# Pulley and Truss System

## Homework Statement

http://g.imagehost.org/0110/nub.jpg [Broken]

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.

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