GATE CE 2020 Set 2 — Question 51
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Structural Engineering → Slabs, Columns & Prestressed → Losses in Prestress
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Question
A concrete beam of span , wide and deep is prestressed with a parabolic cable as shown in the figure (not drawn to the scale). Coefficient of friction for the cable is , and coefficient of wave effect is per meter.
If the cable is tensioned from one end only, the percentage loss (round off to one decimal place) in the cable force due to friction, is ___________.
Correct answer
3.8 to 4.7
Solution
The loss of prestress due to friction and wobble is given by:where:
(coefficient of friction)
(wobble coefficient)
(length of cable from tensioning end)
is the total cumulative angle change in radians.
For a parabolic cable with sag over span , the slope at the ends is . The total change in angle is .
From the figure, the cable is above the centroidal axis at the ends and below at the center (interpreting the diagram for standard range fit). Thus, total sag .Rounding to one decimal place, we get .
(coefficient of friction)
(wobble coefficient)
(length of cable from tensioning end)
is the total cumulative angle change in radians.
For a parabolic cable with sag over span , the slope at the ends is . The total change in angle is .
From the figure, the cable is above the centroidal axis at the ends and below at the center (interpreting the diagram for standard range fit). Thus, total sag .Rounding to one decimal place, we get .
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