Page 305 - Handbook of Civil Engineering Calculations, Second Edition

2.90 REINFORCED AND PRESTRESSED CONCRETE ENGINEERING AND DESIGN

REACTIONS FOR A CONTINUOUS BEAM

With 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:

1. 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 a
M kb /L.
2. Compute the continuity moment at B; then find the reactions
Thus, M p F i e M k F i e con ; M k F i (e e con ) 1160( 14 39.05) 29,060
in.·kips (3283 kN·m). R a 29,060/[120(12)] 20.2 kips (89.8 kN); R B 40.4 kips
( 179.8 kN).

STEEL BEAM ENCASED IN CONCRETE

A 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-
1
tion. The slab has been designed as 4 /2 in. (114.3 mm) thick, with f c
3000 lb/sq.in.
(20.7 MPa). The loading includes the following: live load, 120 lb/sq.ft.(5.75 kPa); fin-
ished floor and ceiling, 25 lb/sq.ft.(1.2 kPa). The steel beams have been tentatively de-
signed as W16 40. Review the design.

Calculation Procedure:

1. 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
2
2
1
beams: at midspan, M ( /20)wL ; at support, M ( /12)wL .
1
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.
2
Record the properties of the W16 40: A 11.77 sq.in. (75.94 cm ); d 16.00 in.
4
4
3
3
(406.4 mm); I 515.5 in (21.457 cm ); S 64.4 in (1055.3 cm ); flange width 7 in.
(177.8 mm). By the AISC Specification, f s 24,000 lb/sq.in. (165.5 MPa). By the ACI
Code, n 9 and f c 1350 lb/sq.in. (9306.9 kPa).
2. 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-
1
1
tive flange width /4L /4(28.5)12 85.5 in. (2172 mm); spacing of beams 120 in.