GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

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Question : 63 of 65

Marks: +1, -0

Four bolts

{P}, {Q}, {R}

and

{S}

of equal diameter are used for a bracket subjected to a load of

130 {kN}

as shown in the figure.

The force in bolt

{P}

is

$32.50 {kN}$
$69.32 {kN}$
$82.50 {kN}$
$119.32 {kN}$

Solution:

F_{1} \;\; =\;{P}/{n}=\;{130}/{4}=32.5 {kN}

F_{2} \;\; =\;{P e 2}/{Σ r_{i}^{2}} × r_{p}

r_{p} \;\; =r_{Q}=r_{R}=r_{S}=√{50^{2}+120^{2}}=130 {mm}

F_{2} \;\; =\;{(130 × 200) × 130}/{4 × 130^{2}}=\;{200}/{4}=50 {kN}

\cos θ \;\; =\;{50}/{130}

⇒ F_{R} \;\; =√{(32.5)^{2}+(50)^{2}+(2 × 32.5 × 50) ×(\;{50}/{130})]}

\;\; =69.33 {kN}

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