GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

Question : 55 of 65

Marks: +1, -0

The planar structure RST shown in the figure is roller-supported at

{S}

and pin-supported at R. Members RS and ST have uniform flexural rigidity (EI) and

{S}

is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffening.

When the structure is subjected to a concentrated horizontal load

P

at the end

T

, the magnitude of rotation at the support

R

, is

Solution:

(Finding support reactions at

{ }^{n} R" & S"

) Using unit load method

∫↙{0}↖{L} \;{M_{x} ⋅ m_{x} ⋅ d x}/{E I} ;

Take

{ }^{n} R^{' '}

as the origin

M_{x} →

B.M due to applied loads/moments in the idealised structure

m_{x} →

B.M in the given structure due to unit load alone

M_{x}=[\;{-P}/{2}] ⋅ x ; 0 ≤ x ≤ L

m_{x}=\{\;{x}/{L}-1\} ; 0 ≤ x ≤ L

θ_{R}=\;{1}/{E I}[(\;{-P}/{2}) x] ⋅\{\;{x}/{L}-1\} d x

=\;{P}/{2}[x-\;{x^{2}}/{L}] d x=\;{P}/{2}[\;{x^{2}}/{2}-\;{x^{3}}/{3 L}]_{0}^{-L}=\;{P L^{2}}/{12 E I}

(Anti-Clock)

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