SSC JE Civil Engineering 23-Mar-2021 Shift 1 Paper

Question : 128 of 200

Marks: +1, -0

A cantilever of beam of span l is fixed at one end, the other end resting freely on the middle of a simply supported cross-beam of the same span and section. If the cantilever beam is now loaded with a uniform load of w per unit length, find the reaction at the free end offered by the cross beam.

$3/8\w\l$
$2/5\w\l$
$6/17\w\l$
$3/17\w\l$

Validate

Solution:

Solution
Concept:
Definition of cantilever beam due to point load

={{\P} 1^{3}}/{3 {\EI}}

Definition of cantilever beam due to udl

={{\w} 1^{3}}/{3 {\SEI}}

Definition of SSB due to point load at mid point

={{\Pt}^{3}}/{4 {\QEI}}

Solution:

Definition at the end of contilever beam is given by,

={{\w} 1^{4}}/{{\QEI}}={{\Rl}^{3}}/{3{\EI}}

Definition at mid point of SSB.

={{\Rl}^{3}}/{4 {\QEI}}

Equating both the cases,

{{\wl}^{4}}/{{\QEI}}={{\Rl}^{3}}/{3 {\EI}}={{\Rl}^{3}}/{4 {\QEI}}

{{\wl}^{4}}/{{\QEI}}={{\Rl}^{3}}/{4 {\QEI}}+{{\Rl}^{3}}/{3 {\EI}}

{{\wl}^{4}}/{{\QEI}}=({1+16}/{48}) {{\Rl}^{3}}/{{\EI}}

{\R}={6 {\wl}}/{17}

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