Page 229 - Handbook of Civil Engineering Calculations, Second Edition

2.14 REINFORCED AND PRESTRESSED CONCRETE ENGINEERING AND DESIGN

o sum of perimeters of reinforcing bars, in. (mm). Then the ultimate shear flow at any
plane between the neutral axis and the reinforcing steel is h u V u /(d a/2).
In conformity with the notational system of the working-stress method, the distance d
a/2 is designated as jd. Dividing the shear flow by the area of contact in a unit length and
introducing the capacity-reduction factor yield

V u
u u (18)
ojd
A section of the ACI Code sets 0.85 with respect to bond, and j is usually assigned
the approximate value of 0.875 when this equation is used.
2. Calculate the bond stress
Thus, o 11.0 in. (279.4 mm), from the ACI Handbook. Then u u 72,000/[0.85(11.0)
(0.875) (15)] 587 lb/sq.in. (4047.4 kPa).
The allowable stress is given in the Code as
9.5( f c
) 0.5
u u,allow (19)
D
0.5
but not above 800 lb/sq.in. (5516 kPa). Thus, u u,allow 9.5(4,000) /0.875 687
lb/sq.in. (4736.9 kPa).

DESIGN OF INTERIOR SPAN OF A
ONE-WAY SLAB

A floor slab that is continuous over several spans carries a live load of 120 lb/sq.ft. (5745
2
2
N/m ) and a dead load of 40 lb/sq.ft. (1915 N/m ), exclusive of its own weight. The clear
spans are 16 ft (4.9 m). Design the interior span, using f c
3000 lb/sq.in. (20,685 kPa)
and f y 50,000 lb/sq.in. (344,750 kPa).

Calculation Procedure:
1. Find the minimum thickness of the slab as governed by
the Code
Refer to Fig. 8. The maximum potential positive or negative moment may be found by ap-
plying the type of loading that will induce the critical moment and then evaluating this
moment. However, such an analysis is time-consuming. Hence, it is wise to apply the
moment equations recommended in the ACI Code whenever the span and loading condi-
tions satisfy the requirements given there. The slab is designed by considering a 12-in.
(304.8-mm) strip as an individual beam, making b 12 in. (304.8 mm).
Assuming that L 17 ft (5.2 m), we know the minimum thickness of the slab is t min
L/35 17(12)/35 5.8 in. (147.32 mm).
2. Assuming a slab thickness, compute the ultimate load
on the member
3
Tentatively assume t 6 in. (152.4 mm). Then the beam weight (6/12)(150 lb/ft 75
lb/lin ft (1094.5 N/m). Also, w u 1.5(40 75) 1.8(120) 390 lb/lin ft (5691.6 N/m).