Floor slabs, cast monolithically with beam, act not only as a horizontal diaphragm for the building, but also as a flange to the beam in flexure. At a section of the beam where it is subjected to positive bending, the floor slab is in compression and concrete in the floor slab cooperates with that of beam in compression. At a section where it is subjected to negative bending, the floor slab is in tension and slab concrete will crack, but re-bars in the floor slab cooperate with beam axial bars in tension. In both cases, not the entire width of the slab, but certain effective width of the slab, plays the cooperating role.
The purpose of the current study was to investigate whether the existing knowledge on the slab effect on flexural behavior of beams, such as initial and inelastic stiffness, yield and ultimate strength, and so on, using ordinary
3 S 5
—
anchor plate (PL-9) S s.
I::::::::::;::: / *
V
r2-DCS<SI50
' r-
I
4-D1.3
)
IV)I 1 270
§
500 I 1080 I 300
i
8~
i
• • — t
r ^
ô*
-D6@135
-D6@145
500 WW | 300
unto
Mil MO I
F i g . 4 . 8 . D e t a i l of s p e c i m e n B S 0 1 .
strength material, is applicable to members made of high strength material.
Five cantilever beams with floor slabs and one beam without slab of about one third scale were tested.
Figure 4.8 shows the detail of a representative specimen of BS01. Beam section is 200 mm by 270 mm with effective depth of 243 mm, and floor slab thickness is 50 mm and width is 1000 mm on one side. The left end of the specimen was bolted to the reaction wall, and a reversed cyclic load was applied in such a way that a point 810 mm away from the critical section of the cantilever is the point of contraflexure. Thus the shear span ratio M/VD is 3.0.
Specimen BS01 was made of 70 MPa concrete whose actual strength at testing was 58.4 MPa and Young's modulus 27.0 GPa. Beam axial re-bars were grade USD685 D13 bars with yield point 714 MPa and tensile strength 950 MPa. Stirrups were grade USD980 D6 bars with yield point 978 MPa and tensile strength 1141 MPa. Slab bars were ordinary grade SD295 D6 bars with yield point 346 MPa and tensile strength 527 MPa.
Other specimens involved variations of test parameters. BS02 had high strength slab reinforcement of grade USD980 bars. BS03 had slab concrete with ordinary strength of 30 MPa, whose actual strength was 28.8 MPa and Young's modulus 29.8 GPa. BS04 was similar to BS01 except that it had fewer slab distributing bars (perpendicular to beam) of D6 at 255 mm on centers.
BS05 had no floor slab. BS06 was a short specimen with 800 mm clear span, and loaded to produce shear span ratio of M/VD = 1.8.
Figure 4.9 shows load-deflection curves of three specimens; BS01, proto- type specimen, BS02, specimen with high strength slab bars, and BS05, speci- men without floor slab. Deflection was measured at the point of contraflexure.
Downward load and deflection associated with negative bending in the usual sense at the critical section were taken positive.
BS01 had flexural cracks in the slab at load 32.3 kN at which point the deflection angle was about 0.12 percent, and beam bars yielded at the deflection angle of about 1.5 percent as shown in Fig. 4.9(a). Positive load did not increase after beam bar yielding. In the negative direction where the floor slab was in compression, yield load was much lower. Figure 4.10 shows final crack pattern of BS01 specimen. Full lines and dotted lines indicate cracks due to positive loading and negative loading, respecitively.
Compared with BS01, BS02 showed much higher yield load, and the load continued to increase after beam bar yielding until the deflection angle reached about 5 percent as shown in Fig. 4.9(b). The behavior in the negative direction
-20 0 20 deflection (mm) (a) BS01- prototype 300
200 100
-200
300 200 100 ' 0
I I
-100 -200
B S 0 2 ;
Flexural cracking.
/Beam bar yielding
-60 -40 20 0 20
deflection (mm) (b) BS02- high strength slab bars
60
B S 0 5 ;
Flexural cracking _
_-Beam bar yielding
0^P'
[ •
-60 -40 -20 0 20 41 deflection (mm)
(c) BS05- without slab Fig. 4.9. Load-deflection curves.
was very similar to BS01. BS05 specimen without floor slab had smaller initial stiffness, and smaller cracking and yield loads as shown in Fig. 4.9(c), which were similar to those in the negative direction of BS01 or BS02. BS03 with ordinary strength concrete in the slab, and BS04 with fewer number of slab distributing bars, showed quite similar behavior as BS01. BS06 with short
R=l/20
Fig. 4.10. Crack pattern of BS01.
shear span showed similar behavior as BS01, if the deflection was expressed in terms of deflection angle (deflection of the point of contraflexure divided by the distance to the point).
Initial stiffness, inelastic secant stiffness at yielding, and cracking load in the positive direction were calculated assuming three kinds of slab effective width, and compared with the measured or observed values in the test in Fig. 4.11.
Initial stiffness was calculated considering elastic uncracked flexural and shear deformations based on the effective span length assuming the fixed end at one quarter the beam depth away from the critical section. Inelastic stiffness at yielding was obtained by multiplying ay, yield stiffness reduction factor originated by S. Sugano (Ref. 4.2), to the above-mentioned initial stiffness
ay = (0.043 + 1.64npt + QMZa/D){d/D)2 (4.1) where
ay : yield stiffness reduction ratio n : modular ratio of steel to concrete
Pt • tensile reinforcement ratio to be obtained as tensile re-bar area divided by uncracked concrete area
2.2- 2.0-
$ 1.6-
| l A
•a u- 5ằ>-
2 0.8-
§ 0.6.
n
" 0.4
8 0.2 0.0
a
ba=0.1L
O O
D
o
• v
•
ba=0.3L
• initial stiffness 4- yield stiffness
<^> cracking load
9
P.. P..
+
D ba=0.5L - i 1 1 r~
1 2 3 4 specimen No.
1
fi
Fig. 4.11. Comparison of measured vs. calculated values of initial stiffness, yield stiffness and cracking load.
a : shear span length (M/V) which is same as the distance to the point of contraflexure
D : beam depth
d : effective beam depth to the centroid of tensile reinforcement.
Cracking strength in Fig. 4.11 was calculated by the theory of elasticity assuming tensile strength of concrete as follows
cat = Q.hl^B (4.2) where
cat : tensile strength of concrete (MPa)
<JB '• compressive strength of concrete (MPa).
In Fig. 4.11, effective width was assumed in three ways, i.e. beam width plus twice the cooperating slab width ba, where cooperating slab width ba was taken to be 0.1L, 0.3L, and 0.5L (L: distance to the point of contraflexure).
As seen, initial stiffness is best estimated by ba = 0.1L, yield stiffness by ba = 0.3L, and cracking strength by ba = 0.5L.
Yield load and ultimate load was also calculated and compared with test results in the positive direction in Fig. 4.12. Entire slab width was assumed to be effective in these calculations, and the moment lever arm in the critical section was approximated by 7/8 times effective depth for yield load, and 0.9 times effective depth for ultimate load. As seen in Fig. 4.12, the assumption of entire width to be effective is a good approximation, slightly on the safe side.
Itemized conclusions are as follows
1.8- 1.6- 1.4- 1.2-
0 . 8 - 0.6- 0 . 4 - 0.2"
o.o-
D
"'!"" -
+ 6 S
full width
0 yield load + ultimate load
?
a
v— without slab
_ \ -
specimen No.
Fig. 4.12. Comparison of measured vs. calculated values of yield load and ultimate load.
(1) High strength of slab re-bars contributes to the beam strength under negative bending (slab in tension).
(2) High strength of slab concrete does not contribute to the beam strength.
(3) Amount of slab distributing bars (bars perpendicular to the beam axis) has no effect on the beam strength.
(4) Slab effective width based on cooperating width on one side of beam of 0.1L, 0.3L and 0.5L, appears to predict well the initial stiffness, yield stiffness, and cracking strength, respectively, under negative bending (slab in tension).
(5) In calculating yield load and ultimate load under negative bending, effective slab width may be assumed to be equal to the entire width.