Page 202 - Civil Engineering Formulas

138 CHAPTER FIVE

where M bending moment
M moment-resisting capacity of compressive steel
s
M moment-resisting capacity of concrete
1

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 b and depth d. For that condition, the
flange thickness t will be greater than the distance c from the extreme compres-
sion surface to the neutral axis,
1.18 d
c (5.80)
1

where constant
1
A f /bd f
s y
c
2
2
A area of tensile steel, in (mm )
s
f yield strength of steel, ksi (MPa)
y
f 28-day strength of concrete, ksi (MPa)
c
When the neutral axis lies in the web, the ultimate moment should not exceed

M u 0.90 (A s A sf )f y d a 2 A sf f y d 2 t (5.81)
where A area of tensile steel required to develop compressive strength of
sf
2 2
overhanging flange, in (mm ) 0.85(b b w )tf c / f y
b width of beam web or stem, in (mm)
w
a depth of equivalent rectangular compressive stress distribution,
in (mm)
(A s A sf )f y / 0.85 f c b w
The quantity should not exceed 0.75 , where is the steel ratio for
f
w
b
b
balanced conditions A /b d and A /b d.
f
w
w
sf
w
s
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,