Calculate the support reactions of beam:

Q: Bending moment diagram (BMD) of the simple supported beam can be given as shown in figure given below. Calculate the support reactions of beam

Linear variation of bending moment in section AC, CD and DB indicate that there is no load on the beam in these sections. Change in slope of bending moment at C and D is indicate that there must be concentrated vertical loads at these points.

Let point load acting at A, B, C, D are RA, RB, P, Q respectively.

Take the three section line of beam which cut the line AC, CD and DB respectively. As value of moment at all section is last value of BM at that section.

Take Section 1-1, Taking moment from C,

M_C = 7 = R_A X 1

R_A = 7KN                                                                                                                                    ...(1)

Take Section 2-2, Taking moment from point D,

M_D = 5 = R_A  X 2 - P X 1

5 = 7 X 2 - P

P = 9KN                                                                                                                                    ...(2)

Take Section 3-3, Taking moment from point B,

M_B = 0 = R_A  X 3 - P X 2 - Q X 1

0 = 7 X 3 - 9 X 2 -Q

Q = 3KN                                                                                                                                    ...(3)

NOW R_A  + R_B  = P + Q

R_B = 5KN

R_A = 7KN and R_B  = 5KN                                               .......ANS