- Select the stirrup size
Use the method given earlier in the ultimate-strength calculation procedure to select the
stirrup size, establish the maximum allowable spacing, and devise a satisfactory spacing.
CAPACITY OFAT BEAM
Determine the flexural capacity of the T beam in Fig. 16a, using/,' = 3000 lb/in^2 (20,685
kPa).
Calculation Procedure:
- Record the pertinent beam values
The neutral axis of a T beam often falls within the web. However, to simplify the analy-
sis, the resisting moment developed by the concrete lying between the neutral axis and the
flange is usually disregarded. Let Af denote the flange area. The pertinent beam values are
/c,aiiow = 1350 lb/in^2 (9308.3 kPa); n = 9;kb = 0.378; nAs = 9(4.00) = 36.0 in^2 (232.3 cm^2 ).
- Tentatively assume that the neutral axis lies in the web
Locate this axis by taking static moments with respect to the top line. Thus Af= 5(16) =
80 in^2 (516.2 cm^2 ); M= [80(2.5) + 36.0(21.5)]/(80 + 36.0) = 8.40 in (213.36 mm).
- Identify the controlling stress
Thus &= 8.40/21.5 = 0.391 > kb; therefore, concrete stress governs.
- Calculate the allowable bending moment
Using Fig. 16c, we see/cl = 1350(3.40)/8.40 = 546 lb/in^2 (3764.7 kPa); C=^1 X 2 (SO)(HSO +
- = 75,800 Ib (337,158.4 N). The action line of this resultant force lies at the centroidal
axis of the stress trapezoid. Thus, z = (^5 / 3 )(1350 + 2 x 546)/(1350 + 546) = 2.15 in (54.61
mm); or z = (^5 A) (8.40 + 2 x 3.40)/(8.40 + 3.40) = 2.15 in (54.61 mm); M = Qd =
75,800(19.35) - 1,467,000 in-lb (165,741 N-m).
(Q) Section
FIGURE 16
(b) Transformed section (c) Stresses and resultant forces
