Understanding Displacement, Deformation, and Normal Strain in Mechanics of Materials

Displacement and deformation in materials play a crucial role when loads are applied, leading to normal strain. This lecture discusses the concepts of displacement, deformation, and strain, covering topics such as types of strain, strain units, normal strain calculations, and the orientation of normal strain in materials. Examples and visuals help illustrate these fundamental principles in Mechanics of Materials.

• Mechanics of Materials
• Displacement
• Deformation
• Normal Strain
• Strain Units

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1. Mechanics of Materials Engr 350 - Lecture 5 Displacement, Deformation, and Normal Strain

2. Strain - background Displacement: movement of a point relative to a frame of reference one response to the application of loads displacement is a? scaler, vector, or tensor On a rigid body, can be due to? translation, rotation Foam example Deformation: individual points on a non-rigid body move relative to each other in response to applied loads Generally non-uniform Common to use Greek symbols normal strain, shear strain Foam example 2

3. Strain Strain is the measure of intensity of deformation Deformation per unit of length of materials Two types of strain Normal strain, , used for elongation/contraction between orthogonal lines Shear strain, , used for change in angle between orthogonal lines 3

4. Strain Units ????= ? ?=? ? May seem like strain is dimensionless Even dimensionless numbers can have dimensions Common Strain Units: in/in, m/m, mm/mm Microstrain, micros, , which is 1*10-6in/in or 1*10-6m/m 4

5. Normal Strain Consider a bar loaded by a force, P Sign Convention for ? + : - : If L = 7,800 m, and ?avg= 0.01 m/m Find: - , the displacement of the tungsten cable - Total length of the elongated cable 5

6. Orientation of Normal strain Consider a rod in tension The equation for normal strain gives you an average strain in a member of homogeneous material of constant cross-sectional area. On the stress to the right, what location and direction do we need to apply load P to get the deformation shown? P P 6

7. Student problem Work in a group to solve example 7