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Understanding Forces vs. Stresses: Average Normal Stress and Examples from Problems

In this lecture, we explore the differences between external and internal forces, and how they relate to stresses in materials. We define normal stresses and discuss their significance in engineering, characterized by tension (positive stress) and compression (negative stress). Examples from problems 1.33, 1.37, and 1.63 illustrate the application of these concepts with varying loads and surface areas. Key units for measuring stress are also defined, including Pascals, psi, and ksi. This lecture is fundamental for understanding how forces affect structural integrity.

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Understanding Forces vs. Stresses: Average Normal Stress and Examples from Problems

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  1. EM 304 Lecture 2 Forces vs. stresses Average normal stress Examples: Problem 1.33 Problem 1.37 Problem 1.63

  2. 200 lb 200 lb 0.1 ft2 1.0 ft2 Forces vs. stresses • External forces and moments quantify the action of an object applied on another object. • Internal forces and moments quantify the action of a part of the object applied on the other part. • Stresses represent the amount of force applied to a unit surface area. • Stresses capture information on: • intensity of force • surface area of material that bears the force Same load Different surface areas Different strengths

  3. Internal loads are applied on a cross-section

  4. Consider an element Normal stresses sx, sy, sz Shear stresses txy, txz, tyz

  5. Normal stress Average normal stress P P

  6. P P Average normal stress s > 0  tension (tensile stress) • < 0  compression (compressive stress) Units: N/m21 Pa = 1 N/m2 1 MPa = 1 N/mm2 lb/in2 = psi 1000 lb/in2 = 1 kip/in2 = 1 ksi

  7. Problem 1.33 • Problem 1.37 • Problem 1.63

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