Lecture 1.12 - Elasticity

Elasticity Definitions Associated With Deformation Stress Is proportional to the force causing the deformation It is the external force acting on the object per unit area Strain Is the result of a stress Is a measure of the degree of deformation Elastic Modulus, cont The elastic modulus in general relates what is done to a solid object to how that object responds Various types of deformation have unique elastic moduli Three Types of Moduli The bar is stretched by an amount DL under the action of the force F The tensile stress is the ratio of the external force to the cross-sectional area A Stress vs. Strain Curve Experiments show that for certain stresses, the stress is directly proportional to the strain This is the elastic behavior part of the curve Stress vs. Strain Curve, cont Shear Modulus Another type of deformation occurs when a force acts parallel to one of its faces while the opposite face is held fixed by another force This is called a shear stress Shear Modulus, cont Shear Modulus, final The shear modulus is the ratio of the shear stress to the shear strain Units are N / m2 Bulk Modulus Another type of deformation occurs when a force of uniform magnitude is applied perpendicularly over the entire surface of the object The object will undergo a change in volume, but not in shape Bulk Modulus, cont The volume stress is defined as the ratio of the magnitude of the total force, F, exerted on the surface to the area, A, of the surface This is also called the pressure The volume strain is the ratio of the change in volume to the original volume Bulk Modulus, final The bulk modulus is the ratio of the volume stress to the volume strain The negative indicates that an increase in pressure will result in a decrease in volume The compressibility is the inverse of the bulk modulus It often used instead of the bulk modulus Moduli and Types of Materials Both solids and liquids have a bulk modulus Liquids cannot sustain a shearing stress or a tensile stress If a shearing force or a tensile force is applied to a liquid, the liquid will flow in response Moduli Values Prestressed Concrete If the stress on a solid object exceeds a certain value, the object fractures The slab can be strengthened by the use of steel rods to reinforce the concrete The concrete is stronger under compression than under tension Prestressed Concrete, cont Click to edit Master title style Click to edit Master text styles Second level Third level Fourth level Fifth level Since it is a linear deformation, we can define the tensile strain as the fractional change in the length of the body u