written 8.4 years ago by | • modified 8.4 years ago |
Let RA, RB, RC, RD be the relations at
A, B, C, D respectively.
Let angle made by RD with horizontal be $\theta $
Now, in triangle OPK, $\tan 65= (0.6/y) \\ y = 0.28 m $
Also, $x = 1.2 - 0.35 - y = 0.57 m $
Hence, in triangle PQR
$\cos\theta = x/(0.95) = 0.57/0.95 = 0.6 \\ \theta = 53.130 $
Now, considering $50KN$ block
Applying Lami's Theorem of equilibrium
$$50/(\sin 180-\theta) = RC/(\sin 90+ \theta) = RD/\sin 90 $$
Calculating, we get, $RC = 37.53 KN $ & $ RD = 62.52 KN$
Now, considering $100KN$ block
Applying conditions of equilibrium,
$\sum Fx= RA \sin 50 - RD\cos 53.130 =0 \\ RA = 48.95 KN \\ \sum FY= RA\cos50 - RD\sin 53.130 + RB - 100 = 0 \\ RB = 118.51 KN $
Reactions at contact points A, B, C, D are $48.95 KN, 118.51 KN, 37.5 KN, 62.5 KN $ respectively