According to the frame below, the goal is to determine the reactions of this frame in order to draw after the diagrams N, T and M.

enter image description here

The frame is asymmetric by reference at point C.

All reactions should be determined: at A and E.

I tried to determine reactions by using the equation of moment of the whole frame at one support (at A) and one equation of moment at the hinge for half of the frame.

For each half of the frame, we can also add equations of forces.

I obtained these equations:

  • Sums of moment for the whole frame seen at A

$$M_A = q \cdot a \cdot a - q \cdot a^2 + \dfrac{q \cdot a^2}{2} - \dfrac{q \cdot a^2}{2} + 3 \cdot q \cdot a^2 - q \cdot a^2 - RVE \cdot 2a = 0$$

  • Sums of moment for the half frame at point C (Right Half Portion)

$$M_C^+ = -RVE \cdot a + RHE \cdot 1.5a - q \cdot a^2 + 2q \cdot a^2 - \dfrac{q \cdot a^2}{2} = 0$$

Thus, after simplification : by $M_A$, $RVE = q \cdot a$ and by $M_C$, we obtained $RHE \cdot 1.5 \cdot a - RVE = -\dfrac{q \cdot a}{2}$

Are these equations correct and if yes, how can I obtain all the reactions values? Because in the equation of the whole frame, I am not sure if I need to integrate reactions of the hinge.

  • $\begingroup$ To be clear, $RVD$ and $RHD$ are the vertical and horizontal reactions at the support at E, right? And what do you mean by "reactions at C"? C is just a hinge, there are no support reactions there. $\endgroup$ – Wasabi May 8 '20 at 13:31
  • $\begingroup$ Yes RVD is the vertical reaction and RHD the horizontal reaction at the support E, sorry for the mistake. And yes of course there is no support (I had in my mind the internal forces... but it is not asked) $\endgroup$ – Lib co May 8 '20 at 13:35
  • $\begingroup$ Found the reactions in the vertical directions; i.imgur.com/LfZc8Vn.jpg $\endgroup$ – Manu G May 11 '20 at 3:49

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