Mechanics question on vector statics

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Discussion Overview

The discussion revolves around determining the reaction forces at points B and D in a static mechanics problem involving vector statics. Participants explore the equations of equilibrium needed to solve for these unknowns, considering the constraints imposed by the hinges at B and D.

Discussion Character

  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant notes that there are four unknown reaction forces at B and D but only three independent equations available from the equilibrium conditions.
  • Another participant suggests considering the forces at point C to potentially provide additional insights into the problem.
  • A later reply proposes that by treating the system as two separate pieces and applying the equations of equilibrium for both, it is possible to derive the necessary equations to solve for all unknowns.
  • One participant expresses gratitude for the assistance and indicates they found the answer, though the specifics of the solution are not detailed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the number of independent equations available, but there is an acknowledgment of the need for additional equations to solve the problem. The discussion remains somewhat unresolved regarding the exact approach to take.

Contextual Notes

The discussion highlights the challenge of finding sufficient independent equations in a statics problem with multiple unknowns and constraints. There is an assumption that the variable "b" is known, but its implications are not fully explored.

Who May Find This Useful

Students and practitioners in mechanics, particularly those dealing with vector statics and equilibrium problems, may find this discussion relevant.

ashishsinghal
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Determine the reactions at B and D when b = 60mm ?
(Diagram is attached)

Since B and D are hinged we don't know the direction as well as magnitude of the reaction forces at B and D. Hence we have 4 unknowns (Bx, By, Dx, Dy).

But I can't find 4 independent equations. I got three by ƩFx= 0, ƩFy= 0 and moment about B = 0. Where is the 4th equation. Please help.
 

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hi ashishsinghal! :smile:

it's static, so what can you say about the forces at C ? :wink:
 
ashishsinghal said:
Determine the reactions at B and D when b = 60mm ?
(Diagram is attached)

Since B and D are hinged we don't know the direction as well as magnitude of the reaction forces at B and D. Hence we have 4 unknowns (Bx, By, Dx, Dy).

But I can't find 4 independent equations. I got three by ƩFx= 0, ƩFy= 0 and moment about B = 0. Where is the 4th equation. Please help.

Call the ABC piece number 1 and the CD piece number 2. You know the force at point A so you have six unknowns, the two components of force at points B, C and D. You have six equations:\sum F_{1x}=0\sum F_{1y}=0\sum F_{2x}=0\sum F_{2y}=0\sum \tau_1=0\sum \tau_2=0 where \tau is torque. (I assume "b" is not an unknown).
 
Thanks Rap I got the answer.
 

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