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Strain energy release (Irwin's modification for plane stress)

A fracture is the separation of an object or material into two, or more, pieces under the action of stress.There are three ways of applying a force to ... more

Griffith's criterion in Linear elastic fracture mechanics (stress intensity factor)

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid ... more

Griffith's criterion in Linear elastic fracture mechanics (critical stress intensity factor)

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid ... more

Micro chevron (MC) test (critical energy release rate)

The wafer bond characterization is based on different methods and tests. Wafer bonds are commonly characterized by three important encapsulation ... more

Maszara model DCB test (surface fracture energy)

Wafer bonds are commonly characterized by three important encapsulation parameters: bond strength, hermeticity of encapsulation and bonding induced ... more

Maszara model DCB test (The compliance of a symmetric DCB speciment)

Wafer bonds are commonly characterized by three important encapsulation parameters: bond strength, hermeticity of encapsulation and bonding induced stress. ... more

Properties of concrete - modulus of elasticity

Concrete has relatively high compressive strength, but significantly lower tensile strength. As a result, without compensating, concrete would almost ... more

Critical Buckling Compressive Loading of a Plate

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may ... more

Shear modulus (related to Young's modulus and Poisson's ratio)

The shear modulus is one of several quantities for measuring the stiffness of materials and describes the material’s response to shear stress (like ... more

Fracture of ductile materials (Dissipated energy)

In ductile materials, a plastic zone develops at the tip of the crack. The plastic loading and unloading cycle near the crack tip leads to the dissipation ... more

Properties of concrete - modulus of elasticity (AASHTO)

The modulus of elasticity of concrete is a function of the modulus of elasticity of the aggregates and the cement matrix and their relative proportions. ... more

Modulus of resilience

Resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is ... more

Properties of concrete - modulus of elasticity for normal weight concrete

The modulus of elasticity of concrete is a function of the modulus of elasticity of the aggregates and the cement matrix and their relative proportions. ... more

Total force on a contact area between a rigid conical indenter and an elastic half-space related to the contact radius

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Total force on a contact area between a rigid conical indenter and an elastic half-space related to the total depth

ontact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Elastic modulus of a contact area between a sphere and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Critical Buckling Stress of a Column with Buckling Coefficient

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Young's Modulus

Young’s modulus, also known as the Tensile modulus or elastic modulus, is a measure of the stiffness of an elastic isotropic material and is a ... more

Relation among Young's modulus, Bulk modulus and Poisson's ratio

For homogeneous isotropic materials simple relations exist between elastic constants (Young’s modulus E, bulk modulus K, and Poisson’s ratio ν) ... more

Maximum Spring Force (Fully Compressed)

A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened ... more

S-wave Velocity

A type of elastic wave, the S-wave, secondary wave, or shear wave (sometimes called an elastic S-wave) is one of the two main types of elastic body waves, ... more

Elastic modulus

An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance’s tendency to be deformed elastically (i.e., ... more

Force exerted by stretched or contracted material

In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each ... more

Speed of sound in three-dimensional solids (shear waves)

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium. Sound travels faster in liquids and ... more

Transverse wave velocity (shear wave)

A transverse (shear) wave is a moving wave that consists of oscillations occurring perpendicular (or right angled) to the direction of energy transfer. For ... more

Speed of sound in three-dimensional solids (pressure waves)

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium. Sound travels faster in liquids and ... more

Longitudinal waves velocity (compressional waves)

Longitudinal waves, are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of travel of ... more

Worksheet 316

Calculate the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it, assuming the bone to be equivalent to a uniform rod that is 45.0 cm long and 2.00 cm in radius.

Strategy

The force is equal to the weight supported:

Force (Newton's second law)

and the cross-sectional area of the upper leg bone(femur) is:

Disk area

To find the change in length we use the Young’s modulus formula. The Young’s modulus reference value for a bone under compression is known to be 9×109 N/m2. Now,all quantities except ΔL are known. Thus:

Young's Modulus

Discussion

This small change in length seems reasonable, consistent with our experience that bones are rigid. In fact, even the rather large forces encountered during strenuous physical activity do not compress or bend bones by large amounts. Although bone is rigid compared with fat or muscle, several of the substances listed in Table 5.3(see reference below) have larger values of Young’s modulus Y . In other words, they are more rigid.

Reference:
This worksheet is a modified version of Example 5.4 page 188 found in :
OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Force on a Contact Area between two cylinders with parallel axes

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Maximum Pressure on a Contact Area between two cylinders with parallel axes

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

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