Reactions at grouted end of cantilever beam:

Q: Find reactions at grouted end of cantilever beam shown in figure given below 

Draw free body diagram of the beam as shown in the figure. First change UDL in to point load. As Point A is fixed point that si, there is three reaction are developed, R_AH, R_AV, M_A. Let ΣH & ΣV is sum of horizontal and vertical component of forces, The supported beam is in equilibrium, thus

R = 0,

∑H = ∑V =0

∑H = 0; R_AH  = 0                                                         .......ANS

∑V = 0; R_AV  - 50 + 15 = 0, ∑R_AV = 35KN           .......ANS

Now taking moment about 'A'

-M_A  + 50 × 2.5 + 100 - 15 × 14.5 = 0

∑M_A = 7.5 KN-m                                                         .......ANS