MEP-Technical Manual CDN 0408.qxd - Hambro

DESIGN PRINCIPLES AND CALCULATIONS
4.3.2 VARIOUS FLEXURE FAILURE STAGES
t
Joist depth “d”
� 1 f’ c
C f a
Upon additional load application, the steel and concrete
strains progress further into their inelastic ranges. The
strain neutral axis continues to rise and the lever arm
continues to increase as the centroid of compression force
continues to rise. In (c), final failure occurs with crushing of
the upper concrete fibres. At this point, the maximum fever
arm e’, has been reached. In load capacity calculations, the
simplified concrete stress block as shown in (c) is universally
used.
According to CAN3-S16.1-M01 (cl.17.9.3) and CSA A23.3-04
(cl.10.1.7), the factored resisting moment of the composite
section is given by:
M rc = ø s A s F y e’ = T r e’
Strain line
T u = A s F y
(a)
Initial steel yield
� 1 f’ c
Where e’ = d + slab thickness – a/2 – y
d = joist depth
a = T r / � 1 ø c f’ c b e
ø s = steel performance factor = 0.90
A s = area of bottom chord
y = neutral axis of bottom chord
E y
T u = A s F y
Elastic
strain
E y
� 1 ø c f’ c
Simplified
concrete
stress block
Inelastic strain
(b)
Secondary yield stages
C u
f’ c
e’
Fig. 13
Elastic
strain
Fy = yield point of steel
øc = concrete performance factor = 0.65
f’ c = concrete compressive strength
be = effective width of concrete top flange
= the lesser of - joist spacing, or
- span /4.
Note: To determine the total allowable service load W s
(see load tables), we convert the factored moment
into a factored linear loading.
Mf = Wf L2 (single span moment)
8
W f = 8 M f
L 2
And
C
T u = A s F y
Inelastic strain
(c)
Ultimate stage
W s = (W f - 1.25 D) + D
1.5
Where D = weight of (slab + joist)
11