REACTIONS FOR A CONTINUOUS BEAMWith reference to the beam in the previous calculation procedure, compute the reactions
at the supports caused by the initial prestressing force designed in part a.Calculation Procedure:
- Determine what causes the reactions at the supports
As shown in Fig. 51, the reactions at the supports result from the continuity at B, and R 0 =
Mkb/L - Compute the continuity moment at B; then find the reactions
Thus, Mp = -F 1 C +Mk = -F 1 -^00n; Mk = Ft(e - econ) = 1160(-14 + 39.05) = 29,060 in-kips
(3283 kN-m). R 0 = 29,060/[120(12)] = 20.2 kips (89.8 kN); RB = -40.4 kips (-179.8 kN).
STEEL BEAM ENCASED IN CONCRETEA concrete floor slab is to be supported by steel beams spaced 10 ft (3.05 m) on centers
and having a span of 28 ft 6 in (8.69 m). The beams will be encased in concrete with a
minimum cover of 2 in (50.8 mm) all around; they will remain unshored during construc-
tion. The slab has been designed as 41 X 2 in (114.3 mm) thick, with// = 3000 lb/in^2 (20.7
MPa). The loading includes the following: live load, 120 lb/ft^2 (5.75 kPa); finished floor
and ceiling, 25 lb/ft^2 (1.2 kPa). The steel beams have been tentatively designed as Wl 6 *
- Review the design.
Calculation Procedure:
- Record the relevant properties of the section and the allowable
flexural stresses
In accordance with the AISC Specification, the member may be designed as a composite
steel-and-concrete beam, reliance being placed on the natural bond of the two materials to
obtain composite action. Refer to Sec. 1 for the design of a composite bridge member. In
the design of a composite building member, the effects of plastic flow are usually disre-
garded. Since the slab is poured monolithically, the composite member is considered con-
tinuous. Apply the following equations in computing bending moments in the composite
beams: at midspan, M= (^1 Ao)WL^2 ; at support, M= (Vi2)wL^2.
The subscripts c, ts, and bs refer to the extreme fiber of concrete, top of steel, and bot-
tom of steel, respectively. The superscripts c and n refer to the composite and noncom-
posite sections, respectively.
Record the properties of the W16 x 40: A = 11.77 in^2 (75.94 cm^2 ); d = 16.00 in (406.4
mm); /= 515.5 in^4 (21.457 cm^4 ); S = 64.4 in^3 (1055.3 cm^3 ); flange width = 7 in (177.8
mm). By the AISC Specification, fs = 24,000 lb/in
2
(165.5 MPa). By the ACI Code, n = 9
and/c = 1350 lb/in^2 (9306.9 kPa). - Transform the composite section in the region of positive
moment to an equivalent section of steel; compute the
section moduli
Refer to Fig. 58a and the AISC Specification. Use the gross concrete area. Then the effec-