Evaluate the reactions at hinge and roller support:

Q: A Force P = 5000N is applied at centre C of beam AB of length 5m as shown in figure given below. Find the reactions at hinge and roller support.                                                                                                       

Sol.: Hinged at A and Roller at point B, FBD of beam is as shown in the figure given below

∑H = 0

R_AH  -5000cos30° = 0

R_AH = 4330.127N                                       .......ANS

∑V = 0

R_AV  + R_BV  -5000sin30° = 0

R_AV  + R_BV = 2500N                                                                                                        ...(i)

By taking moment about B:

∑M_B = R_AV  × 5 - 5000 sin30° × 2.5 = 0

R_AV = 1250N                                               .......ANS

From the equation (i)

R_BV = 1250N                                               .......ANS