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The von Mises yield criterion suggests that the yielding of materials begins when the second deviatoric stress invariant reaches a critical value. For ... more
RESTRICTIONS : σ₁₂ = σ₁₃ = σ₂₃ = 0
The von Mises yield criterion suggests that the yielding of materials begins when the ... more
RESTRICTIONS : σ₃ = 0, σ₃₁ = σ₂₃ = 0
The von Mises yield criterion suggests that the yielding of materials begins when ... more
RESTRICTIONS : σ₃ = 0, σ₁₂ = σ₁₃ = σ₂₃ = 0
The von Mises yield criterion suggests that the yielding of materials begins ... more
RESTRICTIONS : σ₁ = σ₂ = σ₃ = 0, σ₃₁ = σ₂₃ = 0
The von Mises yield criterion suggests that the yielding of materials ... more
A strain is a normalized measure of deformation representing the displacement between particles in the body relative to a reference length.The concept of ... more
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration.
Strain is a normalized
... more
The normal and shear components of the stress tensor on octahedral planes are called octahedral normal stress and octahedral shear stress respectively. ... more
Energy density is the amount of energy stored in a given system or region of space per unit volume or mass, though the latter is more accurately termed ... more
Energy density is the amount of energy stored in a given system or region of space per unit volume or mass, though the latter is more accurately termed ... more
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
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
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
Stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. Any strain ... more
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
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
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
Hooke’s Law of elasticity is an approximation that states that the amount by which a material body is deformed (the strain) is linearly related to ... more
In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each ... more
In materials science, creep (sometimes called cold flow) is the tendency of a solid material to move slowly or deform permanently under the influence of ... more
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
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
Strategy
The force is equal to the weight supported:
and the cross-sectional area of the upper leg bone(femur) is:
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:
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/
In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain. ... more
The Herschel–Bulkley fluid is a generalized model of a non-Newtonian fluid, in which the strain experienced by the fluid is related to the stress in a ... more
Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more
Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more
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
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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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.