MEP-Technical Manual CDN 0408.qxd - Hambro

4
DESIGN PRINCIPLES AND CALCULATIONS
4.1.3 MOMENT CAPACITY
The factored moment resistance of a reinforced concrete
section, using an equivalent rectangular concrete stress
distribution is given by:
t
d
Mr = øsAs Fy (d - a/2)
a = depth of the equivalent concrete stress block
= ø s A s F y
� 1 ø c f’ c b
Where Fy = yield strength of reinforcing steel (400 MPa)
f’ c = compressive strength of concrete (20 MPa)
As = area of reinforcing steel in the direction of
analysis (mm2 /m width)
�1 = 0.85 - 0.0015f’ c ≥ 0.67
b = unit slab width (mm)
d = distance from extreme compression fiber to
centroïd of tension reinforcement (mm)
(see tables 8 and 9 on pages 19 and 20)
øs = performance factor of reinforcing steel (0.85)
øc = performance factor of concrete (0.65)
4.1.3.1 SHEAR CAPACITY
The shear stress capacity V, which is a measure of diagonal
tension, is unaffected by the embedment of the section as
this principal tensile crack would be inclined and radiate away
from the section.
The factored shear capacity is given by:
Vr = Vc = øc�ß f’ c bwd √
(CSA A23.3-04, clause 11.3.4)
Fig. 6
c C
Where � = 1.0 for normal density concrete
ß = 0.21 = (CSA A23.3-04, clause 11.3.6.3)
bw = b = width of slab
And ø c ,f’ c and d are as previously described.
T
a
4.1.4 SERVICEABILITY LIMIT STATES
4.1.4.1. CRACK CONTROL PARAMETER
When the specified yield strength, F y , for tension reinforcement
exceeds 300 MPa, cross sections of maximum positive
and negative moments shall be so proportioned that the
quantity Z does not exceed 30 kN/mm for interior exposure
and 25 kN/mm for exterior exposure. Ref. CSA A23.3-04,
clause 10.6.1.
The quantity Z limiting distribution of flexural reinforcement
is given by:
3
Z = fs dcA x 10-3 √
Where fs = stress in reinforcement at specified loads
taken as 0.6Fy dc = thickness of concrete cover measure from
extreme tension fibre to the center of the
reinforcing bar located closest thereto
(dc ≤ 50 mm)
4.1.4.2 DEFLECTION CONTROL
For one-way slabs not supporting or attached to partitions
of other construction likely to be damaged by large deflections,
deflection criteria are considered to be satisfied if the
following span/depth ratio are met:
at location � t ≥ �n/24
Width
Bar spacing
Fig. 7
at location � t ≥ �n/28 (CSA A23.3-04, table 9.2)
�n=Space between joists or joist to wall
d c
d c