2.7.1 Equivalent loads and linear transformation
The equivalent loading due to prestress can generally be found by simple equilibrium of
forces. For example, for the externally prestressed bridge illustrated in Fig. 2.11(a),
equilibrium of vertical forces gives an upward force at B of:
As the angle, θ, is generally small, this can be approximated as:
(2.7)
It also follows from the small angle that the horizontal force is P cosθ ≈P. Finally, as the
forces are eccentric to the centroid at the ends, there are concentrated
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Fig. 2.11 Prestressed concrete beam with external post-tensioning: (a) elevation showing tendon;
(b) equivalent loading due to prestress
moments there of magnitude (Pcosθ)e2≈Pe2. Hence the total equivalent loading due to
prestress is as illustrated in Fig. 2.11(b). It can be shown that the equivalent loading due to
prestress is always self-equilibrating.
A parabolically profiled prestressing tendon generates a uniform loading which again can
be quantified using equilibrium of vertical forces. A small segment
Fig. 2.12 Segment of parabolically profiled tendon: (a) elevation; (b) equivalent loading
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of such a profile is illustrated in Fig. 2.12(a). At point 1, there is an upward vertical
component of the prestress force of:
(2.8)
As the angles are small:
(2.9)
where x1 is the X coordinate at point 1. This force is upwards when the slope is positive.
Similarly the vertical component of force at 2 is:
(2.10)
where F2 is downwards when the slope is positive. The intensity of uniform loading on this
segment is:
(2.11)
The equivalent loads on the segment are illustrated in Fig. 2.12(b).
相当于载入中由于预应力一般都可以通过简单的平衡
部队。例如,对于体外预应力桥梁说明图。 2月11日(一) ,
平衡垂直力给出了一个向上的力量在B :
由于角, ? ? ,通常很小,这可近似为:
( 2.7 )
它还如下的小角度的水平力为P余弦? ? ? ?体育最后,如
部队偏心的心在两端,有集中
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图。 2月11日预应力混凝土梁与外部后张: (一)海拔显示肌腱;
(二)相当于载入中由于预应力
时刻有级(剂? ? )素E2 ? ? Pe2 。因此,总当量载入中因
预应力是图所示。 2月11日( b )项。有证据表明,相当于载入中因
预应力总是自我平衡。
阿parabolically异形预应力筋产生一个统一的,又可以载入
量化使用平衡垂直力。一小部分
图。 2月12日段parabolically异型肌腱: (一)海拔; (二)相当于载入中
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这样一个形象的说明图。 2月12日(一) 。在第1点,有向上垂直
部分预应力力量:
( 2.8 )
由于角小:
( 2.9 )
如果x1是x坐标点1 。这支部队是向上的斜坡时,是积极的。
同样,垂直分量武力2 :
( 2.10 )
在F2是向下的斜坡时,是积极的。强度统一载入中关于这个
部分是:
( 2.11 )
相当于负载的部分说明了在图。 2月12日( b )项。