美国钢结构设计手册第七章十三十四节

7.13 LRFD FOR COMPOSITE BEAM WITH UNIFORM LOADS

The typical floor construction of a multistory building is to have composite framing. The floor consists of 31⁄4-in-thick lightweight concrete over a 2-in-deep steel deck. The concrete weighs 115 lb/ft3and has a compressive strength of 3.0 ksi. An additional 30% of the dead load is assumed for equipment load during construction. The deck is to be supported onsteel beams with stud shear connectors on the top flange for composite action (Art. 7.12).

Unshored construction is assumed. Therefore, the beams must be capable of carrying their own weight, the weight of the concrete before it hardens, deck weight, and construction loads. Shear connectors will be3⁄4 in in diameter and 31⁄2 in long. The floor system should be investigated for vibration, assuming a damping ratio of 5%.

FIGURE 7.6 Seven locations of the plastic neutral axis used for determining the strength of a composite beam.

(a) For cases 6 and 7, the PNA lies in the web. (b) For cases 1 through 5, the PNA lies in the steel flange.

A typical beam supporting the deck is 30 ft long. The distance to adjacent beams is 10 ft. Ribs of the deck are perpendicular to the beam. Uniform dead loads on the beam are construction, 0.50 kips per ft, plus 30% for equipment loads, and superimposed load, 0.25 kips per ft. Uniform live load is 0.50 kips

per ft.

Q for Partial Composite Design(kips)

TABLE 7.3

n

Location of PNA n Q and concrete compression

（1）

y x F A （2）to （5）

*2y f y s F A F A ∆- （6） 0.5[C(5)+C(7)] †

（7）

0.25y s F A

* A ƒ area of the segment of the steel flange above the plastic neutral axis (PNA). †C (n ) compressive force at location (n ). Beam Selection. Initially, a beam of A36 steel that can support the construction loads is selected. It is assumed to weigh 26 lb /ft. Thus the beam is to be designed for a service dead load of 0.5×1.3+0.026=0.676 kips per ft.

Factored load=0.676*1.4=0.946 kips per ft

Factored moment = u M =0.946×302/8=106.5 kip-ft

The plastic section modulus required therefore is

Z=36

9.0125.106⨯⨯=y u F M φ=39.43in Use a W16 ×26 (Z =44.2 3in and moment of inertia I =301 4in ).

The beam should be cambered to offset the deflection due to a dead load of 0.50 ＋0.026 =0.526 kips per ft.

Camber =1.1301

000,293841230526.053

4=⨯⨯⨯⨯⨯in Camber can be specified on the drawings as 1 in.

Strength of Fully Composite Section.

Next, the composite steel section is designed to support the total loads. The live load may be reduced in accordance with area supported (Art. 7.9). The reduction factor is R = 0.0008(300－150) =0.12. Hence the reduced live load is 0.5(1 － 0.12) = 0.44 kips per ft. The factored load is the larger of the following:

1.2(0.50 + 0.25 + 0.026) × 1.6 ＋0.44= 1.635 kips per ft

1.4(0.5 + 0.25 + 0.026) =1.086 kips per ft

Hence the factored moment is

9.1838/30635.12

=⨯=u M kip-ft

The concrete-flange width is the smaller of b = 10 ×12 = 120 in or b = 2(30 ×12⁄8) =90 in (governs).

The compressive force in the concrete C is the smaller of the values computed from Eqs. (7.24) and (7.25).