GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

Question : 56 of 65

Marks: +1, -0

A concrete beam of span

15 {m}, 150 {mm}

wide and

350 {mm}

deep is prestressed with a parabolic cable as shown in the figure (not drawn to the scale). Coefficient of friction for the cable is

0.35

, and coefficient of wave effect is

0.0015

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 _______.

Solution:

M=0.35, K=0.0045 {/} m

Jacking from one end

∴ {X}= {L}=15 {M}

coefficient (or) wave coefficient

{k}=0.0015 \/ {m}

α=\tan α=\;{8 {h}}/{ {L}}=\;{8 ×(50+70)}/{15,000}=0.064

. . . . . . .

. . . . . . .=p o(M a+t x)

=Po(0.35 × 0.064+(0.0015) × 15)

. . . . . . . . .=\;{P o(M α+k x)}/{P o} × 100

=[(0.35 × 0.064)+(0.0015 × 15)] × 100

=4.49 \%

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