Consider the deformable pin-jointed truss with loading, geometry and section properties as shown in figure. Given that E=2 \times 10^{11} {N} {/} {m}^{2}, A=10 {mm}^{2} L=1 {m} and P=1 {kN}. the horizontal displacement of Joint {C} (in {mm}, up to one decimal place) is

GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 39 of 65

Marks: +1, -0

Consider the deformable pin-jointed truss with loading, geometry and section properties as shown in figure.

Given that

E=2 × 10^{11} {N} {/} {m}^{2}, A=10 {mm}^{2}

L=1 {m}

and

P=1 {kN}

. the horizontal displacement of Joint

{C}

(in

{mm}

, up to one decimal place) is

Solution:

∆_{ {c}}]

horizontal

=Σ \;{ {P}_{ {i}} {u}_{ {i}} {L}}/{ {AE}}

Applying 1 unit load in horizontal direction at

{C}

⇒ ∆_{ {C}}=\;{(√{2} {P})(√{2}) √{2} {L}}/{2 {AE}}+\;{(3 {P})(1) × {L}}/{ {AE}}+\;{( {P})(1)( {L})}/{ {AE}}

⇒ ∆_{ {C}}]_{\;\text "horizmall "\;}=\;{ {PL}}/{ {AE}}(4+√{2})=\;{(1000)(1)(4+1.414) × 1000}/{10 × 2 × 10^{11} {/} 10^{6}}

∆_{ {C}}]_{\;\text "barizanal "\;}=2.707 {mm}

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