求助：桥梁工程专业英语翻译（一）

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
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).

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