Chapter 9 - Static Equilibrium; Elasticity and Fracture

Δl0 G

Tension, Compression, and Shear Stress • An object being pulled on is under tension and experiencing tensile stress • An object being compressed is under compressive stress • An object with equal and opposite forces across its opposite faces is under shear stress • Shear strain can be calculated with 1 F Δl= ________ A.

G

Where ________ is the shear modulus Volume change- Bulk Modulus • Pressure- Force per unit area on an object, equivalent to stress • An object experiencing inward forces from all sides will decrease in volume • The change in volume has its own constant of proportionality called the bulk modulus, B, which can be calculate with ΔP B= − ΔV /V0 Where ΔP is the change in pressure, ΔV is the change in volume, and V0 is the original volume • For liquids and gases, only the bulk modulus applies 9.6 Fracture • Fracture- Occurs when a solid object is under too much stress and breaks • Safety Factor- A factor that maintains the safety of materials by not allowing them to be subject to a certain fraction of their ultimate strengths • Sometimes materials are combined to combine their ultimate strengths, such as reinforces concrete which combines the compressive strength of concrete with the tensile strength of steel 9.7 Spanning a Space: Arched and Domes • Arch- An architectural design made to make its components experience compressive strength in order to avoid excessive deformation • Dome- An arch spanning 3- dimensional space for the same purpose • Each design is not stable until all the stones or other elements are in place.

Equilibrium

State of being at rest

Cantilever

A beam that extends beyond its support, such a beam experiences both force and torque

Stable Equilibrium

The object returns to its original position

Unstable Equilibrium

The object moves even farther from its original position

Neutral Equilibrium

The object remains in its new position

Hooke’s Law

Force exerted on an object will cause its length to change slightly

Elasticity Limit

The point up to which an object will return to its original shape, elongating it beyond this point will deform the object permanently

Ultimate Strength

Also called breaking point, this is the maximum force that can be applied to a material before it breaks

Stress

The force per unit area in an elongating object

Strain

The ratio between an object’s change in length and its original length

Pressure

Force per unit area on an object, equivalent to stress

Fracture

Occurs when a solid object is under too much stress and breaks

Safety Factor

A factor that maintains the safety of materials by not allowing them to be subjectto a certain fraction of their ultimate strengths

Arch

An architectural design made to make its components experience compressive strength in orderto avoid excessive deformation

Dome

An arch spanning 3-dimensional space