Page 211 - Civil Engineering Formulas

146 CHAPTER FIVE

where b perimeter of critical section and ratio of long side to short side
c
o
of critical section.
However, if shear reinforcement is provided, the allowable shear may be
increased a maximum of 50 percent if shear reinforcement consisting of bars is
used and increased a maximum of 75 percent if shearheads consisting of two
pairs of steel shapes are used.
Shear reinforcement for slabs generally consists of bent bars and is designed in
accordance with the provisions for beams with the shear strength of the concrete at
critical sections taken as 2 f c b o d at ultimate strength and V 6 f c b o d .
n
Extreme care should be taken to ensure that shear reinforcement is accurately
placed and properly anchored, especially in thin slabs.

COLUMN MOMENTS

Another important consideration in design of two-way slab systems is the transfer
of moments to columns. This is generally a critical condition at edge columns,
where the unbalanced slab moment is very high due to the one-sided panel.
The unbalanced slab moment is considered to be transferred to the column
partly by flexure across a critical section, which is d/2 from the periphery of the
column, and partly by eccentric shear forces acting about the centroid of the
critical section.
That portion of unbalanced slab moment M transferred by the eccentricity
u
of the shear is given by M :
u

1
v 1 (5.106)
2
1 b 1
3 Bb 2

where b width, in (mm), of critical section in the span direction for which
1
moments are being computed; and b width, in (mm), of critical section in
2
the span direction perpendicular to b .
1
As the width of the critical section resisting moment increases (rectangular
column), that portion of the unbalanced moment transferred by flexure also
increases. The maximum factored shear, which is determined by combining the
vertical load and that portion of shear due to the unbalanced moment being
transferred, should not exceed V , with V given by preceding the V equation.
c
c
c
The shear due to moment transfer can be determined at the critical section by
treating this section as an analogous tube with thickness d subjected to a bend-
ing moment M .

u
The shear stress at the crack, at the face of the column or bracket support, is
limited to 0.2f c or a maximum of 800 A , where A is the area of the concrete
c
c
section resisting shear transfer.
The area of shear-friction reinforcement A required in addition to reinforcement
vf
provided to take the direct tension due to temperature changes or shrinkage should be