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Question Number 169448 by BHOOPENDRA last updated on 30/Apr/22

Commented by BHOOPENDRA last updated on 30/Apr/22

$c a l c u l a t i o n s i r$
Commented by BHOOPENDRA last updated on 30/Apr/22

$t h a n k y o u s i r$
Commented by BHOOPENDRA last updated on 01/May/22

Commented by BHOOPENDRA last updated on 01/May/22

Commented by mr W last updated on 01/May/22

$t h e r e a r e m a n y m e t h o d s t o s o l v e .$ $t e l l w h a t y o u g e t f o r M_{A}, M_{B}, M_{C}, M_{D},$ $m a y b e i c a n c h e c k i f i c a n g e t t h e$ $s a m e .$
Commented by mr W last updated on 01/May/22

$F o r c a l c u l a t i o n b y h a n d w e a p p l y$ $u s u a l l y$ $M e t h o d I :$ $w e t a k e t h e m o m e n t s a t t h e s u p p o r t s$ $a s u n k n o w n s$ $\Rightarrow s y s t e m w i t h 4 u n k n o w n s$ $M e t h o d I I :$ $w e t a k e t h e s l o p e s a t t h e s u p p o r t s B, C$ $a s u n k n o w n s$ $\Rightarrow s y s t e m w i t h 2 u n k n o w n s$ $b o t h a r e e a s y, b u t i t n e e d s t i m e t o$ $w o r k o u t . . .$
	Answered by mr W last updated on 01/May/22

	$M o m e n t u n d e r l o a d s :$ $M_{A, r, 0} = - \frac{1.5 \times 4^{2}}{12} = - 2 K N m$ $M_{B, l, 0} = \frac{1.5 \times 4^{2}}{12} = 2 K N m$ $M_{B, r, 0} = - \frac{7 \times 4}{8} = - 3.5 K N m$ $M_{C, l, 0} = \frac{7 \times 4}{8} = 3.5 K N m$ $M_{C, r, 0} = - \frac{8 \times 1 \times 3^{2}}{4^{2}} = - 4.5 K N m$ $M_{D, l, 0} = \frac{8 \times 3 \times 1^{2}}{4^{2}} = 1.5 K N m$ $M o m e n t u n d e r θ_{1} = s l o p e a t B \times E I = 1 :$ $M_{A, r, 1} = \frac{2}{4} = 0.5 K N m$ $M_{B, l, 1} = \frac{4}{4} = 1 K N m$ $M_{B, r, 1} = \frac{4}{4} = 1 K N m$ $M_{C, l, 1} = \frac{2}{4} = 0.5 K N m$ $M_{C, r, 1} = 0 K N m$ $M_{D, l, 1} = 0 K N m$ $M o m e n t u n d e r θ_{2} = s l o p e a t C \times E I = 1 :$ $M_{A, r, 2} = 0 K N m$ $M_{B, l, 2} = 0 N m$ $M_{B, r, 2} = \frac{2}{4} = 0.5 K N m$ $M_{C, l, 2} = \frac{4}{4} = 1 K N m$ $M_{C, r, 2} = \frac{4}{4} = 1 K N m$ $M_{D, l, 2} = \frac{2}{4} = 0.5 K N m$ $Σ M_{B} = (1 + 1) θ_{1} + 0.5 θ_{2} + 2 - 3.5 = 0$ $\Rightarrow 4 θ_{1} + θ_{2} = 3 . . . (i)$ $Σ M_{C} = 0.5 θ_{1} + (1 + 1) θ_{2} + 3.5 - 4.5 = 0$ $\Rightarrow θ_{1} + 4 θ_{2} = 2 . . . (i i)$ $s o l v i n g (i) a n d (i i) w e g e t$ $θ_{1} = \frac{2}{3}$ $θ_{2} = \frac{1}{3}$ $M_{A, r} = - 2 + 0.5 \times (\frac{2}{3}) = - \frac{5}{3} K N m$ $M_{B, l} = 2 + 1 \times (\frac{2}{3}) + 0 \times (\frac{1}{3}) = \frac{8}{3} K N m$ $M_{B, r} = - 3.5 + 1 \times (\frac{2}{3}) + 0.5 \times (\frac{1}{3}) = - \frac{8}{3} K N m$ $M_{C, l} = 3.5 + 0.5 \times (\frac{2}{3}) + 1 \times (\frac{1}{3}) = \frac{25}{6} K N m$ $M_{C, r} = - 4.5 + 0 \times (\frac{2}{3}) + 1 \times (\frac{1}{3}) = - \frac{25}{6} K N m$ $M_{D, l} = 1.5 + 0 \times (\frac{2}{3}) + 0.5 \times (\frac{1}{3}) = \frac{5}{3} K N m$
	Commented by BHOOPENDRA last updated on 01/May/22

	$t h a n k y o u s i r$
	Commented by mr W last updated on 01/May/22

	Commented by mr W last updated on 01/May/22

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