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Unformatted text preview: Mechanical Design Primer Slide 1 Mechanical Design Load and stress Analysis Daniel Asmar Mechanical Engineering Department American University of Beirut Mechanical Design Primer Slide 2 Outline • Systems in equilibrium • Shear forces and bending moments. • Stresses (3D, 1D, 2D) • Strains • Principal stresses • Mohr’s circle (with example) • Normal stresses with beams in bending • Shear stresses for beams • Torsion Mechanical Design Primer Slide 3 System in equilibrium • A system is an isolated part of a machine or structure. • If a system is assumed motionless or at constant velocity, then it has zero acceleration. • Under such a condition the system is in equilibrium. • If in addition, the system is at rest it is said to be in static equilibrium. Mechanical Design Primer Slide 4 Free Body Diagram ∑ ∑ = = M F D C m o t o r Free body of shaft ¾ The isolated subsystem, together with all forces and moments due to external effects and the reactions with the main system is known as the freebody diagram . Mechanical Design Primer Slide 5 Free Body Diagram (FBD) • Greatly simplify the analysis of complex structures by isolating each part. • Once complete the analysis, synthesize this knowledge to yield information about the total system. Mechanical Design Primer Slide 6 FBD • Advantages: – Establish the directions of reference axes. – Simplifies your thinking (place to store thoughts). – Means of communication of thoughts. – Brings out points that might not be intuitive. – Planning logical attack. – Recording progress. – Allows others to follow your reasoning. Mechanical Design Primer Slide 7 What are shear force and bending moment? Sign Convention F 1 R 1 F 2 F 3 R 2 Mechanical Design Primer Slide 8 How are these values related? • Distributed load: ) ( x q • Shear force: ∫ = − B A x x A B dx x q V V ) ( • Bending Moment: ∫ = − B A x x A B Vdx M M Mechanical Design Primer Slide 9 What is stress? • It is difficult to compare material strength using forces alone. For instance, a large tree trunk can carry more weight than a thin steel wire. That does not mean that wood is stronger than steel. • Need a new metric by which we can measure the forces that can be sustained by any material of any size without failing. That metric is the mechanical stress . Mechanical Design Primer Slide 10 Where did this idea originate from? • The definition of stress originates from two observations of the behavior of a one dimensional body subject to uniaxial loading: – When a wire is pulled it stretches and up to a certain point the stretch ratio is proportional to the force divided by the crosssectional area of the wire. Stress is defined as σ = F/A – Failure occurs when the load exceeds a critical value for the material. The tensile strength (or stress) times the cross section of the material. Mechanical Design Primer...
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This note was uploaded on 02/07/2011 for the course MECH 200 taught by Professor Drramseyhamady during the Fall '06 term at American University of Beirut.
 Fall '06
 DrRamseyHamady
 Mechanical Engineering, Shear, Strain, Stress

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