Five Simplified Integrated Methods of Solution (SIMS) for the Ten Types of Basic Planar Vector Systems in Engineering Mechanics

Narasimha Siddhanti Malladi

Download Paper | Permalink

Conference: 2019 ASEE Annual Conference & Exposition
Location: Tampa, Florida
Publication Date: June 15, 2019
Start Date: June 15, 2019
End Date: June 19, 2019
Conference Session: Mechanics Division Technical Session 3
Tagged Division: Mechanics
Page Count: 24
DOI: 10.18260/1-2--32847
Permanent URL: https://peer.asee.org/32847
Download Count: 671

Request a correction

Paper Authors

biography

Narasimha Siddhanti Malladi Malladi Academy orcid.org/0000-0003-2658-3577

visit author page

Dr. Malladi earned his PhD (Mechanisms) at Oklahoma State University, USA in 1979, MTech (Machine Design) at Indian Institute of Technology (IIT), Madras in 1969, and BE (Mechanical) at Osmania University, India in 1965. He was on the faculty of Applied Mechanics Department, IIT Madras from 1968 till 1973 when he left for US. He received a Republic Day Award for “Import Substitution” by Government of India in 1974 for developing a hydraulic vibration machine at IIT Madras, for Indian Space Research Organization (ISRO), Tumba. In US he worked for the R&D departments of Computer, ATM and Railway Industry. He then resumed teaching at several US academic institutions. He spent two summers at NASA Kennedy Space Center as a research fellow. He received awards for academic, teaching and research excellence. His teaching experience ranges from KG to PG.

After his return to India, Dr. Malladi taught his favorite subject “Engineering Mechanics” at a few engineering institutions and found a need to 1. simplify the subject 2. create a new genre of class books to facilitate active reading and learning and 3. reform academic assessment for the sure success of every student to achieve “Equality”, that is “Equal High Quality” in their chosen fields of education.

The results of his efforts are 1. the following “landmark” paper 2. a class-book titled “Essential Engineering Mechanics with Simplified Integrated Methods of Solution (EEM with SIMS) and 3. material for software development for Improved Assessment Score (IAS), so that even an initially failing student achieves grade A, irrespective of the tier of school one attends.

Dr. Malladi has a simple and practical vision for future Unified Education with Diversity for the world, to develop the four quadrants of each child' brain in four languages and four subjects, namely Math, Management, Design and Technology with their applications. For example application of the study of Geometry of atoms results in Physics or Chemistry. Application of Design will result in Art or Engineering.

Dr. Malladi is willing to offer free workshops and short courses world wide in his Essential Engineering Mechanics, and free consultation on his Simplified Secular Education and Meditation, provided his “single” travel, lodging and alcohol-free pure vegetarian food expenses are met.

Dr. Malladi is a naturalized citizen of USA, and holds Overseas Citizen of India (OCI) Registration. He has US Federal Health Insurance valid anywhere. However he did not use his insurance for decades.

Dr. Malladi lives happily at his birth-place Raja-mahendra-varam, an East Godavary river-town, in the State of Andhra Pradesh, India, with his India born and educated daughter-in-law and US born and Cornell educated son. They both help him in Malladi Academy Activities.

Dr. Malladi can be contacted at malladiacademy@gmail.com

visit author page

Download Paper | Permalink

Abstract

The author was inspired by a classic Timoshenko Statics problem with six unknowns, repeated in several university exams. The traditional textbooks provide lengthy solutions, for this and similar problems, forming simultaneous equations requiring several steps. Based on his earlier unpublished work, the author has developed five Simplified Integrated Methods of Solution (SIMS) with a new Polar Vector Notation, to solve any determinate planar Newtonian Engineering Mechanics problem through equations, each with only one unknown. Ten types in basic planar vector systems are identified and solved by the author, applying the five SIMS systematically to yield solutions with least computing steps. There are four types (T1 to T4) of planar multi-vector systems with two unknowns. T1 has a vector with unknown magnitude and direction related to two or more vectors, each with known magnitude and direction. T2 has Two Vectors, each with unknown direction, related to a vector or resultant, with known magnitude and direction. The first unknown, magnitude of T1 or one of the two directions of T2 is found, by SIM1 through squaring and adding the X, Y components of System's Vector Loop Equation with its single Left Hand Side (LHS) vector containing an unknown direction. The second unknown, the direction of T1 or the other direction of T2 respectively, is found by SIM2 through any inverse trigonometric function with known X and Y components and magnitude of the LHS vector. T3 has two vectors, each with unknown magnitude, in the system. T4 has one vector with unknown magnitude and another with unknown direction, in the system. SIM3 is applied to T3 and T4 through Perpendicular Component Equation (LCE) to the line parallel to a vector with an unknown magnitude and known angle, eliminating that magnitude. The resulting equation with the second unknown, either magnitude or direction is solved. SIM3 is again applied to the vector of the solved unknown and the first eliminated magnitude is found.

T5 and T6 are three concurrent force Free Body Diagrams (FBDs) with three unknowns. In T5 the pin reaction direction is solved by applying SIM2 to the geometry of concurrency. In T6 the common unknown angle in the two reactions is solved with SIM4, by equating the expressions for the common unknown in the geometry of concurrency.

T7 to T10 are multi-force systems with three unknowns as, one force or distance or direction or moment, and two reactions. By SIM5, Moment Equation about a Canonical Moment Center, usually an intersection of reactions, that eliminates all unknowns except one, is obtained and solved. Examples including one on virtual work, are presented and discussed.

Citation
Format

Malladi, N. S. (2019, June), Five Simplified Integrated Methods of Solution (SIMS) for the Ten Types of Basic Planar Vector Systems in Engineering Mechanics Paper presented at 2019 ASEE Annual Conference & Exposition , Tampa, Florida. 10.18260/1-2--32847

TY - CPAPER
AB - The author was inspired by a classic Timoshenko Statics problem with six unknowns, repeated in several university exams. The traditional textbooks provide lengthy solutions, for this and similar problems, forming simultaneous equations requiring several steps. Based on his earlier unpublished work, the author has developed five Simplified Integrated Methods of Solution (SIMS) with a new Polar Vector Notation, to solve any determinate planar Newtonian Engineering Mechanics problem through equations, each with only one unknown. Ten types in basic planar vector systems are identified and solved by the author, applying the five SIMS systematically to yield solutions with least computing steps.

There are four types (T1 to T4) of planar multi-vector systems with two unknowns. T1 has a vector with unknown magnitude and direction related to two or more vectors, each with known magnitude and direction. T2 has Two Vectors, each with unknown direction, related to a vector or resultant, with known magnitude and direction. The first unknown, magnitude of T1 or one of the two directions of T2 is found, by SIM1 through squaring and adding the X, Y components of System&#39;s Vector Loop Equation with its single Left Hand Side (LHS) vector containing an unknown direction. The second unknown, the direction of T1 or the other direction of T2 respectively, is found by SIM2 through any inverse trigonometric function with known X and Y components and magnitude of the LHS vector.

T3 has two vectors, each with unknown magnitude, in the system. T4 has one vector with unknown magnitude and another with unknown direction, in the system. SIM3 is applied to T3 and T4 through Perpendicular Component Equation (LCE) to the line parallel to a vector with an unknown magnitude and known angle, eliminating that magnitude. The resulting equation with the second unknown, either magnitude or direction is solved. SIM3 is again applied to the vector of the solved unknown and the first eliminated magnitude is found.

T5 and T6 are three concurrent force Free Body Diagrams (FBDs) with three unknowns. In T5 the pin reaction direction is solved by applying SIM2 to the geometry of concurrency. In T6 the common unknown angle in the two reactions is solved with SIM4, by equating the expressions for the common unknown in the geometry of concurrency.

T7 to T10 are multi-force systems with three unknowns as, one force or distance or direction or moment, and two reactions. By SIM5, Moment Equation about a Canonical Moment Center, usually an intersection of reactions, that eliminates all unknowns except one, is obtained and solved. Examples including one on virtual work, are presented and discussed.
AU - Narasimha Siddhanti Malladi
CY - Tampa, Florida
DA - 2019/06/15
PB - ASEE Conferences
TI - Five Simplified Integrated Methods of Solution (SIMS) for the Ten Types of Basic Planar Vector Systems in Engineering Mechanics
UR - https://peer.asee.org/32847
DO - 10.18260/1-2--32847
ER -