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Calculate the support reaction:
Q: A beam 8m long is hinged at point A and supported on rollers over smooth surface inclined at 300 to horizontal at point B. The beam is loaded as shown in the figure given below. Determine the support reaction.
Sol.: Free body diagram is as shown in the figure given to us
∑H = 0
RAH + 8 cos45° - RB sin30° = 0
0.5 RB - RAH = 5.66 ...(i)
∑V = 0
RAV -10 - 8 cos45° - 10 + RB cos30° = 0
RAV + 0.866 RB = 25.66 ...(ii)
Taking moment about A:
∑MA = 10 × 2 + 8 cos45° × 4 + 10 × 7 - RB cos30° × 8= 0
RB = 16.3KN .......ANS
From the equation (ii)
RAV = 11.5KN .......ANS
From the equation (1)
RAH = 2.5KN .......ANS
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