CIVIL ENGINEERING FORMULAS

138 CHAPTER FIVE

where Mbending moment
Msmoment-resisting capacity of compressive steel
M 1 moment-resisting capacity of concrete

ULTIMATE-STRENGTH DESIGN OF I- AND T-BEAMS

When the neutral axis lies in the flange, the member may be designed as a rec-
tangular beam, with effective width band depth d. For that condition, the
flange thickness twill be greater than the distance cfrom the extreme compres-
sion surface to the neutral axis,

(5.80)

where 1 constant
Asfy/bd fc
Asarea of tensile steel, in^2 (mm^2 )
fyyield strength of steel, ksi (MPa)
fc28-day strength of concrete, ksi (MPa)

When the neutral axis lies in the web, the ultimate moment should not exceed

(5.81)

whereAsfarea of tensile steel required to develop compressive strength of
overhanging flange, in^2 (mm^2 )0.85
bwwidth of beam web or stem, in (mm)
adepth of equivalent rectangular compressive stress distribution,
in (mm)


The quantity wfshould not exceed 0.75b, where bis the steel ratio for
balanced conditions wAs/bwdandfAsf/bwd.

WORKING-STRESS DESIGN OF I- AND T-BEAMS

For T-beams, effective width of compression flange is determined by the same
rules as for ultimate-strength design. Also, for working-stress design, two cases
may occur: the neutral axis may lie in the flange or in the web. (For negative
moment, a T-beam should be designed as a rectangular beam with width b
equal to that of the stem.)
If the neutral axis lies in the flange, a T-or I-beam may be designed as a rec-
tangular beam with effective width b. If the neutral axis lies in the web or stem,

(AsAsf)fy/ 0.85 fcbw

(bbw)tfc/fy

Mu0.90(AsAsf)fyd

a

2 

Asffyd

t

2 

c

1.18 d

 1