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GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

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Question : 37 of 65

Marks: +1, -0

A rigid, uniform, weightless, horizontal bar is connected to three vertical members

P_{f} Q

R

as shown in the figure (not drawn to the scale). All three members have identical axial stiffness of

10\,\mathrm{kN}/\mathrm{mm}

. The lower ends of bar

P

R

rest on a rigid horizontal surface. When NO load is applied, a gap of

2\,\mathrm{mm}

exists between the lower end of the bar

Q

and the rigid horizontal surface. When a vertical load

W

is placed on the horizontal bar in the downward direction, the bar still remains horizontal and gets displaced by

5\,\mathrm{mm}

in the vertically downward direction.

The magnitude of the load W (in kN, round off to the nearest integer), is

Your Answer:

Solution:

\;\frac{AE}{L}=10\,\mathrm{kN}/\mathrm{mm}

w_{1}+w_{2}+w_{3}=W

from symmetry

\Rightarrow w_{1}=w_{3}

\delta_{p}=5\,\mathrm{mm}=\;\frac{w_{1} L}{A E}

\therefore W_{1}=50\,\mathrm{kN}=w_{3}

\delta_{Q}=\;\frac{w_{2} L}{A E}

\therefore w_{2}=30\,\mathrm{kN}

\therefore W=130\,\mathrm{kN}

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