the Technology Interface / Spring 1998

Bridging the Gap between Mechanics of Materials
Lectures and Homework with MDSolids


Timothy A. Philpot
Department of Industrial and Engineering Technology
Murray State University



Current educational software for the mechanics of materials course is typically presented as either tutorials, worksheets, or basic analysis packages. A new software package, called MDSolids, presents an alternative to these types of products. MDSolids was conceived as a tool to help students solve and understand homework problems typically used in the mechanics of materials course. The software is versatile, graphic, informative, and very easy-to-use. MDSolids is being used at a number of schools around the world, and feedback from users has been uniformly positive and enthusiastic.



For many years, computers and particularly personal computers have offered the promise of a revolution in the way that traditional engineering topics are taught. In some regards, this revolution has occurred. Computer-aided drafting and design (CADD) and sophisticated analysis packages have changed the engineering curriculum, making it possible for students to analyze and design at a level of precision impossible to accomplish with hand-calculations alone. However, much of this improvement occurs at the upper-end of the engineering curriculum. At the introductory level, in courses such as mechanics of materials, the impact of computer software on the teaching of fundamental concepts has been less successful. Although educational software has been packaged with textbooks for a number of years, book company editors know that, in general, book adoption decisions are not strongly influenced by the accompanying software. Therefore, if computers and computer software hold such promise as educational tools, why isn't educational software more effective at teaching engineering fundamentals?


How Do Students Learn Mechanics of Materials

In the field of education, Benjamin S. Bloom proposed a developmental sequence for learning, commonly called the Bloom Taxonomy (1). This taxonomy is comprised of six levels, starting with the least level of sophistication. Typical examples pertaining to the mechanics of materials course are given for each level.

Level 1 - KNOWLEDGE. The student is able to remember either by recognition or recall information, terminology, phenomena, etc. Example: Define the term proportional limit.

Level 2 - COMPREHENSION. The student is able to know an abstraction well enough so that he or she is can correctly demonstrate its use when specifically asked to do so. Example: Compute the normal stress in a rod given the load and cross-sectional area.

Level 3 - APPLICATION. The student is able to apply the appropriate abstraction without having to be prompted as to which abstraction is correct or to be shown how to use it in that situation. Example: Determine the elastic modulus given load-deflection data.

Level 4 - ANALYSIS. The student is able to break down the problem into its constituent parts and to detect relationships among the parts and the way they are organized. Example: Determine the maximum load that a structure can support given limits on both stress and deformation.

Level 5 - SYNTHESIS. The student is able to put together elements and parts to form a complete solution. Relates concepts and processes. Able to adapt knowledge from various sources to solve problems. Creative expression with ideas being learned and with ideas already known. Example: Design a beam, incorporating statics, shear/moment/deflections diagrams, normal and shear stresses, and combined stress analysis to determine principal stresses.

Level 6 - EVALUATION. The student is able to apply standards and determine levels of quality. Example: Design concrete beams to best satisfy several considerations.

As professors, we seek to guide students from Level 1 up to Level 5 in the introductory mechanics of materials class. While more fundamental levels of learning (knowledge, comprehension, and application) may be addressed in lectures, time constraints dictate that in-class examples and problems focus on developing analysis and synthesis skills. Each student learns at his or her own rate, and unfortunately, the pace of lecture topics is sometimes faster than the student finds comfortable. Concepts and problem solving skills that should be firmly in place before proceeding to analysis topics are sometimes absent or underdeveloped.

Homework assignments are the primary device used to develop the student's understanding of the mechanics of materials topics. The typical assignment can be somewhat lengthy; therefore, only selected problems can be assigned. Professors may expect (or hope) that their students will work enough extra problems so that the fundamentals are firmly grasped, but students sometimes struggle just to keep up with the homework and exam schedule. To supplement the student's educational development, the self-study potential offered by software would seem to be the ideal means of filling the gap between the material presented in lectures and the understanding and skills expected in homework and exams.


Educational Benefits Unique to Software

Software can help students study mechanics of materials and develop the necessary problem solving skills in several ways that are not inherent in lectures or customary homework assignments.


Current Mechanics of Materials Educational Software

Most of the current educational software developed for the mechanics of materials course can be grouped into three categories: tutorials, worksheets, and basic analysis packages.

Tutorials direct the student through a series of prepared screens, each focused on a specific concept or skill. In this manner, tutorials are like lectures delivered in a different format. Recent tutorials such as the Multimedia Engineering series (2, 3) feature an impressive presentation, complete with animation, video clips, and audio files. Despite excellent presentation, however, tutorial products are limited in applicability. The student must follow the sequence of the tutorial presentation in the same way that they would follow along in a lecture. The student must master the concept presented by the tutorial and then apply that concept to the particular problems that they are asked to solve in their homework assignments.

Worksheets for equation-solving software such as Mathcad, MatLab, and TKSolver have also been developed to supplement the mechanics of materials course (4, 5). One drawback of worksheets is that the student must be somewhat familiar with the host software package in order to use the worksheet. In a sense, this disadvantage can also be viewed as an advantage since worksheets encourage the student to develop some command of the equation-solving software, and familiarity with the equation-solving software is a skill that is useful in later engineering courses. However, to the student whose immediate goal is learning the mechanics of materials concepts, the added burden of gaining proficiency with the equation-solving software can be daunting.

Basic analysis packages have been included in several widely available mechanics of materials textbooks such as Lardner/Archer (6) and Craig (7). These programs are useful as tools for assisting students in fundamental skills such as plotting shear and bending moment diagrams or performing Mohr's circle calculations. Basic analysis programs may require students to define nodes and elements and to assign section properties and material constants to the elements. While this is the way that the calculations must be organized for the computer, this approach is not user-friendly for the novice engineer. Furthermore, basic analysis programs have typically lacked a well-developed graphical user interface. Input for these programs has typically been very text-based, often requiring a user's manual to ensure that the proper data and the proper sign conventions are used and to help in interpreting the program output.

In all three categories, the software is generally developed from the professor's point of view, emphasizing lecture topics or permitting the student to perform more advanced calculations. To be successful, educational software should be developed from the student's point of view. Rather than forcing the student to solve a problem posed by the software, the software should solve the problem of interest to the student. To do this, educational software must be:


The MDSolids Concept

MDSolids is an educational software package devoted to the introductory mechanics of materials course. The hypothesis of the MDSolids concept is that students are most interested in understanding the specific homework problems assigned by their professors, and that students will use educational software that helps them with their immediate course concerns. In the process, the software can help to develop problem solving skills by giving students an intuitive interface that guides them to the important factors affecting various problem types, helps them visualize the nature of internal stresses and deformations, and provides an easy-to-use means of investigating a greater number of problems and variations. Based on this premise, MDSolids was developed with several objectives in mind:



MDSolids has been used by students at Murray State University for three semesters. The software was made available free-of-charge to the engineering educational community in January, 1998 at the MDSolids website . In the first two months of its availability, over 1500 professors and students from around the world downloaded the software. The response of MDSolids users has been uniformly positive and enthusiastic.


MDSolids Exhibits

Text-based Explanations: MDSolids includes a wide range of routines pertaining to problems typically used in teaching the mechanics of materials course. The Stress-Strain module focuses on introductory problems used to develop an understanding of basic concepts and problem solving skills. All problems in this module have a consistent style, as illustrated by the bolted connections routine.

The user is presented with questions typically asked for this type of problem. Depending on the choice of question, the user is directed to supply the necessary input data. Upon clicking the Compute button, the numeric results are displayed, a simple free body diagram is shown, and a text description of the process used to solve the problem is printed.

One of the most important skills developed in the mechanics of materials course is creation of shear force and bending moment diagrams. In the Determinate Beam module, the student can quickly create a shear force and bending moment diagram, such as shown below.


While the diagrams are useful in themselves, MDSolids also provides tips on constructing the shear force and bending moment diagrams. For example, the student can put the mouse cursor on the beam supports in the load diagram to see the equilibrium equations applicable to the beam:



The student can position the mouse cursor over a region of the shear diagram to get tips on constructing the moment diagram. Clicking the mouse on this region produces further explanation on how to find the area under the shear diagram and how this area dictates the change in the moment diagram.


Calculation of cross-sectional properties is essential in many typical mechanics of materials problems. MDSolids provides a number of typical shapes that the student can select. After defining the appropriate dimensions,

After clicking the Compute button, the student is given a report of the section properties, but additionally, the student can see details of the calculation procedure. These details, shown below for the centroid and moment of inertia calculation, are presented in tabular format referring to the numbered shapes shown in the figure above. 


Visual Communication: MDSolids relies on graphical depictions to help students develop an understanding of the behavior of materials in response to applied loads. For example, bending stresses in a beam (either normal stress or shear stresses) are depicted for a specified beam cross-sectional shape and at any specified point along the beam:

For torsion, the deformations occurring in a circular shaft in response to an applied torque and the shear stresses acting at a typical point are illustrated in addition to the numeric solution: 

In Mohr's circle transformations, the Mohr's circle is constructed from the specified normal and shear stresses:


Elements showing the magnitude and orientation of the principal stresses and of the maximum shear stresses are also shown:

MDSolids is also useful in helping students visualize the behavior of structures. For example, the Euler buckling shape of a column braced at midheight is shown below. While the column buckling theory used to prepare this illustration is beyond the scope of the introductory mechanics of materials course, this type of active sketch can help students to develop intuition about column behavior.


Help Files: MDSolids also contains a number of help files.  While these help files contain instructions for using the software, they also include general discussions describing skills needed to solve mechanics of materials problems. There are also a number of worked example that explain in detail the calculation procedure needed for a hand solution of typical problems.









MDSolids has proven to be a valuable addition to the mechanics of materials courses at Murray State University, and it is becoming known and being used by professors and students around the world. The software is conceived as a tool to help students bridge the gap between topics presented in lectures and the application of that theory in solving problems commonly used in mechanics of materials homework assignments. Using MDSolids, students get numerical, visual, and textual results and details pertinent to a wide range of problems. Since MDSolids is so easy-to-use and because it provides ample feedback, students are encouraged to attempt more mechanics problems and to explore what-if variations. Through this extra repetition, students develop engineering intuition and greater confidence in their problem-solving skills. MDSolids has been successful in helping students attain mastery of the knowledge, comprehension, application, analysis, and synthesis levels of the learning process.



  1. Bloom, B.S., ed. (1956). Taxonomy of Educational Objectives, Handbook I: The Cognitive Domain, David McKay, New York, N.Y.
  2. Gramoll, K., Abbanat, R., and Slater, K. (1996). Multimedia Engineering Statics. Addison Wesley Interactive, Reading, Mass.
  3. Gramoll, K., Abbanat, R., and Slater, K. (1996). Multimedia Engineering Dynamics. Addison Wesley Interactive, Reading, Mass.
  4. Evensen, T.C. (1997). Mathcad Supplement in Gere, J.M. and Timoshenko, S.P. (1997). Mechanics of Materials, 4th ed., PWS Publishing Co., Boston, Mass.
  5. Turcotte, L.H. and Wilson, H.B. (1998). Computer Applications in Mechanics of Materials using MATLAB. Prentice Hall, Upper Saddle River, N.J.
  6. Lardner, T.J. and Archer, R.R. (1994). MECHMAT in Mechanics of Solids: An Introduction, McGraw Hill, New York, N.Y.
  7. Craig, R.R. (1996). MechSolid in Mechanics of Materials, John Wiley & Sons, New York, N.Y.