A simply supported beam PQ is loaded by a moment of 1 kNm at the mid-span of the beam as shown in the figure. The reaction forces $R_{P}$ and $R_{Q}$ at supports P and Q respectively are

1 kN downward, 1 kN upward

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0.5 kN upward, 0.5 kN downward

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0.5 kN downward, 0.5 kN upward

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1 kN upward, 1 kN down ward

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Solution

The correct option is A 1 kN downward, 1 kN upward
$L e t u s a s s u m e t h e d i r e c t i o n o f R_{P} a n d R_{Q} a s u p w a r d, N o w,$

$∴ R_{P} + R_{Q} = 0$

$∴ T a k i n g m o m e n t a b o u t p o i n t Q, w e g e t$

$R_{P} \times 1 + 1 = 0$
$R_{P} = - 1 k N$

$∴ R_{Q} = + 1 k N$

$S i n c e, o u r a s s u m e d d i r e c t i o n o f R_{P} i s w r o n g, t h e r e f o r e, R_{P} = 1 k N w h i c h a c t i n t h e d o w n w a r d d i r e c t i o n a n d R_{Q} = 1 k N a c t i n g i n u p w a r d d i r e c t i o n .$

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