Refer to Sec. 1. Where the bending moment is positive, the critical plane for horizon-
tal shear is considered to be the surface abed in Fig. 59a. For simplicity, however, com-
pute the shear flow at the neutral axis. Apply the relation q = VQII, where Q =
1
/ 2 (9.22)(3.93)
2
= 71.20 in
3
(1166.8 cm
3
) and q = 12,400(71.20)71136 = 777 Ib/lin in (136
N/mm).
Resistance to shear flow is provided by the bond between the steel and concrete along
be and by the pure-shear strength of the concrete along ab and cd. (The term pure shear is
used to distinguish this from shear that is used as a measure of diagonal tension.) The al-
lowable stresses in bond and pure shear are usually taken as 0.03// and 0.12/', respec-
tively. Thus be = 1 in (177.8 mm); ab = (2.52 + 2
2
)
0
- 5
= 3.2 in (81.3 mm); qallow = 7(90) +
2(3.2)360 = 2934 Ib/lin in (419 N/mm), which is satisfactory.
- Investigate the composite member with respect to horizontal
shear in the concrete at the support
The critical plane for horizontal shear is efin Fig. 596. Thus V
c
= 1450(0.5)28.5 = 20,660
Ib (91.9 kN); Q = 1.22(2)(7.26 - 1) = 15.27 in^3 (250.2 cm^3 ); q = 20,660(15.27)7759.5 =
415 Ib/lin in (72.7 N/mm); #allow = 7(90) + 2(2)360 = 2070 Ib/lin in (363 N/mm), which is
satisfactory.
Mechanical shear connectors are not required to obtain composite action, but the beam
is wrapped with wire mesh.
COMPOSITE STEEL-AND-CONCRETE BEAM
A concrete floor slab is to be supported by steel beams spaced lift (3.35 m) on centers and
having a span of 36 ft (10.97 m). The beams will be supplied with shear connectors to ob-
tain composite action of the steel and concrete. The slab will be 5 in (127 mm) thick and
made of 3000-lb/in^2 (20.7-MPa) concrete. Loading includes the following: live load, 200
lb/ft^2 (9.58 kPa); finished floor, ceiling, and partition, 30 lb/ft^2 (1.44 kPa). In addition,
each girder will carry a dead load of 10 kips (44.5 kN) applied as a concentrated load at
midspan prior to hardening of the concrete. Conditions at the job site preclude the use of
temporary shoring. Design the interior girders, limiting the overall depth of steel to 20 in
(508 mm), if possible.
FIGURE 59. Critical planes for horizontal shear.