Structures I : Lab 3

Lab 3: Cantilevered Equilibrium (Part II)

The Problem
The goal of this exercise is to campare modeling and analysis techniques as well as to optimize the initial sculpture through the elimination of superfluous elements or through geometrical adjustments.

The Objectives
The objectives of this lab are:

to evaluate the efficiency of the original structure
to analyze the equilibrium of the sculptures graphically
to analyze the sculpture with the equations of equilibrium
to introduce Multi-Frame 4D (a structural analysis program)

There are three approaches to analyze a structural system:

a physical model of specific scale and materials
a traditional (Newtonian) analysis using Free Body Diagrams
a computer analysis

Each one of these mediums has distinct advantages and disadvantages. A physical model yields information about the spatial and constructional characteristics yet takes a long time to build each one. A Newtonian model depends upon the simplification of both the structural system and material properties for easy analysis. These graphical and numerical techniques are the traditional methods that have been used for centuries and can be repeated with ease. A computer analysis can offer the greatest ease for examining numerous options for changes to each system. They are rapid and can lead to very unexpected results. The difficulty is the divorce of the analysis from the physicality of a structure. A computer analysis depends upon the user taking the time to check the answers to ensure that they fall within the bounds of reality.

The Process
1. As a group, determine three ways to optimize your sculpture. Use the digital camera to record the "before" and "after" states of the sculpture. One person should be designated by the group to document the reasons for all of the changes that were ultimately made to the structure.

2. Assume the weights for the kit of parts are as follows:

Weight of plywood base: 10 lbs
Weight of each block: 3 lbs
Weight of each dowel: 0.5 lbs
Weights of other pieces, negligible

Estimate how heavy the "hanging" block could be before the sculpture would have a stability failure (overturning). Keep in mind that you are looking at the system as a whole and not primarily the specific pieces in this part of the problem.

3. Build a Multi-Frame model of your structure. Be careful with the geometry and the connectivity of each of the pieces. The section properties for the pieces can be found in the "Special Sections" library. Observe the behavior of the structure as it deflects. Make a movie of this deflection. Where would it fail? Is this a strength or stability failure? What are the relative magnitudes of the internal loads?

The Documentation
By the end of the period each group should have a working Multi-Frame model of their structure. The lab report to be submitted must contain:

a written verbal description, with illustrations, of the changes that were made to your structure.
an explanation of the rational for these changes
the maximum weight of the block that could be held by the structure with supporting calculations
a print-out of the Multi-Frame model with the axial forces in each of the members of the structure.
a print-out of the deflected structure diagram
a comparison of the analysis techniques

The Evaluation
The evaluation will be based upon the clarity and degree of completion of the lab report. It will also depend upon the accruacy of the modeling techniques and lucid description of each of their limitations.