GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 49 of 65

Marks: +1, -0

A prismatic beam P-Q-R of flexural rigidity

E I=1 × 10^{4} {kNm}^{2}

is subjected to a moment of 180 kNm at

Q

as shown in the figure.

The rotation at Q (in rad, up to two decimal places) is _________

Solution:

K_{Q} \;\; =K_{ϕ P}+K_{Q R}

\;\; =\;{4 E I}/{5}+\;{4 E I}/{4}=1.8 {EI}

θ_{Q} \;\; =\;{M_{Q}}/{K_{Q}}=\;{180}/{1.8 × 10^{4}}=0.01 {rad}

Alternate solution

M_{Q ρ}=M_{\;\text "fQp "\;}+\;{2 E I}/{l}[2 θ_{Q}+θ_{ρ}]

\{M_{\;\text "fQP "\;}=0, θ_{P}=0\}

=\;{4 × 10^{4}}/{5} × θ_{Q}=8000 θ_{Q}

M_{Q R}=M_{f Q R}+\;{2 E I}/{I}[2 θ_{Q}+θ_{R}]

\{M_{ {rQR}}=0, θ_{R}=0\}

=\;{2 × 10^{4}}/{4} × θ_{Q}=8000 θ_{Q}

Σ M_{Q}=0

⇒ M_{Q P}+M_{Q R}+180=0

⇒ 18000 ⋅ θ_{Q}=-180

⇒ θ_{Q}=0.01

radian (anticlockwise)

Go to Question:

Prev Question

Next Question