CIVIL ENGINEERING FORMULAS

CONCRETE FORMULAS 145

1.The sum of the flexural stiffnesses of the columns above and below the slab
Kcshould be such that

(5.102)

where Kcflexural stiffness of columnEccIc
Eccmodulus of elasticity of column concrete
Icmoment of inertia about centroidal axis of gross section of column
KsEcsIs
KbEcbIb
minminimum value of cas given in engineering handbooks

2.If the columns do not satisfy condition 1, the design positive moments in the
panels should be multiplied by the coefficient:

(5.103)

SHEAR IN SLABS

Slabs should also be investigated for shear, both beam type and punching shear. For
beam-type shear, the slab is considered as a thin, wide rectangular beam. The crit-
ical section for diagonal tension should be taken at a distance from the face of
the column or capital equal to the effective depth dof the slab. The critical
section extends across the full width bof the slab. Across this section, the
nominal shear stress vuon the unreinforced concrete should not exceed the ulti-
mate capacity or the allowable working stress 1.1 , where is the
28-day compressive strength of the concrete, lb/in^2 (MPa).
Punching shear may occur along several sections extending completely
around the support, for example, around the face of the column, or column cap-
ital, or around the drop panel. These critical sections occur at a distance d/2
from the faces of the supports, where dis the effective depth of the slab or drop
panel. Design for punching shear should be based on

(5.104)

wherecapacity reduction factor (0.85 for shear and torsion), with shear
strengthVntaken not larger than the concrete strength Vccalculated from

Vc 2  (5.105)

4

c^2

fcbod 42 fcbod

Vn(VcVS)

2 fc fc fc

s 1 

2 a

4 a

1 

c

min

c

Kc

(KsKb)

 min