How to Calculate Axial and Lateral Loads in a Truss System with a Pulley?

[quantizationx]

Homework Statement

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Total tank weight (with liquid) is around 3.1kips
Lateral load on wall is defined as 6kips[1-(Faxial/6kips)]^2
Faxial is defined as the axial force along a wall -- maximum allowable is 6kips
Maximum allowable force in any truss member is 7.5kips

Joint B is on a pin support, and Joint A is on a roller support.

I need to plot a graph of axial vs. lateral load on the wall, given an x value range from 20 to 50ft.

Homework Equations

None. This is an FBD balancing problem.

The Attempt at a Solution

I imagined that there is a member extending from point D on the truss to the center of the pulley. Looking at the pulley alone, there should be two forces (horizontal and vertical) acting at the center in order to cancel out the tension applied in the rope. These two forces would be represented by:

T*sin(theta) + W = Y and T*cos(theta) = X

Where T is the tension in the rope from the pulley to point E, W is the weight of the tank, and theta is the angle of elevation of the rope. Theta can be defined as:

theta = arctan(20/x)

The horizontal component on the center of the pulley could be equivalent to the horizontal force acting on joint D (in both directions) because the rod connecting the center of the pulley to point D is stationary. Taking this into account, the lateral load on the wall at point B should be equivalent to the following:

T*cos(theta)

Is this the right way of going about this problem? I need to somehow relate x to the lateral and axial loads on the walls in order to compile a program script that could graph what is required.

 

[anathema]

Your approach seems to be on the right track. However, there are a few things to consider:

1. The weight of the tank should be included in the calculation of the vertical force at the center of the pulley. So the equation should be T*sin(theta) + W = Y.

2. The horizontal component of the force at the center of the pulley should be equal to the horizontal forces at both joint D and joint A (since the rod connecting the center of the pulley to joint D is stationary). So the equation should be T*cos(theta) = X + F_A where F_A is the horizontal force at joint A.

3. The lateral load on the wall at point B should be equal to the horizontal force at joint B. So the equation should be F_B = T*cos(theta).

4. To relate x to the lateral and axial loads on the walls, you can use the equations above and solve for T and F_A in terms of x.

5. Once you have T and F_A in terms of x, you can substitute them into the given equations for lateral load on the wall and axial force along the wall to get equations in terms of x.

6. Finally, you can plot these equations for the given range of x values to get the desired graph.

Hope this helps!

 

[nlightner]

I would first verify that the equations provided in the homework statement are correct and applicable to the given scenario. This can be done by checking the units and dimensions of the given values and equations, and ensuring that they are consistent.

Next, I would suggest creating a free body diagram for the system, including all forces acting on the tank, the pulley, and the truss members. This will help visualize the forces and determine how they are related.

From the given information, it seems that the maximum allowable axial force in any truss member (7.5kips) is less than the maximum axial force allowed in the wall (6kips). This could be a potential issue and should be addressed in the solution.

Regarding the approach to the problem, it seems reasonable to consider the forces acting on the pulley and the truss members. However, it may also be necessary to consider the forces acting on the tank itself, as it is the main load in the system.

To relate x to the lateral and axial loads on the walls, I would suggest considering the equilibrium of forces at each joint in the truss system. This will allow you to determine the forces acting on each member of the truss, and therefore, the forces acting on the walls.

Overall, it is important to carefully consider the given information and to approach the problem systematically, considering all relevant forces and equations. As a scientist, it is important to not only find the solution but also to understand the underlying principles and assumptions involved.