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

R_AH + 8 cos45° - R_B sin30° = 0

0.5 R_B - R_AH = 5.66                                                                                                                                 ...(i)

∑V = 0

R_AV  -10 - 8 cos45° - 10 + R_B cos30° = 0

R_AV  + 0.866 R_B = 25.66                                                                                                                            ...(ii)

Taking moment about A:

∑M_A = 10 × 2 + 8 cos45° × 4 + 10 × 7 - R_B cos30° × 8= 0

R_B = 16.3KN                                                                  .......ANS

From the equation (ii)

R_AV = 11.5KN                                                                  .......ANS

From the equation (1)

R_AH = 2.5KN       .......ANS 

 

Posted Date: 10/17/2012 5:21:22 AM | Location : United States

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