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Mechanics of Materials Engr 350 - Lecture 1

This lecture introduces the study of internal effects caused by external loads in mechanics of materials, focusing on stress, which is defined as the intensity of an internal force. The lecture covers normal stress, including its calculation, sign convention, and examples of determining stress in different scenarios. The lecture also discusses stress on inclined planes.

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Mechanics of Materials Engr 350 - Lecture 1

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  1. Mechanics of Materials Engr 350 - Lecture 1

  2. Stress - Normal/Direct shear • Mechanics of Materials • Study of internal effects caused by external loads • Considers real bodies that deform (statics assumes no deformation) • 3 main concerns • Strength - Will it _____________________? • Stiffness - Will it _____________________? • Stability - Will it ______________________?

  3. Stress • Defined as the intensity of an internal force • In equation form: stress= Note: scalar - just a number vector - quantity with magnitude and direction tensor - has magnitude & direction as well as a plane • Stress is a tensor • First subscript is the direction of area normal • Second subscript is direction of the stress component • force • area

  4. Normal Stress • Use method of sections to consider a rectangular bar with an axial load • We “cut a section” through the bar • Now the whole cut surface is resisting the load

  5. Normal stress • The stress is acting normal to the cut surface therefore it is called a normal stress • We use the symbol “σ”for normal stress • Sign convention for normal stress • Positive (tension): • Negative (compression):

  6. Stress Example • Determine the stress in the concrete pilar

  7. Two-bar loading • How to find load carriedby each bar? • Sum x and y forces at joint  Two equations, three unknowns • Why not sum moments? • Calculate F1,allowable based on max stress and area • Solve for F2 and P based on F1,allowable • Check if F2 is higher or lower than F2,allowable • If necessary, repeat using F2,allowable to solve for F1 and P

  8. Demo TK Solver? • Use the following: • A1 = 2.0 in2 • A2 = 1.5 in2 • σ1,max = 12,000 psi • σ2,max= 18,000 psi • At the joint, what are these equations? • ΣFx = 0 • ΣFy= 0 • What are the max allowable forces for F1 and F2?

  9. Stress on inclined plane (TB Section 1.5) • What if we cut the bar at an angle? • What stresses are acting on that surface?

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