sign the slab by the working-stress method, using fc' = 3000 lb/in^2 (20.7 MPa) and fs =
20,000 lb/in^2 (137.9 MPa).
Calculation Procedure:
- Compute the unit loads
The working-stress method of designing reinforced-concrete members is presented in
Sec. 1. The slab is designed as a simply supported beam having a span equal to the hori-
zontal distance between the center of supports. For convenience, consider a strip of slab
having a width of 1 ft (0.3 m).
Assume that the slab will be 5.5 in (139 mm) thick, the thickness of the stairway slab
being measured normal to the soffit. Compute the average vertical depth in Fig. 62b. Thus
sec B = 1.25; h = 5.5(1.25) + 3.75 = 10.63 in (270.0 mm). For the stairway, w = 100 +
10.63(150)712 = 233 Ib/lin ft (3.4-kN/m); for the landing, w = 100 + 5.5(150)712 = 169
Ib/lin ft (2.5 kN/m).
- Compute the maximum bending moment In the slab
Construct the load diagram shown in Fig. 62c, adding about 5 in (127 mm) to the clear
span to obtain the effective span. Thus R 0 = [169(4.2)2.1 + 233(7.7)8.05]/! 1.9 = 1339 Ib
(5.95 kN); x = 1339/233 = 5.75 ft (1.75 m); Mmax =
1
^ 1339)5.75(12) = 46,200 in-lb (5.2
kN-m).
- Design the reinforcement
Refer to Table 1 to obtain the following values: Kb = 223 lb/in
2
(1.5 MPa);y = 0.874. As-
sume an effective depth of 4.5 in (114.3 mm). By Eq. 31, the moment capacity of the
member at balanced design is Mb = Kbbcf = 223(12)4.5
2
= 54,190 in-lb (6.1 kN-m). The
steel is therefore stressed to capacity. (Upon investigation, a 5-in (127-mm) slab is found
to be inadequate.) By Eq. 25, A 8 = Mt(JJd) = 46,200/[20,000(0.874)4.5] = 0.587 in
2
(3.79
cm
2
).
Use no. 5 bars, 6 in (152.4 mm) on centers, to obtain A 8 — 0.62 in
2
(4.0 cm
2
). In addi-
tion, place one no. 5 bar transversely under each tread to assist in distributing the load and
to serve as temperature reinforcement. Since the slab is poured independently of the sup-
porting members, it is necessary to furnish dowels at the construction joints.
FREE VIBRATORYMOTION OFA RIGID BENT
The bent in Fig. 63 is subjected to a horizontal load P applied suddenly at the top. Using
literal values, determine the frequency of vibration of the bent. Make these simplifying
assumptions: The girder is infinitely rigid; the columns have negligible mass; damping
forces are absent.
Calculation Procedure:
- Compute the spring constant
The amplitude (maximum horizontal displacement of the bent from its position of static
equilibrium) is a function of the energy imparted to the bent by the applied load. The fre-
quency of vibration is independent of this energy. To determine the frequency, it is neces-
sary to find the spring constant of the vibrating system. This is the static force that is re-
