Equilibrium and Elasticity Chapter 11 Equilibrium and Elasticity

Goals for Chapter 11 To study the conditions for equilibrium To relate stress and strain and then incorporate them into Hooke’s Law To consider tensile and compressive stress To extend stress and strain to three dimensions by studying bulk stress To examine a two-dimensional situation and the shear modulus To find the limits of Hooke’s Law

Introduction If we find all forces and torques in equilibrium, we can understand situations we see every day … ladders firmly against a wall, bridges, even hanging pictures. Elasticity enters our exploration when we find substances that absorb stresses and then return to their original form.

Conditions for equilibrium The sum of all forces present in the x, y, and z directions are each distinctly equal to zero. The sum of all torques for any given point are equal to zero.

The center of gravity (COG) Calculations begin with the model of all forces and torques acting on the center of gravity for an object. For a straightforward object like a solid sphere of uniform density, the center of gravity is … the center of the sphere.

A “teeter-totter” balancing torques Follow Example 11.1 and use Figure 11.6 to guide you.

Solving rigid-body equilibrium problems Consider Problem-Solving Strategy 11.1. Refer to Figure 11.8 while following the solution of Example 11.2.

The ladder against a wall This is a “classic” problem appearing on most professors’ exams for this material. Follow Example 11.3 and Figure 11.9 (below).

Equilibrium while lifting weights This is another “classic” problem that appears on most professors’ exams for this material. Follow Example 11.4 and Figure 11.10.

Elastic moduli (stretching in one, two, and three dimensions)

Some values of elastic moduli

Tensile stress and strain Consider Example 11.5 and Figure 11.15.

Drop an object into a deep-sea trench Objects will change volume depending on pressure (greater or lesser). Refer to Example 11.6. Figure 11.16 will help you follow the example.

Sheer stress and strain Take your textbook and push on the top cover while the rest remains on a tabletop. Notice the angular distortion. Figure 11.17 will help as you follow Example 11.7.

Elasticity and plasticity If stress continues, Hooke’s Law will cease to apply and strain will be unpredictable. See Figures 11.18 and 11.19 to left and right below.

Approximate breaking stress