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Find support reactions at A and B for the beam loaded as shown in figure. A is hinged and B is roller.

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enter image description here

Load due to rectangular UDL $= 24 ×3=72 KN$

acts at 1.5 m from D.

Load due to triangular UVL $= \dfrac 12 ×24×3=36KN $

acts at 1/3×3=1 m from F.

Since Beam AB is in equilibrium,

$∑M_A=0 \\ -1 ×1.5-72 ×5.5+18+R_B ×9-36 ×11=0 \\ 9 R_B=775.5 \\ R_B=86.1667 KN …

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