of the concrete under the high bearing pressure at the ends of the wires, the effective anchorage lengths of the wires increase with time from the moment of release.
pre-
In boudless structures all stresses must be introduced by anchor- age blocks, regardless of the diameter of the steel. The prestresses may be maintained by the effect of the anchor- age alone or by bond established after the prestressing process is completed, or by bond established at
any later date.
Owing to the preliminary compres sion of the concrete, the principal ten- sion in prestressed concrete is always in structures considerably less than
where no precompression is applied to the conerete. The higher the precom pression, the lower the diagonal tension becomes.
The principal tensile stress remain- ing in prestressed structures can be reduced to zero by the application of an additional precompression.
In bonded beams, this precompres- sion in the second direction can be in- duced by the pre-tensioning of stirrups during construction. In bondless beams, the vertical precompression can be induced by sloping steel cables. The vertical component of the prestressing cable force effectively reduces the shear and also the principal tensile stresses near the supports.
of pre-
A prestressed concrete beam does not continue functioning as prestress- ed concrete up to complete destruction. It retains the characteristics stressed concrete only up to a certain limit of loading which is called the transformation load. Under loads in- creasing up to that limit, the concrete always works below its elastic limit. Beyond the transformation load, in- elastic deformations occur in the con- erete which cancel the effects of the
prestressing process, and the prestress- prestressing process, and the prestress ed beam starts working as an ordinary remforced concrete beam,
With normal working oads and up to the transıormation load, the deflec tions of the prestressed beam are very small
elastic. and practically fully From the transformation load onwards, the deflections increase very consider- ably, and cracks ecur in the tensile zone. When the excess load is re- moved, the cracks close again. How- ever, if the excess lads and the de- flections are increased stil further, the concrete as well as the steel show in- elastic permanent strains. If these loads are not too high, the cracks are still closing at the removal of the ex- cess loads, but the cracks re-appear under smaller loads than in previous cases. This effect is accompanied by a reduction in the effective prestresses. With the repeated application of excess loads, this process of deterioration is progressive.
The basic stipulation on the design with regard to working loads is that prestresses should be induced into the concrete in such a manner and to such a degree that all working stresses re- main within the elastic range.
With regard to the ultimate load. the design should
(a) aim at balancing the strength of the steel and the concrete so that they should fail simultaneously (or 13 nearly as possible);
(b) ensure co-operation of both materials up to the stage when the re- sistance of steel or concrete is exhausted:
(c) avoid failure of concrete due to shear or diagonal tension.
The ultimate load carrying capacity of prestressed beam with low or medium steel ratio is independent of the prestresses. This is illustrated in Fig. 28 by the load-deflection curves derived from a number of loading
tests with beams which were similar in all characteristics but the applied pre- stress. The tests shew that the load under which the first cracks occur in- creases with the prestress, and the breaking load is independent of the
deflections prestress. The
in direct proportion to the applied loads. and entirely elastic up to the limit at which cracks occurred.
were
In prestressed concrete cracking due to primary tensile stresses can only de- eur after both the precompression and the inherent tensile resistance have been exhausted. Within this range of stresses prestressed concrete behaves
The quite clastically.
stress-strain diagram is essentially
a straight line, the
as defined by Hooke's law, and
the conventional design may follow method using a constant modular ratio and permissible stresses. The factor of safety of the structure against cracking may be expressed either by a stress factor, or by a load factor. Due to the elasticity of prestressed Con- erete over this range, both values are identical.
As a rule, the factor of safety against cracking should be not less than 1.5 under statie loads and not less than 1.2 under dynamie loads against fatigue.
Due to the plastic character of the stress-strain diagrams of all types and mixes of concrete in the range of high stresses, a factor of safety applied to the stresses does not tell what the real safety of the structure is against des- truction by the external loads. It is therefore unavoidable that the ultimate strength of structures can only be defined by applying the factor of safety to the loads.
As a rule, the factor of safety against destruction should be not less than 2.5 under static loads and not less than 1.5 under dynamie loads against fatigue.
FIRM FOUNDATIONS FOR ALL TYPES OF STRUCTURES
THE
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VIBRO PILING
COMPANY LIMITED
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