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1.Cable Sizing:
(i) Calculate the factored moment at the critical positive and
negative moment
positions.
(ii) At each critical section, calculate the lever-arm distance
between the centroid
of the assumed compression block of the concrete section and the
centroid ofthe prestress cable group (alowing for necessary cover
and cable spacing).
(iii) Determine required final prestress force by dividing
factored moment by
lever-arm.
(iv) Calculate prestress area by dividing this final prestress
force by the strand
factored resistance (Phi x GUTS)
(v) Confirm number of cables required, and re-check the cable
positioning
constraints in section (and re-calc the lever arm as
required).
2. Back-calculate jacking force:
Jacking force is approximately 25% higher than final prestress
force calculated
above, assuming 20% losses (10% initial losses, 5% creep, 2%
shrinkage, 3%
prestressing steel relaxation). The initial losses come from
typical values of 5%
for friction & wobble, 2.5% for a 6mm wedge slip, and 2.5%
for elastic
deformation of the girder section.
3. Check concrete SLS extreme fibre stresses against code limits
using service
moments, secondary effects from the presressing and C&S and
the following
effective primary prestress forces (i.e. after resp.
losses):
(i) At initial prestress transfer using 90% of jacking force
(ii) At final stage using 80% of jacking force
You probably have the "preliminary sizing" for your cables after
the very quick
step 1, but need to do checks in Step 2 & 3 to confirm that
your whole section
arrangement is working.
Before sizing tendons I would ask myself the following
question:
What do I want to achieve with the prestressing-effect?
This question has many possible answers such as (a) increased
stiffness, (b)
fewer concrete cracks, (c) smaller crack widths, (d) increased
slenderness, (e)
avoiding mild steel congestion, (f) saving material and cost,
(g) an increased
durability and robustness (g) an accelerated construction
process etc.
But there is another point I would like to mention. Eugne
Freyssinet, a pioneer
of prestressed concrete, believed that prestressing should
ensure that the
concrete never experiences any tensile stresses. Today we know
that in many
cases even high degrees of prestress (you will find a definition
in my lastparagraph) did not achieve this objective and did not
deliver the most
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economical solutions. On the other hand, we all know that the
use of high-
strength prestressing steel requires strict crack control rules
and that a low
degree of mild steel may be fatal if cracks do occur.
I believe that partly-prestressed structures with a minimum
amount of mild steel
are the best to achieve effective and durable concrete
structures. The degree ofprestress depends on many factors (e.g.
structural purpose, geometry, dead and
live load, time depending effects).
How does this work in the real world? Ask yourself the following
questions:
1. What is the minimum mild steel prescribed by the design
standard?
2. Does the minimum mild steel required by code provide proper
crack control in
my case?
3. What degree of prestress is required to satisfy the ULS
design scenarios if I
use only the selected mild steel required for crack control?
4. Do I achieve my SLS objectives (e.g. crack control, concrete
and steel
stresses, deformations) with the selected degrees of prestress
and mild steel?
5. What does this mean for detailing (e.g. anchorage zones,
splices, construction
joints)?
6. How can I optimize my design in respect to cost and
construction schedule?
I mentioned several times the terms (i) degree of prestress and
(ii) degree of
mild steel and I owe you definitions. There are no generally
accepted definitions
so I give you mine:
(i) You achieve a 100% degree of prestress if you satisfy SLS
and ULS design
scenarios with high-strength prestressing steel only.
(ii) You achieve a 100% degree of mild steel if you satisfy SLS
and ULS designscenarios with mild steel only.
