[PERSPET
IN SITU PRESTRESSED BOX GRIDER
[CONCRETE MOVEL
115-anchored span
31-0
78-0 central suspended 31-0
115-0
Cantileve
iver
span
C1
སོགཿ
Aj
CJ
B
varies
(21-0° to 24-0)
min
KING'S ROAD
varles (21-0 to 24-0)
varies (24-0 approx).
FALL IN 165
4.9 min.
C-C
Symbolically, the deflection of any point of a structure can be written
as:-
FL3 FL Aj=B. -+B. +B:: +Bi
ΕΙ
FL
EA GA
FL3
GJ
Where F is a load typifying the complete system of loads acting on the structure, L is the length of a typical member of structure, and EA, EI. GA and GJ are the extensional, flexural, shear and torsional rigidities respectively: B1, B2, B. and B. are numerical coefficients which depend upon the geometry of the structure.
For the model to simulate the exact behaviour of the prototype, the de- flections at corresponding points in the model and the prototype must bear a constant ratio.
Therefore,
(B, FL 3
ΕΙ
(6, FL 3
В
ΕΙ
Aj prototype A j model
FL
FL
+ B.:
EA
+ Ba
GA
FL
+B
EA
=
+ B. FLJ3) p
+B +B, FL3),
FL GA
= constant
GJ
N
For perfect similarity it is necessary that the relationships between L. A, I and J are the same for both the model and the prototype. This can only be achieved by complete geome- tric similarity between the model and the prototype.
As a prestressed concrete structure behaves in a linear elastic manner under the working load, its behaviour within this range can be correctly re- presented by a model made with any linear elastic material. However to simulate the ultimate load condition in a model it is necessary that the changes in incremental strains at cor- responding points of the model and the prototype should be in the same ratio.
Thus the stress-strain characteristics of the model material and the pro- totype material must be similar: prac-
B-B
A-A
Fig. 2. Centre-line elevation of curved spans
tically this means that the model must be made of the same material as the prototype.
It was not considered practical to furnish all the required answers with only one model for this investigation. Consequently two models have been fabricated, one in perspex of the cen- tral suspended span together with one anchored span and a second model in prestressed concrete of the central suspended span.
Perspex model
Perspex was chosen as the model material because of its low modulus of elasticity (0.4 X 106 p.s.i.). It is easy to machine and good joints can easily be made by solvent welding.
The scale of the model, 1/24th full size, was chosen so that all the members could be simply machined from %in. and 1⁄2 in. sheet perspex. The modelled structure was simplified by making the top deck of the model flat.
The model was fabricated in radial sections; each section consisting of a top flange, a bottom flange and longitudinal and transverse stiffeners. The bottom flange and the stiffeners were solvent welded to the top flange forming a rigid box. These boxes were then machined to shape and joined together to form the complete model.
As the prototype central suspended span is elastically supported at each end, it was necessary to provide similar supports for the model. From preliminary tests it was determined that, as far as the central suspended span was concerned, the anchored span behaved as a pair of springs having a specific vertical and torsional stiffness. Consequently one end of the central suspended span was supported on two cantilever springs. The model, together with the loading device, is shown in figure 3.
Measurements to be taken are the vertical deflections at 35 points and the strains at 82 points on the top and
48
Fig. 3.
Details of Perspex model and loading system
Far East BUILDER, May 1968.