GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 38 of 65

Marks: +1, -0

A rectangular steel bar of length

500 {mm}

, width

100 {mm}

, and thickness

15 {mm}

is cantilevered to a

200 {mm}

steel channel using 4 bolts, as shown.

For an external load of

10 {kN}

applied at the tip of the steel bar, the resultant shear load on the bolt at

B

, is kN (round off to one decimal place).

Solution:

r_{B}=√{50^{2}+50^{2}}=50 √{2}

P_{B}{'}=\;{P}/{\;\text "No of bolt "\;}=\;{10}/{4}=2.5 {kN}

P_{B}{''}=\;{P_{e} r_{B}}/{(r_{a}^{2}+r_{b}^{2}+r_{c}^{2}+r_{d}^{2})}

\;\; =\;{10 × 10^{3} × 0.4 ×(50 √{2} × 10^{-3})}/{4 ×(50 √{2} × 10^{-3})^{2}}

\;\; =14.14 {kN}

Resultant

=√{(P_{B}^{'})^{2}+(P_{B}^{'})^{2}+2 P_{B}^{'} × P_{B}^{' '} \cos 45^{∘}}

\;\; =16 {kN}

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