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Truss Analysis is one of the most important topics in Statics, which is the first introductory in structural engineering curriculums. Trusses are structures that are widely used in civil engineering applications, such as bridges, steel buildings and roof structures. Trusses also appear in many mechanical and aerospace structures such as cranes, space structures, offshore platforms, and so on.
What is a Truss?
A truss is a structure usually consisting of straight members that are connected to each other at the two ends of each member. All members of a truss structure are connected together with pin joints, such that for the purpose of the design of these structures we assume the joints cannot carry or resist any moments. All external loads acting on a truss are assumed to be acting only at the joints, and therefore, all members of a truss are two-force members.
Why Must We Learn Truss Analysis?
First of all, if we plan to design and build a truss structure, such as a roof structure for carrying external loads, we need to find out how much load is carried by each member of the truss. Secondly, in the case of an existing truss structure, we may need to replace one or a few members. In this case, we need to find the internal forces carried by those few members within the truss structure. In both instances, the objective is to figure out and decide whether the members can sustain the forces or not and what size members and what type of cross sections are required.
Types of Truss Analysis
There are two major methods of analysis for finding the internal forces in members of a truss; the Method of Joints, which is typically used for the case of creating a truss to handle external loads, and the Method of Sections, which is normally used when dealing modifying the internal members of an existing truss. Both of these methods are based on the assumption that when a structure is in equilibrium, all pieces of the structure are also in equilibrium.
In this course, I will present a thorough overview of truss structures in the context of static analysis of structures. I will provide you with an easy-to-follow, 7-step process for the Method of Joints and the Method of Sections. Each of the 7 steps are clearly demonstrated in the presentation and sample problems, which I will walk through.</p>
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|Section 1: Introduction|
This lecture provides you an overview of truss structures, what are the unique characteristics of a truss and differentiates a truss from other structures, and what are the objectives in Truss Analysis. The difference between the Joint Method and the Method of Sections and the application of each method is articulated. Several pictures of truss structures in real world are presented.
|Section 2: Method of Joints|
A 7-step procedure for Truss Analysis using the Method of Joints is presented. This step by step approach, not found in any text book, is clearly explained through an example problem. In addition a simple guideline for identifying zero force members in a truss, and how to determine the tensile or compressive nature of member forces, are presented. This guideline makes it so easy to identify all zero force members.
An example problem that demonstrates how to apply the 7-step procedure, outlined in the lecture, is presented. This example articulates the aforementioned step by step approach in a manner not presented in any textbook.
An example of a truss with more than 10 members is presented. Using a Bamboo Pad, the application of joint method and the utilization of the 7-step approach is presented. This includes the identification of all zero force members and thus, reducing the number of unknown members, and subsequently by drawing the free body diagram of each joint and applying the equations of equilibrium. It is also demonstrated that as a general rule, it is not necessary to fins the external reaction forces as a condition for finding the member forces.
|A more complicated and geometrically challenging truss problem is presented and again, by using a Bamboo Pad and through the application of the 7-step procedure introduced earlier, all zero force members and other member forces are analyzed.
|Section 3: Method of Sections|
|A 7-step procedure for Truss Analysis using the Method of Sections is presented. This step by step approach, not found in any text book,
is clearly explained through an example problem. It is clearly explained in what specific cases this method should be used and the objectives for the utilization of this technique, vs the Method of Joints, are discussed. Once again, the three step
guideline formulated by the author, for identifying zero force members in a truss, is presented. The general procedure and the formulation are accompanied by an animation.
|An example problem that demonstrates how to apply the 7-step procedure, outlined in the lecture, is presented. This example articulates the step by step approach for the Section Method in a manner not presented in any textbook.|
|An example of a truss with several members is presented. Using a
Bamboo Pad, the application of section method and the utilization of the
7-step approach is presented. This includes the identification of all
zero force members and thus, reducing the number of unknown members. Subsequently by introducing an easy to understand approach for finding the most suitable cross section and presenting how to choose the most appropriate section of the truss drawing the free body diagram of each joint and
applying the equations of equilibrium. It is also demonstrated that, as a
general rule, it is not necessary to find the external reaction forces
as a condition for finding the member forces. In particular a simple guideline for finding the member forces by using minimum number of equations is presented.
|Another truss example is presented and by using a Bamboo Pad, the application of the 7 step for using the Method of Sections is further articulated. A few valuable hits are offered that makes it so easy to understand and fully comprehend this technique.
|A complicated and challenging truss example developed by the author is presented that is an indeterminate structure. However, using the proposed 7-step approach it is demonstrated how the desired member force can be easily calculated by using only one equation of equilibrium. This example helps the students to develop a thorough understanding and appreciation of the 7-step approach presented in this course.
As an educator, scholar and an administrator, Dr. Mohammad Noori has over 29 years of experience working in academia and has been a pioneer in establishing innovative industry-university-government and global partnerships. He has long been an advocate for collaboration, innovation and multi-disciplinary study, and throughout his career he has been honored with numerous recognitions for his teaching and research.
His most recent recognitions include President Obama recognizing Cal Poly “as a leading school in the retention and graduation of engineering students" on February 8, 2012, which was the result of the innovative retention and outreach programs developed during his tenure as the Dean of Engineering. Dr. Noori has been honored with numerous recognitions for his teaching, research and professional service. The most recent ones include the American Society for Engineering Education (ASEE) Keating Award for Innovation and Leadership in Lifelong Learning in Graduate Engineering Education, and the ASEE Isadore T. Davis National Award for Excellence in Collaboration of Engineering Education and Industry on June 16, 2014, and on June 12, 2012.
Dr. Noori has written over 200 research papers in his research area of random vibrations, multifunctional and intelligent structures, structural health monitoring, and seismic hazard mitigation. He is also a research paper evaluator for over 40 prestigious journals. Moreover, Dr. Noori has presented over 90 invited and keynote talks at numerous international conferences, universities and industry, and has also had the honor of being invited by President Clinton's Special Commission on Critical Infrastructure Protection, as a national expert, to present a Testimony. He has supervised over 60 post-doctoral and graduate students and their research projects, and has presented over 90 invited, plenary and keynote talks.
Noori has served as the department head at two nationally recognized doctoral institutions and as the dean of engineering at a leading undergraduate university. He has spearheaded, and participated in the creation of industry-university-government consortia and global collaborations. He founded and chaired the ASME Committee on Uncertainty and Probabilistics, and has served on, chaired or co-chaired, over 20 scientific and organizing committees of major international conferences. He has been a consultant to several Fortune 500 companies, and has provided expert witness services, in the areas of vibration, structural safety, mechanical failure, product liability, and seismic mitigation. He also provides strategic planning services, especially on development of industry-university partnerships, outcome-based assessment and program development. He is also an ABET evaluator representing ASME.
Noori is a Fellow of the American Society of Mechanical Engineers, has received the prestigious Fellowship of Japan Society for the Promotion of Science, he has been listed in on numerous Who Is Who publications and is a member of Sigma Xi, Pi Tau Sigma, Chi-Epsilon, and Sigma Mu Epsilon honorary societies.
He currently teaches at Cal Poly State University, while also serving as the Executive Editor of a prestigious scientific journal, as the associate editor of two other international journals, and a member of the editorial board of seven other scientific journals.