Handbook of Civil Engineering Calculations

FIGURE 46. Concrete area under stress at ultimate load.

Calculate the steel index to ascertain that it is below the limit imposed by the ACI
Code. Refer to Fig. 46. Or, area of ABCD = 8(9.53) = 76.24 in^2 (491.900 cm^2 ). The steel
area Asr that is required to balance the force on this web strip is Asr = 5.784(76.24)7298 =
1.48 in^2 (9.549 cm^2 ); q = Asrfsu(b' dfc') = 1.48(219,000)/[8(59.0)(5000)] = 0.137 < 0.30.
This is acceptable.

9. Calculate the required ultimate-moment capacity as given
   by the ACI Code
   Thus, WM = 1.5(892 + 1160) + 1.8(1000) = 4878 Ib/lin ft (71,189.0 N/m); Mu required =
   (!/8)(4878)(90)^2 (12) = 59,270,000 in-lb (6,696,324.6 N-m). This is acceptable. The mem-
   ber is therefore adequate with respect to its ultimate-moment capacity.
   10. Design the web reinforcement
   Follow the procedure given in step 8 of the previous calculation procedure.
   11. Design the end block
   This is usually done by applying isobar charts to evaluate the tensile stresses caused by
   the concentrated prestressing forces. Refer to Winter et al.—Design of Concrete Struc-
   tures, McGraw-Hill.
   12. Compute the camber at transfer
   Referring to earlier procedures in this section, we see that EJ = 3.644(10)^6 (394,800) =
   1.44 x 1012 lb-in^2 (4.132 x 109 N-m^2 ). Also, Aw = -5(892)(90)^4 (1728)/[384(1.44)(10)^12 =
   -0.91 in (-23.11 mm). Apply Eq. 60, or A, = 5(844,000)(31.6)(90)^2 (144)/[48(1.44)
   (1O)^12 ] = 2.25 in (57.15 mm); A 1 = 2.25 - 0.91 - 1.34 in (34.036 mm).

PROPERTIES OFA PARABOLICARC

Figure 47 shows the literal values of the coordinates at the ends and at the center of the

parabolic arc P 1 P 2 P^ Develop equations for y, dyldx, and d^2 y/dx^2 at an arbitrary point P.

Find the slope of the arc at P 1 and P 3 and the coordinates of the summit S. (This informa-

tion is required for the analysis of beams having parabolic trajectories.)

Calculation Procedure:

1. Select a slope for the arc
   Let m denote the slope of the arc.