of the web portion of the beam plus 16
times the thickness of the slab, or (3) the center-to-center distance between beams.
T-beams where the upper flange is not a portion of a slab should have a flange
thickness not less than one-half the width of the web and a flange width not more
than four times the width of the web. For preliminary designs, the preceding
formulas given for rectangular beams with tensile reinforcing only can be used,
because the neutral axis is usually in, or near, the flange. The area of tensile
reinforcing is usually critical.

Beams with Tensile and Compressive Reinforcing Beamswith compressive
reinforcing are generally used when the size of the beam is limited. The
allowable beam dimensions are used in the formulas given earlier to determine
the moment that could be carried by a beam without compressive reinforcement.
The reinforcing requirements may then be approximately determined from

(5.8)

where Astotal cross-sectional area of tensile reinforcing, in^2 (mm^2 )
Asccross-sectional area of compressive reinforcing, in^2 (mm^2 )
Mtotal bending moment, lbin (KNm)
Mbending moment that would be carried by beamof balanced design and
same dimensions with tensile reinforcing only, lbin (KNm)
nratio of modulus of elasticity of steel to that of concrete

As

8 M

7 fsd

Asc

MM

nfcd

bd^2 

M

K

K

1

2

fekjpfsj

TABLE 5.2 CoefficientsK,k,j, and pfor Rectangular Sections*

nfs Kkj p

2000 15 900 175 0.458 0.847 0.0129

2500 12 1125 218 0.458 0.847 0.0161

3000 10 1350 262 0.458 0.847 0.0193

3750 8 1700 331 0.460 0.847 0.0244

*fs16,000 lb/in^2 (110 MPa).

fs