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Angle of deflection of an end loaded cantilever beam

In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.
The angle of ... more

Elastic deflection of a uniformly loaded cantilever beam

Elastic deflection is the degree to which a structural element is displaced under a load.
The deflection, at the free end, of a cantilevered beam ... more

Elastic deflection at any point along the span of a uniformly loaded cantilevered beam

In engineering, deflection is the degree to which a structural element is displaced under a load. The deflection at any point along the span of a uniformly ... more

Elastic deflection at any point along the span of a center loaded beam

Elastic deflection is the degree to which a structural element is displaced under a load.
The deflection at any point, along the span of a center ... more

Elastic deflection to an end loaded cantilever beam

In engineering, deflection is the degree to which a structural element is displaced under a load.
The elastic deflection of a weightless cantilever ... more

Elastic deflection of a center loaded beam supported by two simple supports.

In engineering, deflection is the degree to which a structural element is displaced under a load.
The elastic deflection of a beam, loaded at its ... more

Elastic deflection to any point along the span of an end loaded cantilever beam

In engineering, deflection is the degree to which a structural element is displaced under a load. The deflection at any point along the span of an end ... more

Cantilever Euler Beam - Maximum Displacement

Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... more

Maximum elastic deflection of an off-center loaded beam supported by two simple supports

In engineering, deflection is the degree to which a structural element is displaced under a load.
The maximum elastic deflection on a beam supported ... more

Cantilever Euler Beam - Displacement

Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... 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

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

Maximum value of bending moments for a cantilever beam with uniformly distributed load

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... 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

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

Bending moments at any point along the span of a cantilevered beam with the free end supported on a roller

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Bending moments at any point along the span of a uniformly loaded cantilevered beam

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... 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

Maximum deflection distance of an off-center loaded beam supported by two simple supports

In engineering, deflection is the degree to which a structural element is displaced under a load.
This maximum deflection occurs at a distance x_1 ... more

Curvature of a Bimetallic Beam

A bimetallic strip is used to convert a temperature change into mechanical displacement. The strip consists of two strips of different metals which expand ... 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

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

Second moment of area - I-Beam (W-section)

An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... 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/

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

Moment of Inertia - I-Beam (Ideal cross section)

An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... 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

Maximum value of bending moments for a cantilever beam with end load

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Beam shear

Shear stress,is defined as the component of stress coplanar with a material cross section. The average shear stress is force per unit area. Beam shear is ... more

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