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Unformatted text preview: Overview of Mechanics EAS 209: Introduction
Christine Human Department of Civil, Structural and Environmental Engineering Statics (EAS 207) Statics • Equilibrium Dynamics (EAS 208) Dynamics • Newton’s laws of motion Newton’ Mechanics of Solids (EAS 209) Mechanics • Deformable bodies • Stress and strain Structural Mechanics Structural • Analysis and design of structures Fluid Mechanics Fluid • Flow of liquids and gases Computational Mechanics Computational What did you learn in Statics ?
Equilibrium of rigid bodies Equilibrium
• Determine member forces under applied external loading Procedure for Static Analysis
Set up equilibrium equations Set • ΣFx=0, ΣFy=0, ΣMA=0 Solve for the reactions Solve
RAx
A w F1 w F1
B • Only statically determinate structures were analyzed. RAy RBy Procedure for Static Analysis (cont)
Draw free body diagram Draw Compute internal section forces: axial forces, Compute shear forces, and bending moments F1 V V M w M
RAx
A B N What you did not consider in Statics
How much load the beam can support before How failure (strength) How much it will deflect (stiffness) How F1 w RAy RBy Strength and stiffness are material properties Strength Draw force and moment diagrams Draw 1 Example: Loading to Failure
Axial loading of steel coupon Axial σ (stress) = force/area ε (strain) = elongation/original length Loading Considered in EAS 209
Bars under axial and shear loading AXIAL LOAD compression tension SHEAR LOAD Examples of Loading (cont)
Shafts in torsion (twisting moment) Application of Mechanics of Materials to Engineering Design (1)
Stresses in bicycle helmet impacted with anvil Columns in compression (buckling) Beams in bending (bending moment) Application of Mechanics of Materials to Engineering Design (2)
Rollover of vehicle Application of Mechanics of Materials to Engineering Design (3)
Determine dimensions of columns, beams, and connection details (weld size, bolt size) 2 Stress Levels in Beams
Determine stresses and strains through testing and simulations Connection Details
After testing various configurations, we can see which connection detail works best and what size bolts to use Finite element analysis Laboratory experiment FRANK LLOYD WRIGHT’S WRIGHT’ FALLINGWATER Mechanics is Central to Engineering Design
For a given structure, we must first determine member For forces using statics (or dynamics) statics From member forces we determine stresses in From members (stress depends on the size of the member) • Ensure stresses do not exceed the allowable stress (strength) for the chosen material • Structure satisfies safety requirement Determine deformation Determine • Ensure deformation does not exceed allowable deformation • Structure satisfies serviceability requirement Deflections too large in original design Millions of dollars in repairs Statically Determinate vs. Indeterminate Structures
Statically determinate structures Statically
• Forces can be found from equilibrium alone
1. Method of Study
Understand logical development of the concepts
Derivation Derivation Discussion Discussion Worked examples (class and text) Worked
2. Statically indeterminate structures Statically
• Forces cannot be found by equilibrium alone • Equilibrium equations are supplemented by additional equations pertaining to the displacements of the structure Apply concepts to practical situations
Practice…practice…practice…. which translates Practice… practice… practice… to homework…homework……… homework… homework……… Knowledge of mechanics of materials allows us Knowledge to solve statically indeterminate structures 3 Homework
Will be assigned at the end of each lecture Will Will typically consist of three problems Will • You will only be required to submit ONE of the problems (usually the hardest) for grade Will be due at the start of the next lecture Will • Late homework will not be accepted Solutions will be available in Ketter Hall (1st floor) Solutions It is expected that each student will do all homework It individually – students who copy will receive zero individually General Requirements
Use ENGINEERING paper (one side only) Use Complete in pencil Complete Attach a cover sheet to include: your name, section, date, Attach assignment number Pages MUST be stapled together Pages Figures should be drawn roughly to scale using a ruler Figures Final answers should be boxed and include units where Final applicable and be given the appropriate number of significant figures Homework must follow this format Homework must Given: (statement of problem) (statement Find: (what are you after) Solution: (analysis leading to result) Word on Significant Figures
In engineering problems, the data are seldom know to an In accuracy greater than 0.2% As a rule of thumb: As • Use 4 figures to record numbers beginning with a 1: 12340 N not 12342.3357 N • Use 3 figures in all other cases: 325 lb not 325.3278 lb IMPORTANT
Do not think of your calculations as simply a means Do to get the correct answer, but rather a communication of your approach Consequently, your homework should be clear, Consequently, logical and well laid out Points will be lost if your homework is not well Points organized and neat See Section 1.10 of text See Grading Policy Grading
Homework Homework 4 inclass Exams inFinal Final 10% 50% (12.5% each) 40% Academic Integrity
Please review the UB policies on academic integrity in Please the Rules and Regulations (www.studentaffairs.buffalo.edu/judicial/art3a.shtml) www.studentand in the University catalog (undergradcatalog.buffalo.edu/integrit.html). undergradThey will be strictly enforced. The lowest 5 homework grades will be dropped, therefore NO homework extensions will be given 4 UB Engineering Community Ethic
Act with honesty, integrity and fairness Show respect for others Accept responsibility Give credit where credit is due Serve the larger community Take pride in being a part of UB Engineering Classroom “Etiquette”
Attend classes and pay attention. Attend Come to class on time. If you must enter a class late, do so quietly and do Come not disrupt the class by walking between the class and the instructor. Do instructor. not leave class unless it is an absolute necessity. Do not talk with other classmates while the instructor or another student is Do another speaking. If you have a question or a comment, please raise your hand, rather than starting a conversation about it with your neighbor. Turn off electronics: cell phones, pagers, laptops, and beeper watches. Turn laptops Avoid audible and visible signs of restlessness. These are both rude and Avoid disruptive to the rest of the class. Focus on class material during class time. Sleeping, talking to others, doing Focus work for another class, reading the newspaper, checking email, and and exploring the internet are unacceptable and can be disruptive. Do not pack bookbags or backpacks to leave until the instructor has Do dismissed class Taken from: http://www.studentaffairs.buffalo.edu/judicial/classroom.doc How to pass and do well in this course:
Read appropriate section from text BEFORE class Read Come regularly to class and recitations and pay attention. Come Take good notes, and ask questions if you do not understand Take the material. Before you attempt to solve your homework problems, reread Before the appropriate section from the text and your class notes; try to understand the concepts and solved problems. Do all the assigned homework. Do Use all resources available for additional assistance if you Use need it (e.g., office hours) Start preparing for each exam at least one week before, Start allowing time to work out practice exams Additional Resource
MecMovies for Mechanics of Materials MecMovies
• Timothy Philpot, Missouri University of Science and Technology • Provides opportunities for students to apply concepts learned in class through various interactive features • http://web.mst.edu/~mecmovie/ http://web.mst.edu/~mecmovie/ 5 ...
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This document was uploaded on 12/19/2010.
 Spring '08
 Statics

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