TABLE 4. Calculations for Two-Span Beam: Part a
Section 12345
1 C 1 +0.067 5 +0.095 0 +0.082 5 +0.030 0 -0.062 5
2 C 2 -0.012 5 -0.025 0 -0.037 5 -0.050 0 -0.062 5
3 C 3 +0.0550 +0.0700 +0.0450 -0.0200 -0.1250
4/6w, lb/in^2 -959 -1,221 -785 +349 +2,180
(kPa) (-6,611) (-8,418) (-5,412) (+2406) (+15,029)
5/fal,lb/ -691 -972 -844 -307 +640
in^2 (kPa) (-4,764) (-6,701) -5,819) (-2,116) (+4,412)
6 fbs2, Ib/ +128 +256 +384 +512 +640
in^2 (kPa) (+882) (+1,765) (+2,647) (+3,530) (+4,412)
7/^, lb/in^2 +444 +565 +363 -161 -1,008
(kPa) (+3,060) (+3895) (+2,503) (-1,110) (-6,949)
8/al, lb/in^2 +319 +450 +390 +142 -296
(kPa) (+2,199) (+3,102) (+2689) (+979) (-2,041)
9.4 2 ,lb/in^2 -59 -118 -177 -237 -296
(kPa) (-407) (-813) (-1,220) (-1,634) (-2,041)
10econ,in +17.19 +21.87 +14.06 -6.25 -39.05
(mm) (+436.6) (+555.5) (+357.1) (-158.8) (-991.9)
11 fbp, lb/in^2 +2,148 +2,513 +1,903 +318 -2,243
(kPa) (+14,808) (+17,325) (+13,119) (+2,192) (-15,463)
12 4, lb/in^2 +185 +16 +298 +1,031 +2,215
(kPa) (+128) (+110) (+2,054) (+7,108) (+15,270)
0.85/6/,
13 lb/in^2 +1,826 +2,136 +1,618 +270 -1,906
(kPa) (+12,588) (+14,726) (+11,154) (+1,861) (-13,140)
0.85^
14 lb/in^2 +157 +14 +253 +876 +1,883
(kPa) (+1,082) (+97) (+1,744) (+6,039) (+12,981)
At midspan: C 3 = +0.0625 and econ = +19.53 in (496.1 mm)
mum and minimum potential live-load bending moments at the respective sections. The
values of C 3 also represent the relative eccentricities of a concordant trajectory.
Since the gravity loads induce the maximum positive moment at section 2 and the
maximum negative moment at section B, the prestressing force and its trajectory will be
designed to satisfy the stress requirements at these two sections. (However, the stresses at
all boundary sections will be checked.) The Magnel diagram for section 2 is similar to
that in Fig. 37, but that for section B is much different.
- Compute the value of C 3 at midspan
Thus, C 3 = +0.0625. - Apply the moment coefficients to find the gravity-load stresses
Record the results in Table 4. Thus Mw = C 3 (1500)(120)^2 (12) = 259,200,00OC 3 in-lb
(29.3C 3 kN-m); fbw = -259,200,OOOC 3 /14,860 = -17,44OC 3 ; fbsl = -10,23OC 1 ; fbs2 =
-10,23OC 2 ;/^ = 8065C 3 ;/fti = 4731C 1 ;/^ - 4731C 2.
Since St far exceeds Sb, it is manifest that the prestressing force must be designed to
confine the bottom-fiber stresses to the allowable range.