Civil Engineering Reference
In-Depth Information
σ
ab
=
M
self weigh
t
/
z
ab
+
P
/
A
ab
±
Pe
ab
/
z
ab
,
the monolithic stresses would be
σ
mono
=
M
self weight
/
z
mono
+
P
/
A
mono
±
Pe
mono
/
z
mono
and the design stresses
σ
des
= (
σ
ab
+
φσ
monov
)/(1+
φ
),
where
M
self weight
is the moment due to the weight of the complete cross section.
The bending stresses due to subsequent loads applied to the beams after the second
phase concrete has hardened, such as fi nishes, live loads and prestressing tendons
stressed after the change in section will be calculated using the monolithic section
properties.
Another common occurrence of this problem occurs when a bridge deck consists
of two parallel box girders that are built and fully prestressed, and subsequently
stitched together with a cast-in-situ slab. The bending stresses in the deck may be
calculated ignoring the structural contribution of the slab (considering its self weight
as a superimposed dead load), and then again assuming that the slab was present as
the deck was erected and prestressed. The bending stresses for the two limits may then
be compared. A best estimate of the actual stresses may be made as described in the
paragraph above.
In a prestressed concrete bridge deck, the self weight and the prestress generally
act in opposition to each other. Consequently the uncertainties in the value of
moments and stresses are much reduced with respect to a reinforced concrete deck.
Furthermore, the self weight and prestress constitute only a proportion of the total
bending moments. Consequently the overall effect of creep on the suitability of bridge
decks of medium span to carry their specifi ed loads is generally of limited signifi cance;
excessive accuracy in the calculation of moments and stresses is illusory and should
not be sought. For bridge decks with a span in excess of about 120 m, where the self
weight and prestress moments predominate, more care must be taken to establish
where, between the as-built and monolithic limits, the reality lies.
6.23 Bursting out of tendons
A curved tendon applies pressure to the concrete on the inside of the curve. The
pressure
Q
KN/m =
P/r
, where
P
is the force in the cable and
r
is its radius of curvature.
For a duct radius of 7 m, which is typical of many schemes, a tendon consisting of
12 strand of 13 mm diameter, with a force at stressing of approximately 1,600 kN, the
pressure applied to the concrete would be 230 kN/m, while for a tendon consisting
of 27 strand of 15 mm, with a stressing force of 5,300 kN, the pressure would be
760 kN/m. Where the curve of the tendon is concave towards a free concrete surface,
such that the cover to the tendon may be pushed off by this force, it is necessary to
detail reinforcement that carries the force back, behind the tendon, Figure 6.28 (a).
Examples of such curved tendons may be found for instance in the blisters for internal
tendons described in
6.24
, at rapid changes in thickness of bridge deck webs and in the
curved bottom slabs of variable depth bridges.
The pressure on the inside of the curve may also cause curved tendons that are
stacked in a web to collapse onto the tendon above or below, if the spacing is inadequate,
