GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 37 of 65

Marks: +1, -0

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

{P}_{f} {Q}

and

R

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

10 {kN}{/} {mm}

. The lower ends of bar

{P}

and

{R}

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

2 {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 {mm}

in the vertically downward direction.

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

Solution:

\;{ {AE}}/{ {L}}=10 {kN} \/ {mm}

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

from symmetry

⇒ w_{1}=w_{3}

δ_{p}=5 m m=\;{w_{1} L}/{A E}

∴ W_{1}=50 {kN}=w_{3}

δ_{Q}=\;{w_{2} L}/{A E}

∴ w_{2}=30 {kN}

∴ {W}=130 {kN}

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