Mechanical Engineering - Pin joint Framework problem

[Mactheknife]

Homework Statement

A framework of pin jointed members has to be designed to support a plug introduced into the reservoir wall to prevent leakage and further progression of a crack along the wall. The plug is cylindrical, has a diameter of 0.35 m and is supported by a single pin joint. The frame is anchored to the ground using a pin joint and a roller joint. Firstly, design the simplest framework to hold the plug in place. The problem is to be presented and solved as a system of equations using MathCAD.

Homework Equations

It is deriving the equations on the joints and beams that I am having trouble with.

The Attempt at a Solution

So far I have a diagram of the frame work:

and have worked out the force that is being excerted on the plug:

But I'm having trouble comming up with the 6 equations involving (F1, F2, F3, H2, V2 and V3). Now I think all of the equations will be equal to 0, apart from the sum of the vertical forces in joint 1 which will be equal to 9808 N, and the sum of the horizontal components in joint 1 which will be equal to 5663 N. Apart from that I'm at a loss and don't really understand how to get the equations.

Any help would be greatley appreciated.

 

[PhanthomJay]

The problem says 'design the simplest..". Thinking ideally and simply, since the force applied at the plug acts 30 degrees below the horizontal, I'd tend to just put in a single member F2, inclined at 30 degrees from the horizontal, and pinned top and bottom, to take the axial 11kN+/- load, and that's it (but check buckling). I suppose, though, a frame works better, in case that the member is not installed exactly at 30 degrees. You gave one example of the supporting truss, but with no dimensions. There are countless others, which may be more economic. Anyway, you just have to apply the 3 equilibrium equations (sum of Fx, sum of Fy, and sum of torques, all each equal to 0),to get the support reactions, and apply the method of joints to get the member forces, using the 2 equilibrium equations sum of Fx and sum of Fy at each joint each equal to zero.

 

[Mene]

As a fellow scientist, I can understand the difficulty in deriving the equations for this pin joint framework problem. Here are some suggestions that may help you in solving this problem:

1. Start by considering the forces acting on each joint individually. For example, at joint 1, there are three unknown forces (F1, H2, and V2) and three equations (sum of vertical forces, sum of horizontal forces, and sum of moments) that can be used to solve for these unknowns.

2. To determine the forces at joint 2 and 3, you can use the equations of equilibrium for each joint (sum of forces in x and y directions). Keep in mind that the forces at joint 2 and 3 will be equal to the forces at joint 1, but with opposite signs.

3. You can also use the geometry of the framework to determine the lengths of each member. This will be helpful in calculating the moments at each joint.

4. It may be helpful to draw a free body diagram for each joint, showing all the forces acting on it.

5. Once you have the equations for each joint, you can use a software like MathCAD to solve the system of equations and determine the values of the unknown forces.

I hope these tips help you in solving this problem. Remember to take your time and carefully consider all the forces and equations involved. Good luck!