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# asmar - Mechanical Design Load and stress Analysis Daniel...

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Mechanical Design Primer Slide 1 Mechanical Design Load and stress Analysis Daniel Asmar Mechanical Engineering Department American University of Beirut

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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.

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Mechanical Design Primer Slide 4 Free Body Diagram = = 0 0 M F DC mo 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 free-body 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.

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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

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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 .

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