Evaluate the reactions at hinge and roller support, Mechanical Engineering

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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

930_Evaluate the reactions at hinge and roller support.png

∑H = 0

R_A_H -5000cos30° = 0

R_A_H = 4330.127N .......ANS

∑V = 0

R_A_V + R_B_V -5000sin30° = 0

R_A_V + R_B_V = 2500N ...(i)

By taking moment about B:

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

R_A_V = 1250N .......ANS

From the equation (i)

R_B_V = 1250N .......ANS

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