Calculation of Support Reactions:
The support is fixed hence, it will be subjected to three reactions, sign conventions being horizontal reaction HA (→ positive), VA (↑ positive) and MA (positive). From the above result MA = + 1.992 kNm.
Considering the free body diagram of vertical member AB (Figure 20(a)), we find that it is acted upon by clockwise moments of MA = + 1.992 and MB = + 3.996 kNm at ends A and B respectively; in addition to the unknown reactions HA, VA at end A and HB, VB at end B. Taking moments about the point B, we have 1.992 + 3.996 - HA × 3 = 0, giving HA = 1.9968 kN and is acting toward right as shown.
By consideration of symmetry (or calculation if you so like), the horizontal reaction at D will be of same magnitudes, but opposite in direction. For finding VA, taking moments of all the forces acting on the frame as shown in Figure 20(b) about the point D, we have
+ 1.992 - 1.992 + VA × 6 - (2 × 6) × 3 = 0
giving VA = 6 kN.
The frame with the reactions and loading is shown in Figure 21(a). By vertical equilibrium of whole frame
VA + VD = 2 × 6
∴ VD = 6 kN.
![959_Calculation of Support Reactions.png](https://www.expertsmind.com/../CMSImages/959_Calculation of Support Reactions.png)
![1234_Calculation of Support Reactions1.png](https://www.expertsmind.com/../CMSImages/1234_Calculation of Support Reactions1.png)
(a) While drawing the BM diagram, for the beam BC, the same convention is used for sagging and hogging bending moments; namely the positive sagging moment is drawn below (- ve) the reference line, i.e. on which side of the beam while fibres are in tension, and negative (hogging) moments are drawn above the line where fibres are in tension in this case.