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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

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

Concrete electrical resistivity (rebars method)

Rebar (short for reinforcing bar), is a steel bar or mesh of steel wires used as a tension device in reinforced concrete and reinforced masonry structures ... more

Electrical resistivity measurement of concrete

Electrical resistivity (also known as resistivity, specific electrical resistance, or volume resistivity) is an intrinsic property that quantifies how ... more

Mohr–Coulomb failure criterion

Mohr–Coulomb theory is a mathematical model describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as ... more

Sorptivity

In 1957 John Philip introduced the term sorptivity and defined it as a measure of the capacity of the medium to absorb or desorb liquid by capillarity.
... more

Maximum axial load that a long, slender, ideal column can carry without buckling

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

Critical buckling stress of a column

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

Self-buckling critical height ( for a free-standing, vertical column)

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

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

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

Rule of Mixtures

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and ... more

Inverse Rule of Mixtures

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and ... 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

Elastic potential energy( with respect to Length)

Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume ... 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/

Volume Fraction of the Fibers (Rule of mixtures)

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and ... more

Water hammer (wave speed)

Water hammer (or, more generally, fluid hammer) is a pressure surge or wave caused when a fluid (usually a liquid but sometimes also a gas) in motion is ... more

Lame's first parameter (in three dimensions)

In linear elasticity, the Lame parameters are the two parameters that constitute a parametrization of the elastic moduli for homogeneous isotopic media. ... more

Lame's first parameter (for two-dimensional solids)

In linear elasticity, the Lame parameters are the two parameters that constitute a parametrization of the elastic moduli for homogeneous isotopic media. ... more

Flux (as a single scalar)

Flux is two separate simple and ubiquitous concepts throughout physics and applied mathematics. Within a discipline, the term is generally used ... more

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

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

Rotational stiffness ( depended on rigidity modulus of the material)

Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force. In general, stiffness is not the same ... 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

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

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

Speed of Sound in Fluids (Newton-Laplace equation )

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 ... more

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