Engineering assignment

Applied Statics

1 Truss Analysis The undergraduate statics course addresses problems related to static equilibrium. One problem

important to civil engineers is determining forces in two- and three-dimensional trusses. The complete

set of member forces can be found for a statically determinate problem using the method of joints. The

method of joints uses the equilibrium equations 0 x

F  and 0yF  at each joint. For a truss with

three joints, these two equations lead to six independent equations. Figure 1 depicts a two-dimensional

truss problem with three joints, and thus three members. Joints are noted within the circles and

member numbers are inside the squares. Figure 2 shows the location of the reactions, also known as

zero-displacement boundary conditions, which occur at joint 1 and joint 3. Figure 3 shows the location

and direction of all the possible external forces that may be applied at the three joints. The external

forces are all shown in the positive direction; however, if forces are in the opposite direction, the sign of

the force will just be negative.

Figure 1Three-joint, three-member truss problem. Joint numbers are in circles, while member numbers are in squares.

Figure 2 Zero displacement boundary conditions specified at joint 1 and joint 3. These may also be referred to as reactions.

Applied Statics

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Figure 3 Location of all possible external forces. Forces are shown in the positive direction, however, they can be reversed by specifying the force as negative. Not all forces shown are necessary for every problem involving the three-joint example.

VBA Application Create a general truss analysis problem capable of solving for member forces and reactions for truss

problems of varying sizes. Generate the program such that users define the problem in an input file.

Details required in the input file are:

1. Nodal locations for joints

2. Member connectivity (which joints are the members connected to)

3. Boundary condition locations and directions

4. External force locations and directions

Output from the program should be a list of member forces and reaction forces.

Figure 4 shows an example input file for the three-member example provided in Figures 1, 2, and 3. The

very first line provides the following five arguments in a comma separated list (dimension, number of

nodes, number of elements, number of forces, and number of boundary conditions). For 2D trusses, the

dimension = 2; for space trusses (3D), the dimension would be 3. The location of the joints in the x, y

coordinate system are defined with the *Node keyword. The data lines have information for : joint id, x

location, y location, z location (if using 3 dimensions). The connection of the truss members are defined

by the *Element keyword and have data lines with: element id, first joint, second joint. The external

forces are defined by the *Force keyword. Data lines are: joint location, degree of freedom, force value.

The degree of freed is 1 for the x direction, and 2 for the y direction. The sign of the force corresponding

to the x and y-axis. Figure 3 showed all the forces as positive, but if the force needs reversed, a negative

value should be used, as done in the example problem (2, 2, -1000.5). Lastly, the support locations need

defined with the *Boundary keyword. The data lines have information for: joint number, degree of

freedom. These data lines define the joint and direction in which the displacement is force to be zero.

For a pinned connection, both x and y would have zero displacement. For a roller connection, only the y

direction would have zero displacement.

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The program should provide the member forces and the reaction forces. The format for the output file is

shown in Figure 5. The first line of the output should be the values of ( number of elements, number of

boundary conditions) as a comma separated list. The *Force keyword provides the member forces. Each

data line has the following information: member id, member force. Positive forces correspond to

members in tension, while negative forces are compressive. The *Reaction keyword displays the

reaction forces for joints that were prescribed zero displacement (using the *Boundary) keyword in the

input file. The data lines for the *Reaction keyword have the following information: joint id, degree of

freedom, reaction force.

Figure 5 Output file for the three-member example problem given above

The following pages provides more details regarding the assembly of the system of equations.

2,3,3,2,3 *Node 1, 0, 0 2, 1.5, 1.5 3, 4, 0 *Element 1, 1, 2 2, 1, 3 3, 2, 3 *Force 2, 1, 250.5 2, 2, -1000.5 *Boundary 1, 1 1, 2 3, 2

3 , 3 *Forces 1 ,-751.477731706003 2 , 781.875 3 ,-911.815102556434 *Reactions 1 , 1 ,-250.5 1 , 2 , 531.375 3 , 2 , 469.125

Figure 4 Input file for the three-member example problem given above