Reaction on the beam - mechanics, Mechanical Engineering

Reaction on the beam - mechanics:

Determine algebraically the reaction on the beam loaded as shown in the figure given below. Neglect the thickness and mass of beam. 

 

1277_Reaction on the beam.png

Resolved all the forces in horizontal and vertical direction.

Let reaction at hinged that is, point A is RAH  and RAV, and reaction at the roller support is RBV

Let ∑H & ∑V is the sum of horizontal and vertical component of the forces ,The supported beam is in equilibrium, thus

∑H =  ∑H = 0

∑H = RAH - 20cos60° + 30cos45° - 40cos80° = 0

RAH = - 4.26 KN                                                                                                                    ...(i)

V = RAV - 10 - 20sin60° - 30sin45° - 40sin80° + RBV  = 0

RAV  + RBV =87.92 KN                                                                                                                       ...(ii)

Taking moment about A

10 × 2 + 20sin60° × 6 + 30sin45° × 13 - 40sin80° × 17 - RBV  × 17= 0

RBV = 62.9 KN                                                                                                                      ...(iii)

Putting the value of RBV  in the equation (ii)

RAV   = 25.02 KN

Thus  RAH = - 4.26KN, RAV  = 25.02KN, RBV    = 62.9KN                .......ANS

Posted Date: 10/17/2012 4:16:59 AM | Location : United States







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